# Basic Simplification Quiz Set 011

### Question 1

Mr. X and Mr. Y have certain number of marbles with them. If Mr. X gives 7 marbles to Mr. Y, they will have the same number of marbles. But, if Mr. Y gives 2 marbles to Mr. X, then Mr. X will have twice as many marbles as are left with Mr. Y. How many marbles does Y have?

A

20.

B

22.

C

18.

D

24.

Soln.
Ans: a

Let them have X and Y marbles, respectively. We have X - 7 = Y + 7, which gives X - Y = 14. By the second condition, X + 2 = 2(Y - 2), which can be re-arranged to X - 2Y = -6. Solving for Y, we get Y = 20.

### Question 2

The value of x for which the value of |2x - 6| is minimum is?

A

3.

B

5.

C

9.

D

7.

Soln.
Ans: a

The minimum value of |2x - 6| is 0. So 2x - 6 = 0, when x = 3.

### Question 3

What is xy if x - y = 6 and x2 + y2 = 362?

A

163.

B

165.

C

161.

D

167.

Soln.
Ans: a

We know that 2xy = (x2 + y2) - (x - y)2. Substituting, xy = \${362 - 6^2}/2\$ = \$326/2\$ = 163.

### Question 4

What is 283 + 564 - 1 × 1659 ÷ 553?

A

844.

B

845.

C

843.

D

846.

Soln.
Ans: a

We have by bodmas 283 + 564 - 1 × 1659 ÷ 553 = 283 + 564 - (1 × (1659 ÷ 553)) = (283 + 564) - (1 × (3)) = (283 + 564) - 3 = 847 - 3 = 844.

### Question 5

What is xy if x - y = 8 and x2 + y2 = 284?

A

110.

B

112.

C

108.

D

114.

Soln.
Ans: a

We know that 2xy = (x2 + y2) - (x - y)2. Substituting, xy = \${284 - 8^2}/2\$ = \$220/2\$ = 110. 