Question Banks

Question 1                                                                                                                          Difficulty level: Medium

Positive integer p is 16 percent of 16 percent of positive integer q, and p percent of q equals 16. What is the value of q?

A) 125
B) 160
C) 240
D) 250
E) 4,000

 

Solution:

It's tricky translation, but translation is all this question requires:
p=16/100 (16/100q)
p/100 q=16
Solve for the second equation for p in terms of q, then plug into the first one:
p=16(100/q)=1600/q
1600/q=16/100(16/100q)
Divide 16 out of both sides:
100/q=1/100 (16/100)q
100=1/100 (4/25) q^2
100=1/〖25〗^2  q^2
Take the square root of everything:
10=1/25 q
q=10(25)=250
The answer is D

 

Question 2                                                                                                          Difficulty level: Medium

A closed cylindrical tank contains 45 cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 5 feet. What is the radius of the tank's circular base?
A) 3p
B) 2√3
C) 3√2
D) 3√5
E) 5

 

Solution:

Since we're given the height of the water in the tank at half full, and the volume at half full, we don't need to convert those numbers to the actual size of the tank. Think of the question as concerned a half-sized tank, one with a height of 5 and a volume of 45cubic feet. Given the height and the volume of the tank, we can use the formula for the volume of a cylinder to find the radius of the base:
v=πr^2 h
45π= πr^2 (5)
9=r^2
r=3
The answer is A

 

Question 3                                                                                                          Difficulty level: High

On the rectangular coordinate plane, points P, Q, and R form a right triangle with two sides that are parallel to the x- and y-axes.

If point P is located at (3; 2), point R is located at (3; 6), and the 90-degree angle is at point Q, what is the perimeter of triangle PQR?

A) 10
B) 12
C) 14
D) 17
E) 24

 

Solution:

The third point could be at one of two locations: either (- 3, -6) or (3, 2). It doesn't matter which, so pick the one that will be easiest for you to work with. For now, let's work with (3, 2). Given that point, PQ has a length of 6, from -3 to 3. QR has a length of 8, from 2 to -6. If the two legs of a right triangle are 6 and 8, the third is 10: this should be familiar as a multiple of the 3 : 4 : 5 Pythagorean triangle ratio. Thus, the sides are 6, 8, and 10, so the perimeter is 24.
The answer is E

 

Question 4                                                                                                          Difficulty level: High     

In the multiplication table above, each number in the table is the product of the terms at the top of its column and the left of its row. What is the value of xy?

A) 15
B) 16
C) 21
D) 24
E) 27

Solution:

To find the value of xy, you'll need to find out about both x and y. x is the product of 2 and s, while y is the product of b and t. Clearly there's more work to be done.
Look for variables that can be solved for. For instance, 10 is the product of r and 2, so r = 5. If r = 5, then 30 is the product of 5 and a, a = 6. If a = 6, then 18 is the product of t and 6, so t = 3.
Going back to r = 5, 20 is the product of 5 and b, so b = 4. That gives us all the information we need about y, because y = bt = 4(3) = 12.
To find x, we need the value of s. 4 is the product of b and s, and we know that b = 4, so s = 1. x = 2s = 2(1) = 2.
Finally, since x = 2 and y = 12, xy = 24
The answer is D

Question 5                                                                                                          Difficulty level: Easy     

How many different positive integers are factors of 225?

A) 4
B) 6
C) 7
D) 9
E) 11

 

Solution:

To find the number of factors of a number, start with 1 and work your way up. The first factor of 225 (or any other integer) is 1. When you find each factor, find the number that it can be multiplied by to return the integer - for example, in the case of 1, it pairs with 225. 2 is not a factor of 225, but 3 is. 225/3 = 75, so 75 is another factor. 4 is not a factor, but 5 is. 225/5  = 45,
so 45 is also a factor. 9 is a factor, and 225/9 = 25. The only remaining factor is 15, which is the square root of 225, so there's no other distinct factor that pairs with 15. At this point, your scratch work should show 9 factors -1, 225, 3, 75, 5, 45, 9, 25, and 15.

The answer is D



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