Nova's SAT Diagnostic Test - Math

Test Questions

1. If x and y are both prime and greater than 2, then which of the following CANNOT be a divisor of xy?
(A) 2
(B) 3
(C) 11
(D) 15
(E) 17

2. Cars X and Y leave City A at the same time and travel the same route to City B. Car X takes 30 minutes to complete the trip and car Y takes 20 minutes. Which of the following must be true?

I. The average miles per hour at which car X traveled was greater than the average miles per hour at which car Y traveled.
II. The distance between the cities is 30 miles.
III. The average miles per hour at which car Y traveled was greater than the average miles per hour at which car X traveled.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

3. In the figure above, y =
(A) 75
(B) 76
(C) 77
(D) 78
(E) 79

4. If x = 3y = 4z, which of the following must equal 6x?

I. 18y
II. 3y + 20z
III. (4y + 10z)/3

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

5. The average of four numbers is 20. If one of the numbers is removed, the average of the remaining numbers is 15. What number was removed?
(A) 10
(B) 15
(C) 30
(D) 35
(E) 45

6. The ratio of two numbers is 10 and their difference is 18. What is the value of the smaller number?
(A) 2
(B) 5
(C) 10
(D) 21
(E) 27

7. If 3y + 5 = 7x, then 21y - 49x =
(A) -40
(B) -35
(C) -10
(D) 0
(E) 15

8. Seven years ago, Scott was 3 times as old as Kathy was at that time. If Scott is now 5 years older than Kathy, how old is Scott?
(A) 12 1/2
(B) 13
(C) 13 1/2
(D) 14
(E) 14 1/2

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