**Question 1 :**

Evaluate [(1/2)-(3/4)] ÷ (1/2) =

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

**Solution :**

= [(1/2)-(3/4)] ÷ (1/2)

= [(2 - 3)/4] ÷ (1/2)

= (-1/4) ÷ (1/2)

= (-1/4) ⋅ (2/1)

= -1/2

Hence the answer is -1/2.

**Question 2 :**

Line q intersects the parallel lines p and l. What is y^{3}/3 ?

(A) x^{4}/3 (B) x^{6} (C) x^{9} (D) x^{4}/9 (E) x^{6}/3

**Solution :**

The lines p and l are parallel lines and q is a transversal. So, corresponding angle are equal.

y = x^{2}

y^{3}/3 = (x^{2})^{3}/3

= x^{6}/3

Hence the value y^{3}/3 is x^{6}/3.

**Question 3 :**

Given the arithmetic sequence x, y, 30, z, f then find x + y + z + f.

(A) 60 (B) 80 (C) 120 (D) 130 (E) 140

**Solution :**

In a arithmetic sequence, the common difference is d. Each consecutive terms differs by d. The values of x,y, z and f in terms of the difference d, is

x = 30 - 2d

y = 30 - d

z = 30 + d

f = 30 + 2d

x + y + z + f = 30 - 2f + 30 - d + 30 + d + 30 + 2d

= 120

Hence the answer is 120.

**Question 4 :**

If (-1)^{2} = 1, then the value (-1) ^{2023} is

(A) -2023 (B) -1 (C) 0 (D) 1 (E) 2023

**Solution :**

(-1) ^{2023 }= (-1)^{2022 }⋅ (-1)

= ((-1)^{2})^{1011 }⋅ (-1)

= 1^{1011 }⋅ (-1)

= 1^{1011 }⋅ (-1) = -1

Hence the answer is -1.

**Question 5 :**

Caroline has two times as many marbles as Jake. Jake has 12 less than 7 times as many marbles James has. James has 14 marbles. How many marbles dies Caroline have ?

(A) 52 (B) 54 (C) 86 (D) 98 (E) 172

**Solution :**

Number of marbles with James = 14

Number of marbles with Jake = 7(14) - 12

= 98 - 12

= 86

Number of marbles with Caroline = 2 (86)

= 172

Hence Caroline has 172 marbles.

**Question 6 :**

John is trying to escape a ditch. Every time he jumps 10 meters, he falls back 5 meters right after. The ditch is 19 meters long. What is the minimum number of jumps he needs to make to escape ?

(A) (B) 4 (C) 5 (D) 7 (E) 8

**Solution :**

At the first jump, he reaches 10 meters, but he falls back 5 meters. Now, John crossed 5 m.

At the second jump, he reaches from 5 m to 15 m, but he falls back 5 m. So, he will be at 10 m.

At the third jump, he reaches from 10 m to 20 m, but he falls back 5 m. So, he will be at 15 m

At the fourth jump, he reaches from 15 m to 25 m, but he falls back 5 m. So, he will be at 20 m

So, 4 jumps are required to escape a ditch of length 19 m.

**Question 7 :**

What is the largest number of digits the product of 3 digit and 2 digit number has ?

(A) 4 digit (B) 5 digit (C) 6 digit

(D) 7 digit (E) 8 digit

**Solution :**

The product of 3 digit and 2 digit number will be 4 digit or 5 digit number.

Since we need the largest number of digits, the answer is 5 digits.

**Question 8 :**

If Fn = 2 F_{n-1} + 3 F_{n-2}, then what is F_{3} if F_{1 } = F_{2} = 1 ?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 10

**Solution :**

n = 3

F_{3} = 2 F_{3-1} + 3 F_{3-2}

F_{3} = 2 F_{2} + 3 F_{1}

F_{3} = 2 (1) + 3 (1)

F_{3} = 2 + 3 = 5

**Question 9 :**

Sam walks 3 m to the west, then 4m south, then 4 m North. How far is he from his original location?

(A) 3 m (B) 5 m (C) 7 m (D) 8 m (E) 12 m

**Solution :**

So he will be at 3 m distance from the starting point.

**Question 10 :**

If a = 3 and b = 5, what is the value of 9a/(b-a) ?

(A) 9 (B) 27 (C) 13/5 (D) 27/2 (E) 26/5

**Solution :**

9a / (b - a) = 9(3)/(5-3)

= 27/2

Hence the answer is 27/2.

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