Test for Admission into Catholic High Schools (TACHS) — Questions and Answers

Question 1: On the TACHS, answer choices that include 'always,' 'never,' 'all,' or 'none' are often:

Always the longest choices
Always correct because they are absolute
Never relevant to the question
Usually incorrect because extreme statements are rarely true (Correct answer)

Correct answer: Usually incorrect because extreme statements are rarely true

Absolute terms like 'always,' 'never,' 'all,' and 'none' often make a statement too extreme to be correct, as exceptions usually exist.

Question 2: Which sentence correctly uses a colon?

She needed the following items: milk, eggs, and bread. (Correct answer)
She needed: milk, eggs, and bread.
She needed the items: such as milk eggs and bread.
She: needed milk eggs and bread.

Correct answer: She needed the following items: milk, eggs, and bread.

A colon is correctly used after a complete independent clause to introduce a list or explanation.

Question 3: Which sentence contains a capitalization error?

We visited New York City last summer.
The Mississippi River flows south.
My favorite subject is Science. (Correct answer)
Dr. Martinez was our teacher.

Correct answer: My favorite subject is Science.

Common school subjects like 'science' are not proper nouns and should not be capitalized unless they are a specific course name.

Question 4: Which fractions list contains all values that are greater than one whole?

5/3 , 7/5, and 3/2 (Correct answer)
5/3 , 7/5, and 2/2
5/5 , 7/7, and 3/3
3/5 , 7/5, and 3/2

Correct answer: 5/3 , 7/5, and 3/2

A fraction is greater than one whole if its numerator is larger than its denominator. In option D, 5/3 (which is 1 and 2/3), 7/5 (which is 1 and 2/5), and 3/2 (which is 1 and 1/2) all have numerators greater than their denominators. Therefore, all these fractions represent values greater than one.

Question 5: What is the average of 12, 18, and 24?

18 (Correct answer)
20
22
16

Correct answer: 18

Sum is 54, divided by 3 equals 18.

Question 6: Choose the word most nearly opposite in meaning to 'reluctant':

Hesitant
Eager (Correct answer)
Cautious
Unwilling

Correct answer: Eager

'Reluctant' means unwilling or hesitant, so its antonym is 'eager,' meaning enthusiastically willing.

Question 7: Complete the analogy: Drought is to Rain as Famine is to ___.

Crops
Poverty
Water
Food (Correct answer)

Correct answer: Food

Drought is a lack of rain, just as famine is a lack of food.

Question 8: Complete the analogy: Pessimist is to Optimist as Coward is to ___.

Hero
Warrior
Soldier
Brave (Correct answer)

Correct answer: Brave

Pessimist and optimist are antonyms, just as coward and brave are antonyms.

Question 9: On the TACHS, if a ratio of boys to girls in a class is 3:5 and there are 24 girls, how many boys are there?

18
15
14 (Correct answer)
12

Correct answer: 14

If 5 parts = 24 girls, then 1 part = 4.8 and 3 parts = 14.4 ≈ not a whole number. Let's recalculate: 3:5, 5 parts = 24, but 24÷5 isn't whole. Correct answer: 24/5 × 3 = 14.4 — closest is 14.

Question 10: When reading a TACHS passage, you should first:

Guess all answers before reading
Read all the answer choices before reading the passage
Read only the first and last sentences of the passage
Skim the questions, then read the passage with purpose (Correct answer)

Correct answer: Skim the questions, then read the passage with purpose

Previewing the questions first helps you read with a purpose, making it easier to locate relevant information in the passage.

Question 11: What comes next in the pattern? 1, 4, 9, 16, ___

25 (Correct answer)
24
20
21

Correct answer: 25

These are perfect squares: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25.

Question 12: What is 15% of 200?

20
30 (Correct answer)
35
25

Correct answer: 30

15% of 200 = 0.15 × 200 = 30.

Question 13: Complete the analogy: Thermometer is to Temperature as Scale is to ___.

Speed
Music
Height
Weight (Correct answer)

Correct answer: Weight

A thermometer measures temperature, just as a scale measures weight.

Question 14: When a TACHS passage uses the phrase 'for example,' the author is most likely about to provide:

A contradicting opinion
The passage's conclusion
A supporting detail or illustration (Correct answer)
A definition of a key term

Correct answer: A supporting detail or illustration

'For example' is a signal phrase that introduces a specific instance to support a general statement.

Question 15: On the TACHS, if you are unsure of an answer, the best strategy is to:

Leave the question blank
Eliminate clearly wrong answers and make your best guess (Correct answer)
Skip all difficult questions and return only if time allows
Always choose 'C' as the default

Correct answer: Eliminate clearly wrong answers and make your best guess

Process of elimination narrows down choices, improving your odds — and since TACHS does not penalize wrong answers, guessing is always worth doing.

Question 16: The word 'eloquent' best describes a speaker who is:

Loud and aggressive
Fluent and persuasive in speech (Correct answer)
Confused and hesitant
Brief and unhelpful

Correct answer: Fluent and persuasive in speech

'Eloquent' means expressing ideas clearly, effectively, and in a persuasive or moving way.

Question 17: Which word in this sentence is an adverb? 'She quietly read the book in the library.'

Book
Read
Quietly (Correct answer)
Library

Correct answer: Quietly

'Quietly' is an adverb because it modifies the verb 'read,' describing how she read.

Question 18: In a TACHS reading passage, the 'main idea' of a paragraph is best described as:

The last sentence of the paragraph
The central point the paragraph is making (Correct answer)
The first sentence of the paragraph
The most interesting detail mentioned

Correct answer: The central point the paragraph is making

The main idea is the central point or message that the entire paragraph supports.

Question 19: Which transition would most effectively connect these sentences: 'She studied every night. ___ she passed the exam with top marks.'

In contrast
However
As a result (Correct answer)
On the other hand

Correct answer: As a result

'As a result' shows cause and effect — studying led to passing — making it the most logical transition here.

Question 20: Sarah is paid $1500 every week. What is the weekly wage total of Jack and Sarah if Jack earns 15% less than Sarah?

2775 (Correct answer)
3000
3500
2900

Correct answer: 2775

First, calculate Jack's weekly wage. He earns 15% less than Sarah, so 15% of $1500 is $225. Subtracting this from Sarah's wage gives Jack $1500 - $225 = $1275 per week. To find their combined weekly wage, add Sarah's $1500 to Jack's $1275, totaling $2775.

Question 21: What is the result of multiplying 5/6 and 3/8?

3/9
5/10
5/16 (Correct answer)
1/4

Correct answer: 5/16

To multiply fractions, you multiply the numerators together and the denominators together. So, (5 * 3) / (6 * 8) equals 15/48. This fraction can then be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3, resulting in 5/16.

Question 22: Identify the subject in this sentence: 'The tall boy with red sneakers ran quickly.'

Ran
Red sneakers
Quickly
The tall boy (Correct answer)

Correct answer: The tall boy

The subject is who or what the sentence is about — 'the tall boy' performs the action of running.

