Free Core Academic Skills (Math) Questions and Answers — Questions and Answers

Question 1: Brad and Amy each have $5 for Greta's gift <br> How much money do they have together to buy the gift?

$2
$5
$10 (Correct answer)
$20

Correct answer: $10

To find the total amount of money Brad and Amy have together, you simply add their individual amounts. Brad has $5 and Amy has $5, so $5 + $5 equals $10. This is a basic addition problem.

Question 2: Patrice has 3 boxes of cards. Each box is 2 inches thick. The boxes are stacked on top of each other. <br> How high is the stack?

3 inches
6 inches (Correct answer)
9 inches
10 inches

Correct answer: 6 inches

To find the total height of the stack, you multiply the number of boxes by the thickness of each box. Patrice has 3 boxes, and each box is 2 inches thick, so 3 boxes multiplied by 2 inches per box equals 6 inches. This is a basic multiplication problem.

Question 3: Gina is buying a shirt that costs $10.00. The sales tax is 7.5% <br> How much will the tax be?

$ 0.07
$ 0.13
$ 0.75 (Correct answer)
$ 1.30

Correct answer: $ 0.75

To calculate the sales tax, you need to find 7.5% of $10.00. First, convert the percentage to a decimal by dividing by 100, which gives 0.075. Then, multiply the decimal by the original price: $10.00 * 0.075 = $0.75. Therefore, the tax will be $0.75.

Question 4: Jackson Elementary will have 120 first-grade students next year. Each class can have 24 students. <br> Using the equation 24x = 120, how many first-grade classes will the school need?

4
5 (Correct answer)
6
7

Correct answer: 5

The given equation, 24x = 120, represents the total number of students (120) divided by the number of students per class (24) to find the number of classes (x). To solve for x, divide both sides of the equation by 24. This calculation yields x = 5, meaning the school will need 5 first-grade classes.

Question 5: The sum of the first five multiples of 6 is?

30
90 (Correct answer)
60
120

Correct answer: 90

First, identify the first five multiples of 6, which are 6, 12, 18, 24, and 30. Then, add these numbers together to find their sum. The sum of 6 + 12 + 18 + 24 + 30 is 90.

Question 6: For a number to be divisible by 2, it must have ______ in the ones place.

0
Both 3 and 5
2,4
0,2,4,6,8 (Correct answer)

Correct answer: 0,2,4,6,8

A number is divisible by 2 if it is an even number. Even numbers are defined as integers that can be divided by 2 without leaving a remainder. This property holds true for any number ending in 0, 2, 4, 6, or 8 in its ones place.

Question 7: Which is the only number having only one factor?

0
2
1 (Correct answer)
3

Correct answer: 1

A factor of a number is an integer that divides the number evenly. The number 1 is unique because its only factor is itself. All other positive integers have at least two factors: 1 and the number itself (and potentially more).

Question 8: Which of the following numbers is not divisible by 3?

3162
7956
5482 (Correct answer)
8085

Correct answer: 5482

A number is divisible by 3 if the sum of its digits is divisible by 3. For 5482, the sum of the digits is 5 + 4 + 8 + 2 = 19, and 19 is not divisible by 3. In contrast, the sums of the digits for the other options (3162 -> 12, 7956 -> 27, 8085 -> 21) are all divisible by 3.

Question 9: Which of the following numbers is divisible by 8?

1372
10568 (Correct answer)
7833
3206

Correct answer: 10568

A number is divisible by 8 if its last three digits form a number that is divisible by 8. For 10568, the last three digits are 568. Dividing 568 by 8 gives 71, with no remainder, confirming that 10568 is divisible by 8.

Question 10: Two consecutive prime numbers whose difference is 2 are called

Twin primes (Correct answer)
Even numbers
Co-primes
Composite numbers

Correct answer: Twin primes

Twin primes are defined as a pair of prime numbers that differ by exactly 2. Examples include (3, 5), (5, 7), and (11, 13). This specific definition distinguishes them from other types of prime number pairs.

Question 11: The HCF of two consecutive number is

2
their product
1 (Correct answer)
0

Correct answer: 1

The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two consecutive integers is always 1. This is because consecutive integers share no common factors other than 1. For example, the HCF of 4 and 5 is 1.

Question 12: Which of the following is not correctly matched?

Only even number which is prime - 2
Smallest prime number - 2
Smallest composite number - 1 (Correct answer)
Factor of every number - 1

Correct answer: Smallest composite number - 1

The smallest composite number is 4, not 1. A composite number is a positive integer that has at least one divisor other than 1 and itself. The number 1 is neither prime nor composite, making option C incorrectly matched.

Question 13: The prime factorisation of 88 is

2 x 2 x 11
2 x 2 x 2 x 11 (Correct answer)
2 x 44
2 x 22 x 2

Correct answer: 2 x 2 x 2 x 11

Prime factorization involves breaking down a number into its prime factors. For 88, you can repeatedly divide by 2: 88 ÷ 2 = 44, 44 ÷ 2 = 22, and 22 ÷ 2 = 11. Since 11 is a prime number, the prime factorization of 88 is 2 x 2 x 2 x 11.

Question 14: How many prime numbers are there from 1 to 100?

18
25 (Correct answer)
22
24

Correct answer: 25

There are exactly 25 prime numbers between 1 and 100. These numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. This is a known mathematical fact.

Question 15: There are 3 prime numbers between

40 and 50
70 and 80
50 and 60
Both A and C (Correct answer)

Correct answer: Both A and C

To find the correct answer, we must identify which ranges contain exactly three prime numbers. The prime numbers between 40 and 50 (Option A) are 41, 43, and 47, which is three primes. The prime numbers between 50 and 60 (Option C) are 53 and 59. Therefore, only option A factually meets the condition of having three prime numbers. If 'Both A and C' is the correct answer, it implies an error in the question's premise regarding option C.

Question 16: Find the LCM of 10, 15, 18.

90 (Correct answer)
150
60
80

Correct answer: 90

To find the Least Common Multiple (LCM) of 10, 15, and 18, we can use prime factorization. The prime factors are 10 = 2x5, 15 = 3x5, and 18 = 2x3^2. The LCM is found by taking the highest power of all prime factors present: 2^1 * 3^2 * 5^1 = 2 * 9 * 5 = 90.

Free Core Academic Skills (Math) Questions and Answers

Brad and Amy each have $5 for Greta's gift
How much money do they have together to buy the gift?

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