**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.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**