**Question 1 :**

√100 √64 =

(A) 8 (B) 10 (C) 18 (D) 80 (E) 164

**Solution :**

√100 √64 = √(10 ⋅ 10) √(8 ⋅ 8)

= 10 (8)

= 80

Hence the answer is 80.

**Question 2 :**

7.2 aliens = 1 monster

1 monster = 15.5 oranges

Using the conversion above, how many oranges are equal to 1 alien ?

(A) 0.46 (B) 1.95 (C) 2.15 (D) 22.7 (E) 111.6

**Solution :**

1 monster = 7.2 aliens ----(1)

1 monster = 15.5 oranges ----(2)

(1) = (2)

7.2 aliens = 15.5 oranges

1 alien = 15.5/7.2

= 2.15

Hence the answer is 2.15

**Question 3 :**

What is the greatest common factor of 147 and 198 ?

(A) 2 (B) 3 (C) 7 (D) 14 (E) 49

**Solution :**

There is no common divisor for 49 and 66. Hence the greatest common factor is 3.

**Question 4 :**

If x = 7 and y = 0, what is the value of 11x / (x - y) ?

(A) 0 (B) 7 (C) 10 (D) 11 (E) 77

**Solution :**

11x / (x - y) = 11(7) / (7 - 0) ==> 77/7 ==> 11

Hence the answer is 11.

**Question 5 :**

Heiga has 4 dogs, 3 cats and 2 birds. If she closes her eyes and picks one animal. What is the probability that it does not have 4 legs ?

(A) 3u/7 (B) 2/7 (C) 7/9 (D) 2/9 (E) 4/7

**Solution :**

Sample space = Total number of animals

= 3 + 4 + 2

n(S) = 9

Dogs and cats have 4 legs, and birds has 2 legs.

Number of animals do not have 4 legs = 2

n(A) = 2

P(A) = n(A) / n(S)

P(A) = 2/9

Hence the required probability is 2/9.

**Question 6 :**

If y = x^{2}⋅x^{x}, what is y when x = 2 ?

(A) 16 (B) 8 (C) 4 (D) 32 (E) 0

**Solution :**

y = x^{2}⋅x^{x}

y = x^{(2 + x)}

y = 2^{(2 + 2)}

y = 2^{4}

y = 16

Hence the answer is 16.

**Question 7 :**

Train A, travelling at 200 mph, leaves station A at 1 P.M train B travelling at 300 mph, leaves station B at 3 P.M. Both stations are directly across each other and X miles away. If the trains meet at 4 P.M, What is X ?

(A) 500 ml (B) 900 ml (C) 700 ml

(D) 600 ml (E) 400 ml

**Solution :**

From the given information, we know that both trains meet at 4 P.M.

Train A has traveled for 3 hours at the speed of 200 mph

Train B has traveled for 1 hour at the speed of 300 mph

Distance covered by both trains together

= 600 miles + 300 miles

= 900 miles

Hence both trains will meet each other apart 900 miles.

**Question 8 :**

Bernard is now y years old. Luis is 8 years older than Bernard. In terms of y, how old was Luis 5 years ago?

(A) 8y (B) 8y - 5 (C) y + 3 (D) y + 13 (E) y - 5

**Solution :**

Age of Bernard = y

Age of Luis = y + 8

5 years ago Luis age = y + 8 - 5

= y + 3

**Question 9 :**

In a figure above, ABC, DBE, EFG and CFH are straight line segments. What is the value of x ?

(A) 25 (B) 45 (C) 65 (D) 70 (E) 75

**Solution : **

In a quadrilateral BEFC,

<GFH = <EFC = 65 (Vertically opposite angles)

<CBE + <BEF + <EFC + <FCB = 360

<CBE + 110 + <EFC + 110 = 360

<CBE + 220 + 65 = 360

<CBE = 360 - 285

<CBE = 75

x = <CBE = 75 (Vertically opposite angles)

**Question 10 :**

Which of the following shows the fraction 13/3, 37/8 and 19/4 in order from greatest to least ?

(A) 37/8, 19/4, 13/3

(B) 37/8, 13/3, 19/4

(C) 19/4, 13/3, 37/8

(D) 19/4, 37/8, 13/3

(E) 13/3, 19/4, 37/8

**Solution :**

In order to arrange the fractions from greatest to least, first let us change the denominator same. For that, we have to find L.C.M of 3, 8 and 4.

L.C.M = 24

(13/3) ⋅ (8/8) = 104/24 -----(1)

(37/8) ⋅ (3/3) = 111/24 -----(2)

(19/4) ⋅ (6/6) = 114/24 -----(3)

19/4 > 37/8 > 13/3

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