**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 = 5^{2 }⋅ 7^{3}

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, 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 9 :**

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 10 :**

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.

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