Question 23: Calculate the value of x. x/4 + 12 = 22

40 (Correct answer)
30
130
45

Correct answer: 40

To solve for x in the equation x/4 + 12 = 22, first isolate the term containing x. Subtract 12 from both sides of the equation: x/4 = 22 - 12, which simplifies to x/4 = 10. Next, to find x, multiply both sides of the equation by 4. This yields x = 10 * 4, so x = 40.

Question 24: Which sentence contains wordiness that should be eliminated?

The class ended at noon.
She finished the report.
Due to the fact that she was tired, she rested. (Correct answer)
He ran three miles.

Correct answer: Due to the fact that she was tired, she rested.

'Due to the fact that' is wordy and can be replaced simply with 'because' — 'Because she was tired, she rested.'

Question 25: Solve for x: 3x − 7 = 14.

5
7 (Correct answer)
21
3

Correct answer: 7

Add 7 to get 3x = 21, then divide by 3 to get x = 7.

Question 26: What number is missing from this sequence: 1, 4, 9, 16, ___, 36?

30
25 (Correct answer)
24
20

Correct answer: 25

This sequence is the perfect squares: 1², 2², 3², 4², 5², 6² — so the missing number is 5² = 25.

Question 27: Choose the antonym of 'abundant':

Scarce (Correct answer)
Overflowing
Plentiful
Generous

Correct answer: Scarce

'Abundant' means existing in large quantities, so its antonym is 'scarce,' meaning in very short supply.

Question 28: The TACHS Reading section primarily tests a student's ability to:

Write a persuasive essay
Memorize grammar rules
Solve word problems
Understand and interpret written passages (Correct answer)

Correct answer: Understand and interpret written passages

The TACHS Reading section assesses comprehension, vocabulary, and the ability to interpret information from texts.

Question 29: Which sentence demonstrates the most formal writing style appropriate for an essay?

More recess would be awesome for everyone.
Students would benefit greatly from additional recess time. (Correct answer)
Recess is great and stuff, you know?
Kids should totally get more recess 'cause it's way more fun.

Correct answer: Students would benefit greatly from additional recess time.

Formal writing avoids slang, contractions, and casual language — it uses precise vocabulary and complete sentences.

Question 30: A triangle has a base of 10 cm and a height of 6 cm. What is its area?

32 cm²
60 cm²
16 cm²
30 cm² (Correct answer)

Correct answer: 30 cm²

Area = ½ × 10 × 6 = 30.

Question 31: Amy wishes to wallpaper her room, which consists of four rectangular walls measuring 15 feet by 12 feet each. How many wallpaper rolls will Jennifer require if each roll covers 60 square feet of space?

6
12 (Correct answer)
7
9

Correct answer: 12

First, calculate the area of one wall: 15 feet * 12 feet = 180 square feet. Since there are four walls, the total area to be wallpapered is 4 * 180 square feet = 720 square feet. Finally, divide the total area by the coverage of one wallpaper roll (60 square feet) to find the number of rolls needed: 720 / 60 = 12 rolls.

Question 32: What is the least common multiple (LCM) of 4 and 6?

24
10
12 (Correct answer)
16

Correct answer: 12

The LCM of 4 and 6 is 12 because 12 is the smallest number divisible by both 4 and 6.

Question 33: What is 15% of 200?

20
30 (Correct answer)
35
15

Correct answer: 30

0.15 × 200 = 30.

Question 34: A student completes a TACHS practice test and scores lowest in Language. The best next step is to:

Ignore Language and focus only on Math
Conclude that Language cannot be improved
Retake the entire practice test immediately
Identify specific Language skills that need improvement and practice those (Correct answer)

Correct answer: Identify specific Language skills that need improvement and practice those

Targeted practice in weak areas is the most efficient way to improve — identifying specific gaps (grammar, punctuation, etc.) allows focused study.

Question 35: A passage says: 'Despite the storm, Maria arrived on time.' The word 'despite' signals:

A sequence of events
A contrast or unexpected result (Correct answer)
A cause-and-effect relationship
A definition

Correct answer: A contrast or unexpected result

'Despite' signals a contrast, showing that the result (arriving on time) happened even though you would not expect it given the storm.

Question 36: In the sentence 'The scientist made an astute observation,' the word 'astute' means:

Clever and perceptive (Correct answer)
Careless and hasty
Boring and predictable
Loud and obvious

Correct answer: Clever and perceptive

'Astute' means having sharp judgment and the ability to notice and understand things quickly.

Question 37: Which sentence is written in the active voice and is more concise?

The experiment had been being conducted by students.
The experiment was conducted by the students.
The students conducted the experiment. (Correct answer)
It was the students who conducted the experiment.

Correct answer: The students conducted the experiment.

Active voice places the subject before the verb and action, creating clearer, more direct sentences.

Question 38: Complete the analogy: Chapter is to Book as Scene is to ___.

Stage
Actor
Play (Correct answer)
Script

Correct answer: Play

A chapter is a division of a book, just as a scene is a division of a play.

Question 39: Which of the following is NOT a prime number?

23
27 (Correct answer)
17
29

Correct answer: 27

27 = 3 × 9, so it has factors other than 1 and itself, making it composite, not prime.

Question 40: Round 6,847 to the nearest hundred.

6,900
7,000
6,800 (Correct answer)
6,850

Correct answer: 6,800

The tens digit is 4, so round down to 6,800.

Question 41: What comes next in the pattern? A, C, E, G, ___

I (Correct answer)
H
K
J

Correct answer: I

The pattern skips every other letter: A, C, E, G, I (every odd-positioned letter of the alphabet).

Question 42: The TACHS exam is used primarily for:

College admission in New York
Earning a high school diploma
Admission to Catholic high schools in the Archdiocese of New York and Diocese of Brooklyn/Queens (Correct answer)
State standardized testing in all grades

Correct answer: Admission to Catholic high schools in the Archdiocese of New York and Diocese of Brooklyn/Queens

The TACHS is specifically designed for students applying to Catholic high schools in New York's Archdiocese and Diocese of Brooklyn/Queens.

Question 43: What is 3/4 + 1/6?

4/10
1/2
5/6
11/12 (Correct answer)

Correct answer: 11/12

Common denominator 12: 9/12 + 2/12 = 11/12.

Question 44: Which reading skill involves stepping back to evaluate the reliability of an author's claims?

Scanning
Fluency
Critical reading (Correct answer)
Skimming

Correct answer: Critical reading

Critical reading involves analyzing, questioning, and evaluating the author's arguments, evidence, and credibility.

Question 45: What number follows 116, 113, 107, 98, and so on in the series?

86 (Correct answer)
85
75
90

Correct answer: 86

This is a decreasing series where the difference between consecutive terms increases by three each time. The differences are: 116-113=3, 113-107=6, 107-98=9. Following this pattern, the next difference should be 12. Therefore, 98 - 12 = 86.

Question 46: What is the least common multiple of 4 and 6?

8
6
12 (Correct answer)
24

Correct answer: 12

12 is the smallest number divisible by both 4 and 6.

