# Problems on Numbers Quiz Set 019

### Question 1

x should be replaced by which minimum number so that 936219x862 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., 9 + 3 + 6 + 2 + 1 + 9 + x + 8 + 6 + 2, should be divisible by 3. So we can see that \$x + 46\$ should be divisible by 3. By inspection, x = 2.

### Question 2

8 times the middle of three consecutive even numbers is 22 more than 5 times the smallest of the three numbers. What is the middle number?

A

4.

B

5.

C

3.

D

6.

Soln.
Ans: a

This is the general solution. Let the numbers be 2n - 2, 2n and 2n + 2. We are given 8 × 2n = 22 + 5 × (2n - 2).
⇒ 8 × 2n = 22 + 5 × 2n - 5 × 2.
⇒ 2n × (8 - 5) = 22 - 5 × 2, so 2n = \${22 - 5 × 2}/{8 - 5} = 4\$

### Question 3

x should be replaced by which minimum number so that 275198x123 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., 2 + 7 + 5 + 1 + 9 + 8 + x + 1 + 2 + 3, should be divisible by 3. So we can see that \$x + 38\$ should be divisible by 3. By inspection, x = 1.

### Question 4

x should be replaced by which minimum number so that 99938x3687 is completely divisible by 9?

A

1.

B

2.

C

4.

D

3.

Soln.
Ans: a

If the above number has to be divisible by 9, the sum of the digits, i.e., 9 + 9 + 9 + 3 + 8 + x + 3 + 6 + 8 + 7, should be divisible by 9. So we can see that \$x + 62\$ should be divisible by 9. By inspection, x = 1.

### Question 5

What is 0.99999999...?

A

\$1/1\$.

B

\$2/1\$.

C

\$1/2\$.

D

\$1/3\$.

Soln.
Ans: a

0.99999999... is same as \$0.\ov 99\$. Let y = \$0.\ov 99\$. Multiply by 100, 100y = 99 + \$0.\ov 99\$ which is same as 99 + y. So 99y = 99, ⇒ y = \$99/99\$. So answer = 1.