PSAT MATH PRACTICE

Question 1 :

If 8575 = 5^x⋅ 7^y, what is (xy) - 5 ?

(A) 1 (B) 3 (C) 6 (D) 7 (E) 12

Solution :

First, let us find the prime factors of 8575.

8575 = 5²⋅ 7³

x = 2 and y = 3

xy - 5 = 2(3) - 5

= 6 - 5

= 1

Hence the answer is 1.

Question 2 :

When d is divided by 8, the remainder is 3. What is the remainder when d + 3 is divided by 8 ?

(A) 1 (B) 3 (C) 4 (D) 6 (E) 7

Solution :

Let d = 11

Here we choose 11, because it is greater than 8, when we divide 11 by 8, we get the remainder 3.

Then d + 3 = 11 + 3 = 14

By dividing this d + 3 by 8, we get 6(3 + 3) as remainder.

Hence the answer is 6.

Note : The number chosen should be 3 more than the multiple of 8.

Question 3 :

Tommy is making as 6 letter password using only the letters A, B, C, D, E and F. How many different codes can Tommy make, if every letter can only be used once in each code ?

(A) 1 (B) 6 (C) 120 (D) 720 (E) 46, 656

Solution :

Let us mark 6 blank spaces.

____ ____ ____ ____ ____ ____

The first letter chosen be placed in any of the above 6 dashes.

Now, we have remaining 5 letters.

The second letter chosen, out of 5 may be placed in any one of the remaining 5 places.

In this way, we may create 6! codes by using 6 letters.

Hence the answer is 720.

Question 4 :

-5 (x -3) ≥ 20 what is the solution to the inequality shown above ?

(A) x ≥ -1 (B) x ≥ 7 (C) x ≤ -1 (D) x ≤ 7 (E) x ≥ 1

Solution :

-5 (x -3) ≥ 20

-5x + 15 ≥ 20

Subtract 15 on both sides, we get

-5x ≥ 20 - 15

-5x ≥ 5

Divide by -5 on both sides, we get

x ≤ -1

Question 5 :

Which numbers line below shows the solution to the inequality -2 < x/3 ≤ 2 ?

Solution :

= -2 < x/3 ≤ 2

Multiply the entire inequality by 3. So we get,

= -6 < x ≤ 6

The fourth option represents the the solution which is greater than -6 and less than or equal to 6.

Question 6 :

There are 15000 teens whose favorite genre is comedy. How many teens have a favorite genre of action ?

(A) 30 (B) 41,250 (C) 52,500

(D) 56,250 (E) 70,000

Solution :

Let "x" be the total population

8% of x = 15000

0.08 x = 15000

x = 15000/0.08

x = 187500

The number of teens whose genre is action

= 30% of 187500

= 56250

Question 7 :

A computer originally prices at $550.50 is on sale for 20% off. Jamie used a 5% discount coupon which was applied to the sales price. How much did Jamie pay for the computer ?(Assume there is no tax)

(A) $412.88 (B) $418.38 (C) $440.40

(D) $522.98 (E) 539.49

Solution :

Original price of computer = $550.50

From the 100% of price, the shop is going to give 20% off. Hence we have to pay 80% of the original price for the computer.

80% of 550.50 = $440.40

Again we have 5% discount, so we have to calculate 95% of discounted price.

0.95 (440.40) = 418.38

Hence the final amount for the computer is 418.38.

Question 8 :

Given the following value 4, 760 solve the following, x²/y, if x represents the smallest prime factor of the given value and y represents the greatest prime factor of the given value.

(A) 119/4 (B) 4/17 (C) 2/119 (D) 4/119 (E) 2/17

Solution :