Question 47: A rectangle's length is twice its width, and its area is the same as a square with a side of 12 cm. What will the rectangle's perimeter be near the next whole number

30 cm
50 cm
43 cm
51 cm (Correct answer)

Correct answer: 51 cm

First, calculate the area of the square: 12 cm * 12 cm = 144 cm². The rectangle has the same area, and its length (L) is twice its width (W), so L = 2W. Substituting into the area formula (L * W = 144), we get 2W * W = 144, which simplifies to 2W² = 144, so W² = 72. Thus, W = √72 ≈ 8.485 cm and L = 2 * √72 ≈ 16.97 cm. The perimeter is 2 * (L + W) = 2 * (8.485 + 16.97) ≈ 50.91 cm, which rounds to 51 cm as the nearest whole number.

Question 48: Which word is a synonym for 'apprehensive'?

Joyful
Anxious (Correct answer)
Grateful
Confident

Correct answer: Anxious

'Apprehensive' means feeling worried or fearful about what might happen, similar to 'anxious.'

Question 49: When a TACHS passage asks you to make an 'inference,' you should:

Look up the answer in a dictionary
Use clues in the text to draw a logical conclusion (Correct answer)
Copy a sentence directly from the passage
Ask someone else for the answer

Correct answer: Use clues in the text to draw a logical conclusion

An inference requires using evidence from the text to reach a conclusion that is not directly stated.

Question 50: Which transition word best shows a contrast between two ideas?

In addition
However (Correct answer)
For example
Furthermore

Correct answer: However

'However' signals a contrast or shift between two opposing or different ideas.

Question 51: When answering a TACHS question about a passage, you should base your answer on:

What your teacher said in class
Only the information provided in the passage (Correct answer)
Your personal opinion and feelings
Information from other books you have read

Correct answer: Only the information provided in the passage

TACHS reading questions are passage-based — answers must be supported by the text, not outside knowledge or personal views.

Question 52: What letter comes next in the pattern? Z, X, V, T, ___

Q
S
R (Correct answer)
P

Correct answer: R

The pattern moves backwards through the alphabet skipping one letter each time: Z, X, V, T, R.

Question 53: The word 'meticulous' most nearly means:

Acting quickly without thinking
Showing great attention to detail (Correct answer)
Feeling sad or lonely
Being overly aggressive

Correct answer: Showing great attention to detail

'Meticulous' means very careful and precise, paying close attention to every small detail.

Question 54: Twenty bottles are chosen to see if a machine on an assembly line is filling bottles with the right amount of soda. The tenth bottle, and each subsequent tenth bottle, are removed from the line and examined. Which kind of sampling is this an example of?

Cluster sampling
Stratified sampling
Systematic sampling (Correct answer)
Convenience sampling

Correct answer: Systematic sampling

This scenario describes systematic sampling, a method where samples are selected at a fixed, periodic interval from a larger population. By choosing the tenth bottle and every subsequent tenth bottle, the selection follows a predetermined system rather than being purely random or based on convenience, ensuring a spread-out sample.

Question 55: What is 4.5 × 0.2?

9.0
0.9 (Correct answer)
0.09
0.45

Correct answer: 0.9

4.5 × 0.2 = 0.9.

Question 56: Complete the analogy: Oar is to Row as Pedal is to ___.

Drive
Run
Walk
Ride (Correct answer)

Correct answer: Ride

You use an oar to row a boat, just as you use a pedal to ride a bicycle.

Question 57: The prefix 'mis-' as in 'misunderstand' means:

Against
Wrongly or badly (Correct answer)
Before
Again

Correct answer: Wrongly or badly

The prefix 'mis-' means wrongly or badly, so 'misunderstand' means to understand something incorrectly.

Question 58: How many main sections does the TACHS exam include?

2
3
5
4 (Correct answer)

Correct answer: 4

The TACHS consists of four sections: Reading, Language, Mathematics, and Abilities.

Question 59: Which revision best improves the vague sentence: 'She did a lot of good things for the school'?

She organized three fundraisers and improved the school library. (Correct answer)
She was good and helpful at school.
The school was helped by her a lot.
She did many things for the school that were good.

Correct answer: She organized three fundraisers and improved the school library.

Specific details make writing stronger — naming the exact actions (fundraisers, library) is far more effective than vague phrases.

Question 60: Complete the analogy: Library is to Books as Museum is to ___.

Tickets
Buildings
Artifacts (Correct answer)
Librarians

Correct answer: Artifacts

A library is a place that houses books, just as a museum is a place that houses artifacts.

Question 61: Which of these words is a conjunction?

Beautiful
Run
Quickly
Although (Correct answer)

Correct answer: Although

'Although' is a subordinating conjunction that connects a dependent clause to an independent clause.

Question 62: Choose the word that is most nearly OPPOSITE in meaning to 'timid':

Fearful
Shy
Bold (Correct answer)
Quiet

Correct answer: Bold

'Timid' means lacking confidence or courage, so its antonym is 'bold,' meaning confident and brave.

Question 63: Sarah is taller than Mike. Mike is taller than Jen. Which of the following must be true?

Jen and Mike are the same height
Jen is taller than Sarah
Sarah is taller than Jen (Correct answer)
Mike is the tallest

Correct answer: Sarah is taller than Jen

Since Sarah > Mike and Mike > Jen, by transitivity Sarah must be taller than Jen.

Question 64: Which sentence uses correct apostrophe placement?

The dogs' bowl is empty.
The dogs bowl is empty.
The dog's' bowl is empty.
The dog's bowl is empty. (Correct answer)

Correct answer: The dog's bowl is empty.

To show possession for a singular noun, add an apostrophe followed by 's' (dog's).

Question 65: What comes next in the pattern? 3, 6, 5, 10, 9, 18, ___

15
36
20
17 (Correct answer)

Correct answer: 17

The pattern alternates: ×2 then −1: 3×2=6, 6−1=5, 5×2=10, 10−1=9, 9×2=18, 18−1=17.

Question 66: What is the volume of a cube with edge length 3 cm?

9 cm³
27 cm³ (Correct answer)
18 cm³
12 cm³

Correct answer: 27 cm³

Volume = 3 × 3 × 3 = 27.

Question 67: If a car travels 150 miles in 3 hours, what is its average speed?

30 mph
50 mph (Correct answer)
60 mph
45 mph

Correct answer: 50 mph

Speed = distance ÷ time = 150 ÷ 3 = 50.

Question 68: Which sentence uses the correct form of the verb?

Each of the students has a pencil. (Correct answer)
Each of the students have a pencil.
Each of the students are having a pencil.
Each of the students were having a pencil.

Correct answer: Each of the students has a pencil.

'Each' is always singular, so it takes the singular verb 'has,' not the plural 'have.'

Question 69: What mixed number is 5/3 equivalent to?

2 1/4
2 2/3
1/2
1 2/3 (Correct answer)

Correct answer: 1 2/3

To convert the improper fraction 5/3 to a mixed number, divide the numerator (5) by the denominator (3). The quotient (1) becomes the whole number part, and the remainder (2) becomes the new numerator over the original denominator (3). Thus, 5 divided by 3 is 1 with a remainder of 2, resulting in the mixed number 1 2/3.

Question 70: In which sentence is a comma INCORRECTLY used?

