# Problems on Numbers Quiz Set 016

### Question 1

How many odd numbers are there between -1690 and 2188?

A

1939.

B

1940.

C

1938.

D

1941.

Soln.
Ans: a

Odd numbers are in an AP. First term \$a = -1689\$, common difference \$d = 2\$, the last term \$t_n\$ is given as 2187. By the AP formula, \$2187 = -1689 + (n - 1) × 2\$ ⇒ \$n = 1 + {{2187 - (-1689)}/2} = 1939\$.

### Question 2

x should be replaced by which minimum number so that 9961x95681 is completely divisible by 9?

A

0.

B

1.

C

3.

D

2.

Soln.
Ans: a

If the above number has to be divisible by 9, the sum of the digits, i.e., 9 + 9 + 6 + 1 + x + 9 + 5 + 6 + 8 + 1, should be divisible by 9. So we can see that \$x + 54\$ should be divisible by 9. By inspection, x = 0.

### Question 3

The sum of two numbers is 11. Their product is 28. One of the two numbers is?

A

7.

B

8.

C

6.

D

9.

Soln.
Ans: a

Let the numbers be \$a\$ and \$11 - a\$. We are given their product as a × (11 - a) = 28, which is a quadratic expression that can be simplified to \$(a - 7) × (4 - a) = 0\$. So the numbers could be 7 and 4.

### Question 4

If  \$x/3 = y/17 = z/22\$, then \${x + y + z}/x\$ = ?

A

14.

B

15.

C

13.

D

\$5{2/3}\$.

Soln.
Ans: a

Let \$x/3 = y/17 = z/22\$ = k. Then \${x + y + z}/x\$ is same as \${3k + 17k + 22k}/{3k}\$ which equals 14.

14 is same as 14.

### Question 5

What is the digit at units place: 7020 × 8374 × 4473?

A

0.

B

1.

C

3.

D

2.

Soln.
Ans: a

The digit at units place = (last digit of 7020) × (last digit of 8374) × (last digit of 4473) = 0 × 4 × 3 = 0, which = 0. 