SSAT Practice Test (Upper Level: Mathematics)
In city driving, a car gets 20 miles per gallon of gas and 30 miles per gallon on the highway. How many gallons of gas will the automobile use on a 300-mile trip if 4/5 of the trip is on the highway and the rest is in the city at these rates?
Correct answer: 11
Choice (E) is correct. The highway portion of the trip will be 4/5 x 300 = 240 miles. Since the car uses 30 miles per gallon on the highway, it will use 240/30=8 gallons of gas on the highway portion of the trip. The remainder of the trip, 300 – 240 =60 miles, will be in the city, so the car will use 60/20 = 3 gallons in the city. Therefore, the car will use 8 + 3 =11 gallons of gas altogether.
The sum of six negative integers equals -80. What is the biggest possible value of one of the other five integers if the smallest of these integers is -16?
Correct answer: -10
The largest possible value of one of the other five integers is -10.
There are sixteen empty chairs in Mrs. Bernardo's classroom. When every student is present, all of the chairs are filled. How many pupils make up her entire class if 2/5 of them are absent?
Correct answer: 40
Since 16 chairs are empty, and this represents 2/5 of the total enrollment, then the full class must consist of
Class = 5/2 × 16 = 40 students
Use proportions
2/5 = 16/x Cross multiply.
2x = 80 Divide each side by 2 to solve for x.
x = 40 students
Solve the equation: 503.384 ÷ 62.3 =
Correct answer: 8.08
503.384 ÷ 62.3 = 8.08
If x=5 and y=7, evaluate the expression. |4x+3y|−|4x−3y|
Correct answer: 40
|4x+3y|−|4x−3y|
To solve, we replace each variable with the given value.
|4(5) + 3(7)| - |4(5) - 3(7)| .
|20 + 21] - |20 — 21|
Simplify. Remember that terms inside of the absolute value are always positive.
|41| - |-1| = 41 - 1 = 40
What is the average speed James must drive in order to go to his friend's house, which is 450 miles away, in 6 hours?
Correct answer: 75 mph
Distance = rate x time
Plug in the the values for distance and time, and solve for rate.
450 = r x 6
and
r = 75
Solve the equation: 2.01 ÷ 1.02 =
Correct answer: 1.97
2.01 ÷ 1.02 = 1.97
Jolina purchased $24.15 worth of vegetables. She purchased two pounds of onions, three pounds of carrots, and twelve pounds of mushrooms. What is the price per pound of mushrooms if onions cost $3.69 per pound and carrots cost $4.29 per pound?
Correct answer: $2.60
Begin by determining the total cost of the onions and carrots, since these prices are given. This will equal (2 x $3.69) + (3 x $4.29) = $20.25. Next, this sum is subtracted from the total cost of the vegetables to determine the cost of the mushrooms: $24.15 - $20.25 = $3.90. Finally, the cost of the mushrooms is divided by the quantity (lbs) to determine the cost per pound:
Cost per lb = $3.90/1.5 = $2.60
The pink bag contains 14 marbles, whereas the blue bag contains 18 marbles. How many marbles in the pink bag are less than the marbles that each child will receive if the sum of the marbles in both bags is shared evenly between two children?
Correct answer: 2
There are 2 marbles pink bag has less than the marbles that each child will receive.
If a + 3 equals 14, then 2a-6 equals
Correct answer: 16
a+3 = 14 => a = 11
2a-6 = 2(11) – 6 = 22-6 = 16
Give the equation for a line that has a slope of 1 and passes through the point (4,7).
Correct answer: x−y=−3
We can use the point slope form of a line, substituting
m = 1, x₁ = 4,y₁ = 7.
y - y₁ = m(x - x₁)
y - 7 = 1(x - 4)
y - 7 = x - 4
y - 7 - y + 4 = x - 4 - y + 4
-3 = x - y
or
x - y = -3
Solve the equation: -3 - [(2 - 1) - (3 + 4)] =
Correct answer: 3
Begin working with the innermost parentheses and work your way out.
-3 - [(2 - 1) - (3+4)]
= -3 - [(1) - (7)]
= -3 - [1 - 7]
=-3 - [-6]
=-3 + 6
=3
A, B, and C are points on the number line in the diagram, with O representing the origin. What is the distance BC to distance AB ratio?
Correct answer: 3:11
Since the figure represents the number line, the distance from point A to point B will be the difference, B-A, which is 5 – (-6) = 11. The distance from point B to point C will also be the difference, C-B, otherwise 8 – 5 = 3. So the ratio BC:AB will be 3:11.