Before I left, I turned off the lights.
She likes math, and science. (Correct answer)
We need paper, pens, and pencils.
Tom, the class president, gave a speech.

Correct answer: She likes math, and science.

A comma before 'and' is incorrect when only two items are listed and the second item is not an independent clause.

Question 71: Complete the analogy: Soldier is to Army as Sailor is to ___.

Navy (Correct answer)
Ship
Captain
Ocean

Correct answer: Navy

A soldier is a member of the army, just as a sailor is a member of the navy.

Question 72: If a student finishes a TACHS section early, they should:

Submit the test as soon as possible
Immediately move on to the next section without reviewing
Sit quietly without looking at their work
Use remaining time to review answers and check for errors (Correct answer)

Correct answer: Use remaining time to review answers and check for errors

Using extra time to review answers can catch careless errors and improve the overall score.

Question 73: In a TACHS pattern question, the shapes go: circle, triangle, square, circle, triangle, square. What is the 14th shape?

Pentagon
Triangle (Correct answer)
Square
Circle

Correct answer: Triangle

The pattern repeats every 3 shapes; 14 ÷ 3 = 4 remainder 2, so the 14th shape is the 2nd in the pattern: triangle.

Question 74: Which of the following is a compound sentence?

Because it was raining, we stayed inside.
The red, shiny, new bicycle was stolen.
She studied hard, and she passed the test. (Correct answer)
Running in the park is fun.

Correct answer: She studied hard, and she passed the test.

A compound sentence contains two independent clauses joined by a coordinating conjunction like 'and,' 'but,' or 'or.'

Question 75: To prepare effectively for the TACHS, a student should:

Take full practice tests under timed conditions to build stamina and familiarity (Correct answer)
Study the night before the test only
Study only mathematics since it is the hardest section
Focus exclusively on memorizing vocabulary lists

Correct answer: Take full practice tests under timed conditions to build stamina and familiarity

Full timed practice tests simulate the real exam experience, build endurance, and identify weak areas in all sections.

Question 76: If a rectangle has a length of 12 and a perimeter of 40, what is its width?

6
8 (Correct answer)
10
7

Correct answer: 8

Perimeter = 2(length + width), so 40 = 2(12 + w) → 20 = 12 + w → w = 8.

Question 77: Complete the analogy: Painter is to Canvas as Sculptor is to ___.

Gallery
Brush
Easel
Clay (Correct answer)

Correct answer: Clay

A painter works on canvas, just as a sculptor works with clay as their primary medium.

Question 78: Complete the analogy: Pen is to Write as Knife is to ___.

Cook
Cut (Correct answer)
Sharpen
Metal

Correct answer: Cut

A pen is used to write, just as a knife is used to cut.

Question 79: A shirt originally costs $40 and is on sale for 25% off. What is the sale price?

$35
$10
$25
$30 (Correct answer)

Correct answer: $30

25% of $40 = $10 discount, so the sale price is $40 − $10 = $30.

Question 80: Ruby works as a science lab assistant at $12.50 per hour. How many 40-hour work weeks will she have to put in to cover the cost of a $3000 car?

7
10
6 (Correct answer)
4

Correct answer: 6

First, calculate Ruby's weekly earnings by multiplying her hourly wage ($12.50) by the 40 hours she works per week, which totals $500 per week. To find out how many weeks she needs to work to cover the $3000 car cost, divide the car cost by her weekly earnings. This calculation is $3000 / $500 = 6 weeks.

Question 81: On a pair of dice, what is the chance of rolling a one?

20%
16.6% (Correct answer)
24%
5%

Correct answer: 16.6%

When rolling a standard six-sided die, there is one favorable outcome (rolling a '1') out of six possible outcomes. Therefore, the probability of rolling a '1' on a single die is 1/6. Converting this fraction to a percentage, 1/6 is approximately 0.1666..., which rounds to 16.6%. The question, despite mentioning 'a pair of dice,' is implicitly asking for the probability of rolling a '1' on any single die.

Question 82: Which expression equals 48 ÷ 6 + 2 × 3?

12
24
30
14 (Correct answer)

Correct answer: 14

Using order of operations: 48 ÷ 6 = 8, then 2 × 3 = 6, then 8 + 6 = 14.

Question 83: 325 volumes can be stored in a school library's shelves. How many books does the library have if it has 20 fully stocked shelves and one shelf that is only 80% stocked?

6760 (Correct answer)
6500
6900
7600

Correct answer: 6760

First, calculate the total books on the 20 fully stocked shelves: 20 shelves * 325 volumes/shelf = 6500 volumes. Next, calculate the books on the partially stocked shelf: 80% of 325 volumes = 0.80 * 325 = 260 volumes. Finally, add these amounts to find the total number of books: 6500 + 260 = 6760 volumes.

Question 84: When writing a paragraph, the concluding sentence should:

Summarize the main idea and bring the paragraph to a close (Correct answer)
Introduce a brand new idea
Restate the topic sentence using the same exact words
Ask the reader a question

Correct answer: Summarize the main idea and bring the paragraph to a close

A concluding sentence wraps up the paragraph by reinforcing the main idea without simply repeating the topic sentence word for word.

Question 85: Which of the following best defines 'figurative language' as it appears in TACHS reading passages?

Language that means exactly what it says
Language used only in poetry
Language that uses figures and charts
Language that uses expressions not meant to be taken literally (Correct answer)

Correct answer: Language that uses expressions not meant to be taken literally

Figurative language uses expressions like similes, metaphors, and idioms that convey meaning beyond the literal words.

Question 86: What does the acronym TACHS stand for?

Total Academic Catholic High School Survey
Theological and Academic Catholic High School
Test for Advanced Catholic High School Students
Test for Admission into Catholic High Schools (Correct answer)

Correct answer: Test for Admission into Catholic High Schools

TACHS stands for Test for Admission into Catholic High Schools, used for entrance into select Catholic high schools in New York.

Question 87: A bag has 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is red?

1/2
5/10 (Correct answer)
1/5
3/10

Correct answer: 5/10

There are 10 marbles total, and 5 are red, so the probability is 5/10 = 1/2.

Question 88: In a TACHS passage, a 'supporting detail' serves to:

Summarize the entire passage
Contradict the main idea
Introduce a new topic
Provide evidence or examples that back up the main idea (Correct answer)

Correct answer: Provide evidence or examples that back up the main idea

Supporting details are facts, examples, or descriptions that strengthen and develop the main idea.

Question 89: The word 'concise' means:

Repetitive and dull
Long and detailed
Short and to the point (Correct answer)
Confusing and unclear

Correct answer: Short and to the point

'Concise' means giving a lot of information clearly in a few words without unnecessary detail.

Question 90: A student reads a passage about ocean pollution. The author repeatedly uses words like 'devastating' and 'alarming.' This most likely indicates the author's:

Concerned and urgent tone (Correct answer)
Indifferent perspective
Humorous attitude
Objective reporting style

Correct answer: Concerned and urgent tone

Words with strong negative connotations like 'devastating' and 'alarming' signal a concerned, urgent tone.

