Problems on Numbers Quiz Set 020

Question 1

The sum of two numbers is 10. Their product is 9. One of the two numbers is?

A

9.

B

10.

C

8.

D

11.

Soln.
Ans: a

Let the numbers be \$a\$ and \$10 - a\$. We are given their product as a × (10 - a) = 9, which is a quadratic expression that can be simplified to \$(a - 9) × (1 - a) = 0\$. So the numbers could be 9 and 1.

Question 2

What is x in \$2{19/x}\$ × \$1{10/17}\$ = \$3{2/5}\$?

A

135.

B

136.

C

134.

D

137.

Soln.
Ans: a

We can see that \$2{19/x}\$ = \${17/5}\$ × \${17/27}\$. ⇒ \${2x + 19}/x\$ = \${289/135}\$ ⇒ x = 135.

Question 3

The difference between a two digit number and the one obtained by reversing its digits is 81. If one of the digits is 4, what is the other?

A

Cannot exist.

B

6.

C

7.

D

8.

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) = 81, ⇒ a - b = \$81/9\$ = 9, ⇒ the difference between the digits is 9. If one of the digits is 4, the other cannot be determined.

Question 4

How many odd numbers are there between -1570 and 2426?

A

1998.

B

1999.

C

1997.

D

2000.

Soln.
Ans: a

Odd numbers are in an AP. First term \$a = -1569\$, common difference \$d = 2\$, the last term \$t_n\$ is given as 2425. By the AP formula, \$2425 = -1569 + (n - 1) × 2\$ ⇒ \$n = 1 + {{2425 - (-1569)}/2} = 1998\$.

Question 5

The sum of three consecutive integer numbers is -96. The smallest of the three is?

A

-33.

B

-32.

C

-30.

D

-31.

Soln.
Ans: a

Let the numbers be n - 1, n and n + 1. The sum is 3n. We are given 3n = -96, ⇒ n = \$-96/3\$, i.e., n = -32. So the smallest is -33.