**PSAT Math Practice Test :**

Here we are going to see some sample questions for PSAT exams. For each and every questions, you will have solutions with step by step explanation.

**Question 11 :**

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 = 5^{2 }⋅ 7^{3}

x = 2 and y = 3

xy - 5 = 2(3) - 5

= 6 - 5

= 1

Hence the answer is 1.

**Question 12 :**

When d is divide 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 13 :**

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 14 :**

-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 15 :**

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 16 :**

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 17 :**

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 18 :**

Given the following value 4, 760 solve the following, x^{2}/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 :**

4760 = 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 7 ⋅ 17

Smallest prime factor = 2, largest prime factor = 17

x^{2}/y = 2^{2}/17 = 4/17

Hence the answer is 4/17.

**Question 19 :**

An adult male Diptera has a mass of 11.5 milligrams. What is the Diptera's mass in grams?

(A) 0.0115 g (B) 0.115 g (C) 1.15 g

(D) 11.5 g (E) 115 g

**Solution :**

1000 milli grams = 1 gram

= (11.5/1000) grams

= 0.0115 grams.

**Question 20 :**

Michel has a project due in exactly 83 hours. It is currently 8 : 30 on Monday morning. What time is his project due ?

(A) 6:30 PM Friday (B) 7:30 PM Friday

(C) 7:30 AM Thursday

(D) 7:30 PM Thursday (E) 9:30 PM Thursday

**Solution :**

Every day consists of 24 hours. In 83 hours, we have three consecutive days and 11 hours remaining.

It is currently 8 : 30 on Monday morning.

Then, we have

Monday (8:30 A.M) to Tuesday (8 : 30 A.M) ==> 24 hours

Tuesday (8:30 A.M) to Wednesday (8 : 30 A.M) ==> 24 hours

Wednesday (8:30 A.M) to Thursday (8 : 30 A.M) ==> 24 hours

Thursday 8:30 A.M + 11 hours = Thursday 7.30 P.M.

So, the project is due at 7.30 pm Thursday.

After having gone through the stuff given above, we hope that the students would have understood, how to solve PSAT math problems.

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