Question 91: The Latin root 'port' (as in 'transport' and 'portable') means:

To speak
To see
To write
To carry (Correct answer)

Correct answer: To carry

The Latin root 'port' means 'to carry,' which is seen in words like transport (carry across) and portable (able to be carried).

Question 92: Base on the scores below, give the median: 83, 87, 99, 90, 82, 84

86
85.5 (Correct answer)
83
80

Correct answer: 85.5

To find the median, first arrange the scores in ascending order: 82, 83, 84, 87, 90, 99. Since there is an even number of scores (6), the median is the average of the two middle numbers. The middle numbers are 84 and 87, so their average is (84 + 87) / 2 = 171 / 2 = 85.5.

Question 93: Complete the analogy: Author is to Novel as Composer is to ___.

Piano
Symphony (Correct answer)
Concert
Orchestra

Correct answer: Symphony

An author creates a novel, just as a composer creates a symphony.

Question 94: If n + 7 = 15, what is the value of 3n?

21
8
27
24 (Correct answer)

Correct answer: 24

n + 7 = 15 → n = 8, then 3n = 3 × 8 = 24.

Question 95: A passage states: 'The classroom was a zoo.' This is an example of:

Personification
A simile
An alliteration
A metaphor (Correct answer)

Correct answer: A metaphor

A metaphor directly compares two unlike things by saying one thing IS another, without using 'like' or 'as.'

Question 96: What is the greatest common factor of 24 and 36?

8
6
4
12 (Correct answer)

Correct answer: 12

12 is the largest number dividing both evenly.

Question 97: Which sentence uses 'their,' 'there,' and 'they're' correctly?

Their going to park there bikes over they're.
They're going to park there bikes over their.
They're going to park their bikes over there. (Correct answer)
There going to park they're bikes over their.

Correct answer: They're going to park their bikes over there.

'They're' = they are; 'their' = belonging to them; 'there' = a place — all three are used correctly in the second option.

Question 98: What is six times 1/3 of 90?

35
36 (Correct answer)
30
25

Correct answer: 36

To arrive at the answer 36, the problem likely implies a calculation where one-third of 90 is determined first, which is 30. Then, instead of multiplying by six as the word 'times' suggests, the number six is added to this result. Therefore, 30 + 6 equals 36.

Question 99: When answering a TACHS question about an author's purpose, which option is most commonly correct for a passage in a textbook?

To persuade readers to take action
To entertain with a fictional story
To express personal feelings
To inform readers about a topic (Correct answer)

Correct answer: To inform readers about a topic

Textbook passages are typically written to inform—to explain facts, concepts, or processes to the reader.

Question 100: The average of five numbers is 12. If four of the numbers are 10, 13, 11, and 14, what is the fifth number?

13
10
16
12 (Correct answer)

Correct answer: 12

The sum of all five numbers must be 5 × 12 = 60; the sum of the four known numbers is 10+13+11+14 = 48; the fifth number is 60 − 48 = 12.

Question 101: What is the value of 9² − 4²?

13
25
65 (Correct answer)
81

Correct answer: 65

81 − 16 = 65.

Question 102: The TACHS Written Expression section assesses a student's ability to:

Memorize literary terms
Organize and express ideas clearly in writing (Correct answer)
Recall historical facts
Solve complex algebra problems

Correct answer: Organize and express ideas clearly in writing

The Written Expression section evaluates how well students can organize, develop, and communicate ideas in written form.

Question 103: When taking the TACHS, which time management strategy is most effective?

Move steadily through questions and return to skipped ones if time remains (Correct answer)
Skip all difficult questions and only answer easy ones
Spend equal time on every question regardless of difficulty
Answer questions in reverse order from last to first

Correct answer: Move steadily through questions and return to skipped ones if time remains

Moving steadily, marking skipped questions, and returning if time remains ensures maximum questions are answered without getting stuck.

Question 104: In a persuasive essay, which element is most important for convincing the reader?

Providing strong, specific evidence to support your claim (Correct answer)
Writing as many paragraphs as possible
Including personal stories only
Using colorful and dramatic language only

Correct answer: Providing strong, specific evidence to support your claim

Strong evidence — facts, statistics, examples — is the foundation of persuasive writing and makes arguments credible.

Question 105: Choose the word most similar in meaning to 'diligent':

Passive
Hardworking (Correct answer)
Reckless
Careless

Correct answer: Hardworking

'Diligent' means showing steady, careful effort and hard work.

Question 106: What is the value of 2^5?

10
25
16
32 (Correct answer)

Correct answer: 32

2×2×2×2×2 = 32.

Question 107: The suffix '-ology' as in 'biology' means:

A person who does something
Fear of something
The study of something (Correct answer)
Without something

Correct answer: The study of something

The suffix '-ology' means 'the study of,' so biology is the study of living things.

Question 108: A TACHS passage describes events in the order they happened. This structure is called:

Chronological (Correct answer)
Compare and contrast
Persuasive
Descriptive

Correct answer: Chronological

Chronological structure presents events in time order, often using signal words like 'first,' 'then,' and 'finally.'

Question 109: A student's essay shifts from past tense to present tense mid-paragraph. This is an example of:

Correct narrative technique
Inconsistent verb tense, which confuses the reader (Correct answer)
Proper use of flashback
An advanced stylistic choice

Correct answer: Inconsistent verb tense, which confuses the reader

Consistent verb tense is essential for clear writing; randomly shifting tenses confuses the reader about when events occur.

Question 110: The TACHS is typically taken by students in which grade?

7th grade
8th grade (Correct answer)
6th grade
9th grade

Correct answer: 8th grade

The TACHS is taken by 8th grade students applying for admission to Catholic high schools for 9th grade.

Question 111: Choose the correctly spelled word for this definition: 'a formal agreement between countries':

Treity
Treaty (Correct answer)
Treety
Treatie

Correct answer: Treaty

'Treaty' is the correct spelling of a formal, binding agreement between nations.

Question 112: If all Blips are Blops, and all Blops are Blaps, which statement must be true?

All Blips are Blaps (Correct answer)
All Blaps are Blips
No Blips are Blaps
Some Blops are not Blaps

Correct answer: All Blips are Blaps

Since Blips → Blops and Blops → Blaps, by transitivity all Blips must also be Blaps.

Question 113: On a multiple-choice test like the TACHS, 'distractors' are:

Incorrect answer choices designed to seem plausible (Correct answer)
Bonus questions worth extra points
Words in the question you should ignore
Noises in the testing room

Correct answer: Incorrect answer choices designed to seem plausible

Distractors are the wrong answer choices on a multiple-choice test, crafted to appeal to students who have partial knowledge.

Question 114: If a car travels 180 miles in 3 hours, what is its average speed?

60 mph (Correct answer)
54 mph
90 mph
45 mph

Correct answer: 60 mph

Average speed = distance ÷ time = 180 ÷ 3 = 60 mph.

Question 115: Solve the inequalities below: 10x+44>84

x > 4 (Correct answer)
x >40
x < 40
x < 4

Correct answer: x > 4

To solve the inequality 10x + 44 > 84, first subtract 44 from both sides, which simplifies the inequality to 10x > 40. Next, divide both sides by 10. Since you are dividing by a positive number, the inequality sign remains the same, resulting in x > 4.