A cabinet's price has been reduced by 50% to $530. How much did it cost at first?
Correct answer: $1,060
1,060 - 50% = 530
What is the equation of the perpendicular line if it is perpendicular to the line y = 3x - 4 and passes through the point (0,6)?
Correct answer: y = -(1/3)x+6
The slopes of two perpendicular lines are negative reciprocals of each other. This also means that the product of the two slopes equals -1. A perpendicular line has the negative reciprocal slope of another line. Since the slope of the given line is 3 , the slope of a perpendicular line is -1/3 . The basic equation is then y = (-1/3)x+b. We need to use the point (0,6) to find b. Let’s do that: 6 = -1/3(0)+b . Therefore, b=6 , and the complete perpendicular line equation is y = -(1/3)x+6.
In the following sequence, give the next number:
3,5,10,12,24,26,52,54,____
Correct answer: 108
The sequence is generated by alternately adding 2, then multiplying by 2:
3 + 2 = 5
5 X 2 = 10
10 + 2 = 12.
12 x 2 = 24
24 + 2- = 26
26 x 2 = 52
52 + 2- = 54
54 x 2 = 108
Solve the equation: 3003 - 699 =
Correct answer: 2304
3003 - 699 = 2304
Candidate X received 36,800 votes in a Kimball County election. Candidate Y, his opponent, received 32,100 votes. Write-in candidates received 2,100 votes. Candidate X received what percentage of the vote?
Correct answer: 51.8%
Candidate A’s vote percentage is the number of votes that he obtained divided by the total number of votes cast. Then, multiply that decimal by 100 to convert the decimal into a percentage. Therefore, Candidate A’s Vote is: Percentage 36800/(36800 + 32100 + 2100) × 100 = 51.8%
What is the value of x if the perimeter of the following figure is 33?
Correct answer: 11
The value of X is 11.
A 350-student secondary school offers biology and chemistry classes. Biology has 213 students enrolled, while chemistry has 155 students. Both subjects are studied by 78 students. How many students aren't enrolled in either course?
Correct answer: 60
The correct answer is A. 60 students. To solve this problem, first find the total number of students in the combined biology and chemistry courses [213 + 155 = 368] Subtract from this total the number of students taking both courses, as they should only be counted once [368 - 78 = 290] . This leaves you with the number of students enrolled in biology and/or chemistry. The difference between this total of students and the number of students in the high school will be the number of students not studying either subject [350 - 290 = 60] .60 students are not enrolled in Biology and/or Chemistry. A is the correct answer.
A. Correct.
B. 70 would be an answer resulting from faulty arithmetic or other human errors.
C. 50 would be an answer resulting from faulty arithmetic or other human errors.
D. 78 is the number of students studying both subjects.
E. 18 is the difference between the actual number of students in the high school class and the total number of enrolled students in the combined science courses. This is a trap answer that faulty logic may lead one to choose.
Four congruent sides of length t+1 make create a hexagon with a perimeter of 60. Its other two sides are in sync with one another. In terms of t, calculate the length of each of the other sides.
Correct answer: 28−2t
The perimeter of a polygon is the sum of the lengths of its sides.
Let:
X = Length of one of those other two sides
Now we can set up an equation and solve it for x in terms of t:
2x + 4(t + 1) = 60
=> 2x + 4t + 4 = 60
=> 2x = 60 - 4 - 4t
=> 2x = 56 - 4t
=> x = 28 - 2t
What is the 140% of 70?
Correct answer: 98
This is a good problem to do in your head. Note that 10% of 70 is 7. 140%, then, is 14 × 7, or 98.
Bren's savings account held $80. She made a deposit when she got her paycheck, bringing the total to $120. As a result of this deposit, by what percentage did the total amount in her account increase?
Correct answer: 50%
The rate of increase equals the change in the account balance divided by the original amount, $80. Multiply that decimal by 100 to yield the percentage of increase. To determine the change in the balance subtract the original amount from the new balance: Change = $120 - $80 = $40. Now, determine the percentage of increase as described above: Percent = $40/$80 × 100 = 50%.
In the following sequence, what number is missing? 3,4,6,9,13,18,24,___,39
Correct answer: 31
3,4,6,9,13,18,24,31,39
Billy covered 360 feet in his run. John ran 30 yards. What is the ratio of Billy's running distance to John's running distance?
Correct answer: 4:1
Choice (E) is correct. Jamal ran 360 feet, which is equal to 120 yards. Thus, the ratio of Jamal's distance to Lonnie's distance is 120 yards to 30 yards, which is the same as 4:1