# Problems on Numbers Quiz Set 012

### Question 1

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 2

If \$5{3/4}\$ of a number is 3, what is \${3/14}\$ of that number?

A

\${18/161}\$.

B

\$1{19/160}\$.

C

\$2{14/163}\$.

D

\$3{12/163}\$.

Soln.
Ans: a

Let the number be N. Then it is given that \$5{3/4}\$ x N = 3. ⇒ N = 3 X \${4/23}\$. ⇒ \${3/14}\$ x N = \${3/14}\$ x 3 X \${4/23}\$ = \${18/161}\$.

\${23/4}\$ is same as \$5{3/4}\$.

### Question 3

How many odd numbers are there between -1386 and 814?

A

1100.

B

1101.

C

1099.

D

1102.

Soln.
Ans: a

Odd numbers are in an AP. First term \$a = -1385\$, common difference \$d = 2\$, the last term \$t_n\$ is given as 813. By the AP formula, \$813 = -1385 + (n - 1) × 2\$ ⇒ \$n = 1 + {{813 - (-1385)}/2} = 1100\$.

### Question 4

What is the digit at units place: 7575 × 1390 × 9505?

A

0.

B

1.

C

3.

D

2.

Soln.
Ans: a

The digit at units place = (last digit of 7575) × (last digit of 1390) × (last digit of 9505) = 5 × 0 × 5 = 0, which = 0.

### Question 5

The difference between a two digit number and the one obtained by reversing its digits is 72. If one of the digits is 0, what is the other?

A

8.

B

9.

C

10.

D

11.

Soln.
Ans: a

Let the numbers be a and b. ab = 10a + b, and ba = 10b + a. The difference is 10a + b - (10b + a) = 9(a - b). It is given that 9(a - b) = 72, ⇒ a - b = \$72/9\$ = 8, ⇒ the difference between the digits is 8. If one of the digits is 0, the other can be 8.