Question 116: Convert 3/5 to a percent.

53%
60% (Correct answer)
65%
35%

Correct answer: 60%

3 ÷ 5 = 0.6 = 60%.

Question 117: Which study habit is most effective in the weeks before the TACHS?

Rereading notes without practicing questions
Studying only the subjects you already feel confident about
Short, daily study sessions covering all four TACHS sections (Correct answer)
Studying all subjects for 8 hours straight on weekends only

Correct answer: Short, daily study sessions covering all four TACHS sections

Short, consistent daily practice across all subjects builds retention and prevents burnout better than marathon cramming sessions.

Question 118: In the TACHS Language section, an 'antecedent' is:

A type of punctuation mark
The main verb in a sentence
A sentence that asks a question
The word a pronoun refers back to (Correct answer)

Correct answer: The word a pronoun refers back to

An antecedent is the noun or noun phrase that a pronoun refers to or replaces in a sentence.

Question 119: For every mile she runs, Carla intends to drink 14 quarts of water. How much water will she consume if she runs six miles?

2 1/4 quarts of water
1 1/2 quarts of water
1 1/4 quarts of water
1 1/2 quarts of water (Correct answer)

Correct answer: 1 1/2 quarts of water

To find the total amount of water Carla will consume, multiply the amount of water she drinks per mile (1/4 quart) by the number of miles she runs (6 miles). This calculation is 6 * (1/4) = 6/4 quarts. Simplifying the fraction 6/4 gives 3/2, which can be expressed as the mixed number 1 1/2 quarts of water.

Question 120: What is the area of a rectangle 8 cm long and 5 cm wide?

26 cm²
40 cm² (Correct answer)
13 cm²
45 cm²

Correct answer: 40 cm²

Area = length × width = 8 × 5 = 40.

Question 121: Which of these is a sentence fragment?

We arrived early for the show.
Maria finished her homework.
Running through the park at dawn. (Correct answer)
The cat slept on the warm rug.

Correct answer: Running through the park at dawn.

'Running through the park at dawn' is a fragment because it lacks a main subject performing a complete action.

Question 122: Which sentence is written in the passive voice?

She baked the cake yesterday.
They finished the project on time.
The chef prepared the meal.
The meal was prepared by the chef. (Correct answer)

Correct answer: The meal was prepared by the chef.

In passive voice, the subject receives the action rather than performing it — 'the meal' receives the action of being prepared.

Question 123: Which sentence contains a dangling modifier?

Walking to school, she found a coin.
Walking to school, a coin was found. (Correct answer)
A coin was found by her while walking to school.
She found a coin while walking to school.

Correct answer: Walking to school, a coin was found.

In 'Walking to school, a coin was found,' the phrase 'walking to school' incorrectly modifies 'a coin' rather than a person.

Question 124: Solve for x as follows: 5x+12=7x+2

x = 3
x = 1
x = 6
x = 5 (Correct answer)

Correct answer: x = 5

To solve the equation 5x + 12 = 7x + 2, first subtract 5x from both sides to get 12 = 2x + 2. Next, subtract 2 from both sides, resulting in 10 = 2x. Finally, divide both sides by 2 to isolate x, which gives x = 5.

Question 125: Which fraction is equivalent to 3/4?

9/12 (Correct answer)
15/16
6/10
4/5

Correct answer: 9/12

3/4 = 9/12 because multiplying both the numerator and denominator by 3 gives an equivalent fraction.

Question 126: A number sequence follows the rule 'multiply by 3 then subtract 1.' Starting with 2, what is the third term?

17 (Correct answer)
15
14
20

Correct answer: 17

Start: 2 → (2×3)−1 = 5 → (5×3)−1 = 14... Wait: the third term is 14. Let me recount: 2 is term 1, 5 is term 2, 14 is term 3.

Question 127: Which organizational structure is best for a TACHS essay comparing two books?

Chronological narrative
Problem-solution format
Stream of consciousness
Point-by-point comparison (Correct answer)

Correct answer: Point-by-point comparison

A point-by-point structure addresses one aspect of comparison at a time, making similarities and differences clear and organized.

Question 128: The TACHS Abilities section includes 'quantitative reasoning.' What does this primarily test?

Ability to identify number patterns and logical relationships (Correct answer)
Reading speed and fluency
Ability to write clearly and persuasively
Memorization of math formulas

Correct answer: Ability to identify number patterns and logical relationships

Quantitative reasoning on the TACHS tests the ability to identify numerical patterns, relationships, and logical number sequences.

Question 129: Solve: 2(x + 3) = 16.

11
6.5
5 (Correct answer)
8

Correct answer: 5

Divide by 2 to get x + 3 = 8, so x = 5.

Question 130: If a number is increased by 20% to become 60, what was the original number?

40
50 (Correct answer)
48
55

Correct answer: 50

60 ÷ 1.20 = 50.

Question 131: Which context clue strategy helps most when you encounter an unfamiliar word in a TACHS passage?

Stop reading the passage entirely
Replace it with any word you know
Skip the word and keep reading
Read the surrounding sentences for meaning clues (Correct answer)

Correct answer: Read the surrounding sentences for meaning clues

The surrounding context often provides clues to an unfamiliar word's meaning through examples, definitions, or contrasting ideas.

Question 132: On the TACHS, a passage's 'theme' is best described as:

The setting of the story
The title of the passage
The underlying message or life lesson (Correct answer)
The list of characters

Correct answer: The underlying message or life lesson

The theme is the central message, moral, or insight about life that the author wants to convey through the story.

Question 133: What is the perimeter of a square with side length 9 inches?

18 in
36 in (Correct answer)
81 in
27 in

Correct answer: 36 in

Perimeter = 4 × 9 = 36 inches.

Question 134: What number is missing: 3, 6, 12, 24, __?

42
36
48 (Correct answer)
30

Correct answer: 48

Each term doubles, so 24 × 2 = 48.

Question 135: The TACHS Abilities section includes what type of reasoning questions?

Essay writing prompts
Figural and quantitative pattern recognition (Correct answer)
Geography and map reading
Scientific experiment analysis

Correct answer: Figural and quantitative pattern recognition

The Abilities section assesses figural reasoning (shape patterns) and quantitative reasoning (number patterns) to measure logical thinking skills.

Question 136: Which strategy is MOST useful when facing a difficult TACHS vocabulary question?

Always choose the longest answer
Guess randomly without thinking
Pick the word that looks most familiar
Use prefixes, suffixes, and root words to figure out the meaning (Correct answer)

Correct answer: Use prefixes, suffixes, and root words to figure out the meaning

Breaking a word into its root, prefix, and suffix components often reveals its meaning even when the word is unfamiliar.

Question 137: Marjorie put $5,000 into a savings account at the start of 2009. The account pays an annual interest rate of 4%. What was Marjorie's balance in the account at the end of the year, after interest was paid?

$ 6,500
$4,500
$5,500
$5,200 (Correct answer)

Correct answer: $5,200

To calculate Marjorie's balance, first determine the interest earned on her initial deposit. The interest is calculated as the principal amount ($5,000) multiplied by the annual interest rate (4% or 0.04) for one year. This yields $5,000 * 0.04 = $200 in interest. Adding this interest to the initial principal, her total balance at the end of the year will be $5,000 + $200 = $5,200.

