# Basic Simplification Quiz Set 008

### Question 1

1/15 of a boy's score in Maths exceeds 1/13 of his score in English by 19 marks. What is his score in English, if his total score in English and Maths is 509?

A

104 marks.

B

106 marks.

C

102 marks.

D

108 marks.

Soln.
Ans: a

Let the score in English be E, then his score in math is 509 - E. We have also been given \$(509 - E)/15 = E/13 + 19\$. Solving for E, we get E = 104.

### Question 2

What is 180 × 99?

A

17820.

B

17829.

C

17811.

D

17838.

Soln.
Ans: a

This is a multiplication by a number that contains 9 only. Proceed like this: 180 × 99 = 180 × (100 - 1) = 180 × 100 - 180 = 18000 - 180 = 17820.

### Question 3

What is xy if x - y = 2 and x2 + y2 = 312?

A

154.

B

156.

C

152.

D

158.

Soln.
Ans: a

We know that 2xy = (x2 + y2) - (x - y)2. Substituting, xy = \${312 - 2^2}/2\$ = \$308/2\$ = 154.

### Question 4

Cost of 1 kg of a metal is Rs. \$43{1/2}\$. What is the cost of \${86/87}\$ kg?

A

Rs. 43.

B

Rs. 44.

C

Rs. 42.

D

Rs. 45.

Soln.
Ans: a

We have to find \$43{1/2}\$ × \${86/87}\$, which can be written as \${87/2}\$ × \${86/87}\$, which simplifies to 86/2 = Rs. 43.

### Question 5

The value of x for which the value of |4x - 24| is minimum is?

A

6.

B

8.

C

4.

D

10.

Soln.
Ans: a

The minimum value of |4x - 24| is 0. So 4x - 24 = 0, when x = 6.