# Problems on Numbers Quiz Set 011

### Question 1

The sum of two numbers is 53. Their difference is 19. They are in the ratio?

A

\$2{2/17}\$.

B

\$3{5/16}\$.

C

1.

D

\$4{11/19}\$.

Soln.
Ans: a

Let the numbers be a and b, and let their ratio be k such that \$a/b = k\$. We are given \$a + b = 53\$ ⇒ \$b(k + 1) = 53\$. Similarly, from the difference we can obtain \$b(k - 1) = 19\$. Dividing we get \${k + 1}/{k - 1} = 53/19\$. By componendo and dividendo, \$k = {53 + 19}/{53 - 19}\$ = \${36/17}\$, which is same as: \$2{2/17}\$.

### Question 2

The sum of two numbers is 30. Their product is 161. One of the two numbers is?

A

23.

B

24.

C

22.

D

25.

Soln.
Ans: a

Let the numbers be \$a\$ and \$30 - a\$. We are given their product as a × (30 - a) = 161, which is a quadratic expression that can be simplified to \$(a - 23) × (7 - a) = 0\$. So the numbers could be 23 and 7.

### Question 3

x should be replaced by which minimum number so that 39242x6416 is completely divisible by 3?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

If the above number has to be divisible by 3, the sum of the digits, i.e., 3 + 9 + 2 + 4 + 2 + x + 6 + 4 + 1 + 6, should be divisible by 3. So we can see that \$x + 37\$ should be divisible by 3. By inspection, x = 2.

### Question 4

The sum of three consecutive odd integer numbers is 657. The middle among the three is?

A

219.

B

220.

C

218.

D

221.

Soln.
Ans: a

Let the numbers be 2n - 3, 2n - 1 and 2n + 1. The sum is 3(2n - 1) = 3 x middle. We are given 3 x middle = 657, ⇒ middle = \$657/3\$, i.e., middle = 219.

### Question 5

Which term of this arithmetic series is zero: 70, 63, 56 ...?

A

11.

B

12.

C

10.

D

13.

Soln.
Ans: a

The first term is 70, common difference is d = -7, n-th term is 0. So \$0 = 70 + (n - 1) × -7\$ which gives \$n = 1 + {70/7} = 11\$. 