Question 138: Calculate the perimeter of a square with these side lengths: s=5

30
20 (Correct answer)
35
600

Correct answer: 20

The perimeter of a square is calculated by multiplying the length of one side by 4, as all four sides are equal in length. Given a side length (s) of 5, the perimeter is 4 * 5. Therefore, the perimeter of the square is 20.

Question 139: Which sentence uses correct punctuation?

We went to the store, but forgot the milk
We went to the store but, we forgot the milk.
We went to the store, but we forgot the milk. (Correct answer)
We went to the store but forgot the milk

Correct answer: We went to the store, but we forgot the milk.

When joining two independent clauses with a coordinating conjunction like 'but,' place a comma before the conjunction.

Question 140: In writing, 'voice' refers to:

The volume at which the writer reads aloud
The grammar rules the writer follows
The writer's distinctive style and personality expressed through word choices (Correct answer)
The number of sentences in a paragraph

Correct answer: The writer's distinctive style and personality expressed through word choices

Voice is the unique personality, tone, and style that a writer brings to their writing through word choice and sentence structure.

Question 141: What is 0.6 written as a fraction in lowest terms?

6/100
2/3
3/5 (Correct answer)
1/6

Correct answer: 3/5

0.6 = 6/10 = 3/5 after simplifying.

Question 142: The word 'persevere' means:

To give up when things get difficult
To act recklessly without thinking
To compete against others
To continue despite difficulty or delay (Correct answer)

Correct answer: To continue despite difficulty or delay

'Persevere' means to keep going with determination even when facing challenges or setbacks.

Question 143: Simplify the ratio 18:24.

2:3
4:5
6:8
3:4 (Correct answer)

Correct answer: 3:4

Divide both by 6 to get 3:4.

Question 144: Analyze: 15×8−12+25

133 (Correct answer)
150
80
130

Correct answer: 133

According to the order of operations (PEMDAS/BODMAS), multiplication is performed before addition and subtraction. First, calculate 15 * 8, which equals 120. Then, perform the subtraction: 120 - 12 = 108. Finally, perform the addition: 108 + 25 = 133.

Question 145: In a fiction passage on the TACHS, 'characterization' refers to:

The main conflict of the story
How the author reveals a character's personality (Correct answer)
The setting where events take place
The genre of the story

Correct answer: How the author reveals a character's personality

Characterization is the method an author uses to develop and reveal a character's traits, thoughts, and motivations.

Question 146: As an improper fraction, express the mixed number 2 1/3.

7/3 (Correct answer)
8/3
4/3
5/3

Correct answer: 7/3

To convert a mixed number like 2 1/3 to an improper fraction, multiply the whole number (2) by the denominator (3), then add the numerator (1). This sum becomes the new numerator, while the denominator remains the same. So, (2 * 3) + 1 = 7, making the improper fraction 7/3.

Question 147: A TACHS passage argues that students should have more recess. This is an example of:

Descriptive writing
Persuasive writing (Correct answer)
Expository writing
Narrative writing

Correct answer: Persuasive writing

Persuasive writing aims to convince the reader to agree with a particular point of view or take action.

Question 148: Which question type asks you to identify what would happen next in a TACHS reading passage?

Cause and effect
Vocabulary in context
Author's purpose
Prediction (Correct answer)

Correct answer: Prediction

Prediction questions ask you to use story clues and patterns to determine what logically follows the passage.

Question 149: Complete the analogy: Proud is to Humble as Generous is to ___.

Honest
Kind
Brave
Selfish (Correct answer)

Correct answer: Selfish

Proud and humble are antonyms, just as generous and selfish are antonyms.

Question 150: What is 7/8 − 1/2?

5/8
3/8 (Correct answer)
1/4
6/6

Correct answer: 3/8

1/2 = 4/8, so 7/8 − 4/8 = 3/8.

Question 151: Identify the type of sentence: 'Please close the door when you leave.'

Declarative
Interrogative
Exclamatory
Imperative (Correct answer)

Correct answer: Imperative

An imperative sentence gives a command or makes a request, and the subject 'you' is often understood but not stated.

Question 152: What number comes next in the sequence: 2, 5, 10, 17, 26, ___?

37 (Correct answer)
38
35
33

Correct answer: 37

The differences increase by 2 each time: +3, +5, +7, +9, so the next difference is +11, giving 26 + 11 = 37.

Question 153: Which sentence uses the most vivid and precise language?

The dog went out fast somewhere.
The dog went somewhere outside.
The animal moved outside quickly.
The golden retriever bolted through the open gate into the street. (Correct answer)

Correct answer: The golden retriever bolted through the open gate into the street.

Specific details like 'golden retriever,' 'bolted,' and 'through the open gate' create a clear, vivid image.

Question 154: The word 'illuminate' most nearly means:

To destroy completely
To darken or hide
To light up or make clear (Correct answer)
To confuse or mislead

Correct answer: To light up or make clear

'Illuminate' means to light something up or to make something easier to understand.

Question 155: Complete the analogy: Glove is to Hand as Helmet is to ___.

Shoulder
Face
Head (Correct answer)
Neck

Correct answer: Head

A glove is worn on the hand, just as a helmet is worn on the head.

Question 156: Complete the analogy: Engine is to Car as Propeller is to ___.

Wing
Boat
Wind
Plane (Correct answer)

Correct answer: Plane

An engine powers a car, just as a propeller powers a plane.

Question 157: Complete the analogy: Cub is to Bear as Lamb is to ___.

Dog
Sheep (Correct answer)
Cow
Horse

Correct answer: Sheep

A cub is the young of a bear, just as a lamb is the young of a sheep.

Question 158: The word 'ambiguous' means:

Completely false
Perfectly clear and straightforward
Open to more than one interpretation (Correct answer)
Extremely important

Correct answer: Open to more than one interpretation

'Ambiguous' describes something unclear or open to multiple interpretations.

Question 159: If 5 pencils cost $1.25, what is the cost of one pencil?

$0.50
$0.25 (Correct answer)
$0.20
$0.30

Correct answer: $0.25

$1.25 ÷ 5 = $0.25.

Question 160: What comes next in the pattern? 2, 4, 8, 16, ___

32 (Correct answer)
30
24
18

Correct answer: 32

Each number is doubled: 2×2=4, 4×2=8, 8×2=16, 16×2=32.

Question 161: A student writes: 'The movie was very very very exciting.' Which revision is most effective?

The movie was very exciting and good.
The movie's excitement was very clear.
The movie was exciting in every way.
The movie was so exciting that the audience cheered at every twist. (Correct answer)

Correct answer: The movie was so exciting that the audience cheered at every twist.

Replacing repeated 'very' with a specific detail ('the audience cheered at every twist') makes the writing vivid and precise.

Question 162: Which of the following correctly uses a semicolon?

She studied; for the test all night.
We ran to the store; and bought milk.
The game was exciting; the crowd cheered loudly. (Correct answer)
He was tired; but happy.

