SSAT Practice Test (Upper Level: Mathematics)

Question 1

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?

Accepted Answer

11

Answer

First, calculate the miles driven on the highway: (4/5) * 300 miles = 240 miles. The remaining city miles are 300 - 240 = 60 miles. Next, calculate the gas used for each part: Highway: 240 miles / 30 mpg = 8 gallons. City: 60 miles / 20 mpg = 3 gallons. The total gas used is 8 + 3 = 11 gallons.

Question 2

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?

Accepted Answer

-10

Answer

Let the six distinct negative integers be -16, x1, x2, x3, x4, and M, where M is the integer we want to maximize. To maximize M, the other four integers (x1, x2, x3, x4) must be as small as possible while still being distinct negative integers greater than -16. These would be -15, -14, -13, and -12. The sum of these five integers and -16 is -16 + (-15) + (-14) + (-13) + (-12) + M = -80. This simplifies to -70 + M = -80, which means M = -10. Thus, the biggest possible value for one of the other five integers is -10.

Question 3

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?

Accepted Answer

40

Answer

If 16 chairs are empty and 2/5 of the students are absent, it means that 16 students represent 2/5 of the total class. To find the total number of students, we can set up the equation (2/5) * Total Students = 16. Solving for Total Students gives 16 * (5/2) = 8 * 5 = 40. Therefore, there are 40 pupils in her entire class.

Question 4

Solve the equation: 503.384 ÷ 62.3 =

Accepted Answer

8.08

Answer

To solve 503.384 ÷ 62.3, perform the division. You can estimate by rounding to 500 ÷ 60, which is approximately 8. Performing the precise calculation, 503.384 divided by 62.3 equals 8.08. This aligns with the estimation and is one of the provided options.

Question 5

If x=5 and y=7, evaluate the expression. |4x+3y|−|4x−3y|

Accepted Answer

40

Answer

To solve 2.01 ÷ 1.02, perform the division. You can approximate it as 2 divided by 1, which is 2. Performing the precise calculation, 2.01 divided by 1.02 gives approximately 1.970588... When rounded to two decimal places, this is 1.97.