Directions : What value should come in the place of question mark (?) in the following questions?

1. 112 × 4√4096 – 268 = ? × 9 + 241
1) 51
2) 45
3) 55
4) 42
5) 60

2. 81^2 – 49^2 = ? × 26
1) 150
2) 145
3) 158
4) 160
5) 165

3. [(1382 + 3007) / (513 + 114)] of 4/7 + 161 = ?
1) 165
2) 160
3) 155
4) 169
5) 164

Directions: In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. Give answer

1) if x > y
2) if x >= y
3) if x < y
4) if x <= y
5) if x = y or relationship between x and y cannot be determined.

4.
I. 18x^2 – 9x + 1 = 0
II. 48y^2 – 58y + 15 = 0

5.
I. x^2 – 5x – 36 = 0
II. y^2 – 17y + 72 = 0

6.
I. 169x^2 = 49
II. 13y = sqroot(81) – sqroot(4)

7.
I. x^2 – 21x + 104 = 0
II. y^2 – 29y + 210 = 0

Directions: Each question below is followed by two statements A and B. You have to determine whether the data given in the statement is sufficient to answer the question. You should use the data and your knowledge of mathematics to choose between the possible answers. Give answer:

1) if the statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.
2) if the statement B alone is sufficient to answer the question, but the statement A alone is not sufficient.
3) if the both statement A and B together are needed to answer the question.
4) if either the statement A alone or B alone is sufficient to answer the question.
5) if you cannot get the answer from the statements A and B together, but needed even more data.

8. What is the number?
A. The sum of the two digits is 10. The ratio of the two digits is 4:1.
B. The product of two digits of a number is 16. The quotient of two digits is 4.

9. Rs. 4800 is divided amongst P, Q and R. Find the share of P.
A. P gets one–third of what Q and R together get.
B. Q get half as much as P and R together get.

10. What is the total number of votes polled?
A. The looser get 18% of the votes polled.
B. The winner get 82% of the votes and is elected by a majority of 1488 votes.

1. 1
121 * 8 - 268 = ? * 9 + 241
? = (700 - 241)/9 = 51

2. 4
? = [(81 + 49)(81 - 49)]/26 = 160

3. 1
? = (4389 / 627) * 4/7 + 161 = 165

4. 3;
I. (6x – 1) (3x – 1) = 0
x = 1/6, 1/3
II. (8y – 3) (6y – 5) = 0
y = 3/8,5/6
x < y

5. 5
I. (x + 4) (x – 9) = 0
x = –4, 9
II. (y – 8) (y – 9) = 0
y = 8, 9
No relationship between ‘x’ and ‘y’

6. 4:
I: x^2 = 49/169
x = +/- 7/13
y = 9-2/13 = 7/13
x <= y

7. 3;
I. (x – 8) (x – 13) = 0
x = 8, 13
II. (y – 14) (y – 15) = 0
y = 14, 15
x < y

8. 4;
Let the number be 10x + y.
From A, x + y = 10 and x/y = 4/1
5y = 10
y = 2, x = 8

From B, xy = 16 and x/y = 4
y = 2 ; x = 8
Either from (A) or (B) ; the number is 82.

9. 1;
P + Q + R = 4
From A, P = 1/3 (Q + R)
3P = Q + R
4P = 4800
P = Rs. 1200

From B, Q = 1/2 (P+R)
2Q = P+R
Thus, we cant find the share of P from the statement B

10. 2
Let the total number of votes polled be x.
From statement B,
82% of x – (100 – 82) % of x = 1488
or, (82% – 18%) of x = 1488
64/100X = 1488
X = 1488 * 100/64 = 2325