# Problems on Numbers Quiz Set 003

### Question 1

x should be replaced by which minimum number so that 4618521x98 is completely divisible by 3?

A

1.

B

2.

C

4.

D

3.

Soln.
Ans: a

If the above number has to be divisible by 3, the sum of the digits, i.e., 4 + 6 + 1 + 8 + 5 + 2 + 1 + x + 9 + 8, should be divisible by 3. So we can see that \$x + 44\$ should be divisible by 3. By inspection, x = 1.

### Question 2

12 times the middle of three consecutive even numbers is 152 more than 8 times the smallest of the three numbers. What is the middle number?

A

34.

B

35.

C

33.

D

36.

Soln.
Ans: a

This is the general solution. Let the numbers be 2n - 2, 2n and 2n + 2. We are given 12 × 2n = 152 + 8 × (2n - 2).
⇒ 12 × 2n = 152 + 8 × 2n - 8 × 2.
⇒ 2n × (12 - 8) = 152 - 8 × 2, so 2n = \${152 - 8 × 2}/{12 - 8} = 34\$

### Question 3

Which term of this arithmetic series is zero: 110, 100, 90 ...?

A

12.

B

13.

C

11.

D

14.

Soln.
Ans: a

The first term is 110, common difference is d = -10, n-th term is 0. So \$0 = 110 + (n - 1) × -10\$ which gives \$n = 1 + {110/10} = 12\$.

### Question 4

The sum of three consecutive odd integer numbers is 909. The middle among the three is?

A

303.

B

304.

C

302.

D

305.

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 = 909, ⇒ middle = \$909/3\$, i.e., middle = 303.

### Question 5

What is 0.94949494...?

A

\$94/99\$.

B

\$95/99\$.

C

\$94/100\$.

D

\$94/101\$.

Soln.
Ans: a

0.94949494... is same as \$0.\ov 94\$. Let y = \$0.\ov 94\$. Multiply by 100, 100y = 94 + \$0.\ov 94\$ which is same as 94 + y. So 99y = 94, ⇒ y = \$94/99\$. So answer = \${94/99}\$. 