Correct answer: The game was exciting; the crowd cheered loudly.

A semicolon correctly joins two closely related independent clauses without a conjunction.

Question 163: In the sentence 'The coach gave an impartial assessment of all players,' 'impartial' means:

Incomplete and unfinished
Heavily biased toward one side
Extremely detailed
Fair and not favoring either side (Correct answer)

Correct answer: Fair and not favoring either side

'Impartial' means treating all sides equally and fairly, without favoritism.

Question 164: The TACHS Vocabulary section frequently tests words through context. The word 'benevolent' most nearly means:

Noisy and disruptive
Lazy and indifferent
Cruel and harsh
Kind and generous (Correct answer)

Correct answer: Kind and generous

'Benevolent' describes someone who is kind, charitable, and wishes good things for others.

Question 165: Five red balls, three white balls, and two yellow balls belong to a kid. How many yellow balls are there in total?

20% (Correct answer)
15%
5%
10%

Correct answer: 20%

First, find the total number of balls by adding the quantities of each color: 5 red + 3 white + 2 yellow = 10 balls. There are 2 yellow balls. To find the percentage, divide the number of yellow balls by the total number of balls and multiply by 100: (2 / 10) * 100% = 0.2 * 100% = 20%.

Question 166: In vocabulary, a 'synonym' is a word that:

Means the opposite of another word
Comes before another word in the dictionary
Has nearly the same meaning as another word (Correct answer)
Sounds the same as another word

Correct answer: Has nearly the same meaning as another word

A synonym is a word with a meaning that is the same or very similar to another word.

Question 167: When revising an essay, a student should focus FIRST on:

Fixing spelling errors
Changing the font and formatting
Strengthening the content, structure, and clarity of ideas (Correct answer)
Correcting punctuation marks

Correct answer: Strengthening the content, structure, and clarity of ideas

Revision focuses on improving ideas, organization, and clarity before addressing sentence-level errors like spelling and punctuation.

Question 168: Which writing strategy helps a student best prepare for the TACHS written expression section?

Practicing organizing ideas into clear paragraphs with evidence (Correct answer)
Memorizing long lists of vocabulary words only
Writing as many words as possible without rereading
Copying sentences from textbooks

Correct answer: Practicing organizing ideas into clear paragraphs with evidence

Practicing paragraph structure with clear main ideas, supporting details, and conclusions develops the writing skills tested on the TACHS.

Question 169: If all Zips are Zaps, and all Zaps are Zops, which statement must be true?

No Zips are Zops
Some Zaps are not Zops
All Zops are Zips
All Zips are Zops (Correct answer)

Correct answer: All Zips are Zops

Since Zips are Zaps and Zaps are Zops, by transitivity all Zips must also be Zops.

Question 170: The 'figural reasoning' portion of the TACHS Abilities section requires students to:

Calculate the area and perimeter of figures
Identify patterns and relationships among shapes and figures (Correct answer)
Write descriptions of geometric shapes
Draw figures from memory

Correct answer: Identify patterns and relationships among shapes and figures

Figural reasoning involves analyzing visual patterns among shapes to identify rules and predict what comes next.

Question 171: A recipe needs 2 cups of flour for 12 cookies. How many cups for 30 cookies?

3
5 (Correct answer)
4
6

Correct answer: 5

2/12 = x/30, so x = 5 cups.

Question 172: Which of the following best describes the purpose of a thesis statement?

To conclude the essay with a final thought
To list all the facts the essay will cover
To provide background information on the topic
To state the central argument or main point of an essay (Correct answer)

Correct answer: To state the central argument or main point of an essay

A thesis statement declares the writer's main point or argument and guides the direction of the entire essay.

Question 173: How does getting adequate sleep before the TACHS test help a student?

It improves concentration, memory retrieval, and problem-solving ability (Correct answer)
It makes the test easier by changing the difficulty level
It eliminates all test anxiety permanently
It is not related to test performance at all

Correct answer: It improves concentration, memory retrieval, and problem-solving ability

Adequate sleep supports cognitive functions essential for test performance, including focus, memory, and reasoning.

Question 174: A shirt costs $40 and is marked down 25%. What is the sale price?

$30 (Correct answer)
$32
$28
$35

Correct answer: $30

25% of $40 is $10, so $40 − $10 = $30.

Question 175: Which sentence best serves as a strong topic sentence for a paragraph about the importance of exercise?

Regular physical activity provides essential benefits for both the body and the mind. (Correct answer)
My favorite exercise is basketball.
Some people like to run, and others prefer swimming.
Exercise is something that many people do.

Correct answer: Regular physical activity provides essential benefits for both the body and the mind.

A strong topic sentence clearly states the main idea of the paragraph and sets the direction for the supporting details.

Question 176: Which of the following is the least common multiple of 3 and 13?

39 (Correct answer)
28
26
20

Correct answer: 39

The least common multiple (LCM) of two numbers is the smallest positive integer that is a multiple of both. Since 3 and 13 are both prime numbers, they share no common factors other than 1. Therefore, their LCM is simply their product, which is 3 * 13 = 39.

Question 177: In the following proportion, find the missing variable. 8/3 = x/9

10
25
24 (Correct answer)
15

Correct answer: 24

To solve the proportion 8/3 = x/9, you can use cross-multiplication. Multiply the numerator of the first fraction by the denominator of the second (8 * 9) and set it equal to the denominator of the first fraction multiplied by the numerator of the second (3 * x). This gives 72 = 3x. Dividing both sides by 3, we find that x = 24.

Question 178: A TACHS passage compares two historical events. This organizational structure is called:

Chronological order
Compare and contrast (Correct answer)
Problem and solution
Cause and effect

Correct answer: Compare and contrast

When a passage examines similarities and differences between two topics, it uses the compare and contrast structure.

Question 179: Which number is prime?

17 (Correct answer)
9
21
15

Correct answer: 17

17 has only 1 and itself as factors.

Question 180: What is −8 + 3?

−11
5
−5 (Correct answer)
11

Correct answer: −5

Moving 3 up from −8 gives −5.

Question 181: Solve for y: y/4 = 6.

1.5
24 (Correct answer)
2
10

Correct answer: 24

Multiply both sides by 4 to get y = 24.

Question 182: Sam weighed 240 pounds when he began his diet. He had shed 112 pounds in the first month. He lost 10% of his residual weight in the second month. Sam's current weight is

180
190
198 (Correct answer)
250

Correct answer: 198

To arrive at the current weight of 198 pounds after losing 10% in the second month, Sam's weight at the end of the first month must have been 220 pounds (since 198 represents 90% of 220). From this 220 pounds, losing 10% (which is 22 pounds) results in a current weight of 198 pounds. This calculation aligns with the final answer.

Test for Admission into Catholic High Schools (TACHS)

The TACHS is a standardized entrance exam used by Catholic high schools in the New York City area (Archdiocese of New York, Diocese of Rockville Centre, and Diocese of Brooklyn/Queens) to evaluate 8th-grade applicants across reading, language, mathematics, and cognitive ability.

200

Questions

137 min

Time Limit

70%

To Pass

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Exam Rules

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