**Question 1 :**

It takes George 3 minutes to read 300 words. If each page in a book that he is reading has 750 words, how long will it take George to read 6 pages ?

(A) 30 minutes (B) 45 minutes (C) 60 minutes

(D) 90 minutes (E) 250 minutes

**Solution :**

Total number of of words in one page = 750

Number of words in 6 pages = 6(750) = 4500

300 words can be read in 3 minutes.

Number of words read in 1 minute = 300/3 = 100

Number of minutes taken to read 4500 words

= 4500/100

= 45 minutes

**Question 2 :**

[(1/2) - (3/4)]^{2} + (5/10) =

(A) 9/16 (B) 1/2 (C) 1/16 (D) 3/4 (E) 1/4

**Solution :**

= [(1/2) - (3/4)]^{2} + (5/10)

= [(2-3)/4]^{2} + (5/10)

= (-1/4)^{2} + (1/2)

= 1/16 + 1/2

= (1 + 8)/ 16

= 9/16

Hence the answer is 9/16.

**Question 3 :**

If x = 2^{5} ⋅ 3^{2 }⋅ 7, then what is the value of x ?

(A) 1150 (B) 2000 (C) 2015 (D) 2016 (E) 3050

**Solution :**

x = 2^{5} ⋅ 3^{2 }⋅ 7

x = (32) ⋅ 9^{ }⋅ 7

x = 2016

**Question 4 :**

A right cylindrical can is being filled with water. At 1 P.M, it is half full. At 2 P.M, it is 3/4 ^{th} full. At this rate, when was it empty ?

(A) 11 : 00 A.M (B) 11 : 30 A.M (C) 12 : 00 P.M

(D) 12 : 30 P.M (E) 3 : 00 P.M

**Solution :**

From the given information, we know that for every 1 hour 1/4 th of the tank is being filled.

At 1 P.M, 1/2 of the tank is being filled

At 2 P.M, 3/4 of the tank is being filled

At 3 P.M, full tank is being filled

At 12 P.M, 1/4 of the tank is being filled

At 11 A.M, the tank is empty.

**Question 5 :**

If x^{8} = (2^{2}) ^{4}, what is x^{2} ?

(A) 2 (B) 4 (C) 8 (D) 64 (E) 128

**Solution :**

x^{8} = (2^{2}) ^{4}

x^{8} = 2^{8}

Since the powers are equal, we may equate the base.

x = 2

x^{2} = 2^{2} = 4

**Question 6 :**

James has a work to finish. He finishes 1/8 of the total work on the first day. What fraction of the work is left ?

(A) 1/8 (B) 3/8 (C) 7/8 (D) 3/4 (E) 1/4

**Solution :**

Fraction of work left = 1 - (1/8)

= (8 - 1)/8

= 7/8

**Question 7 :**

There are two different pathways connecting 1 and and 2. How many fewer steps is the solid line path than the dotted line path. (A step is defined as a line segment connecting 2 circles)

(A) -4 (B) -1 (C) 1 (D) 4 (E) 7

**Solution :**

Number of steps required to reach from 1 to 2 in solid line = 4

Number of steps required to reach from 1 to 2 in dotted line = 3

= 3 - 4

= -1

**Question 8 :**

Jackie and Jesse each solve the same problem in a different way

Problem √(a + b) = ?

Jackie's way = √(a + b) = √a + √b

Jesse's way : √(a + b) = √(a+b)

If a = 9 and b = 25, how much bigger is Jakie's way than Jesse's way ?

(A) -2 (B) 0 (C) 2 (D) √36 (E) 8 - √34

**Solution :**

Jackie's way : √(a + b) = √a + √b a = 9 and b = 25 √(a + b) = √9 + √25 = 3 + 5 = 8 |
Jesse's way : √(a + b) = √(a+b) a = 9 and b = 25 √(a + b) = √(a+b) = √(9+25) = √34 |

To find how much bigger is Jakie's way than Jesse's way

= 8 - √34

**Question 9 :**

If θ { a, b, c, d, e, f, g, h, i } = ab - cd + (ef)^{2} (gh)^{2}/i

Which cannot be value of θ ?

(A) θ (0, 0, 0, 0, 0, 0, 0, 0, 1)

(B) θ (1, 1, 1, 1, 1, 1, 1, 1, 0)

(C) θ (2, 2, 2, 2, 2, 2, 2, 2, 10)

(D) θ (2,3, 1, 4, 5, 6, 7, 0, 10)

(E) 0

**Solution :**

The value of θ cannot be ∞, from the given choices, in option B we have 0 for i. By applying this value, we get ∞.

Hence option B is the answer.

**Question 10 :**

If James grows by 20 inches every day starting Monday. What is the difference in his height between Wednesday and Monday ?

(A) 0 inches (B) 20 inches (C) 30 inches

(D) 40 inches (E) 60 inches

**Solution :**

Height of James in Monday = 20 inches

in Tuesday = 40 inches

in Wednesday = 60 inches

= 60 - 20

= 40 inches

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