# Problems on Numbers Quiz Set 005

### Question 1

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 2

When a two digit number is reversed and added to itself we get 154. The product of the digits of that number is 49. What is the number?

A

77.

B

78.

C

76.

D

79.

Soln.
Ans: a

Let the number be ab. When it is reversed and added to itself we get (10a + b) + (10b + a) = 11 × (a + b). We are given 154 = 11 × (a + b) ⇒ \$a + b = 154 / 11 = 14\$, so the digits are \$a\$ and \$14 - a\$. We are given their product as a × (14 - a) = 49, which is a quadratic expression that can be simplified to \$(a - 7) × (7 - a) = 0\$. So the number could be 77 or 77.

### Question 3

What is the digit at units place: 2840 × 2492 × 6032?

A

0.

B

1.

C

3.

D

2.

Soln.
Ans: a

The digit at units place = (last digit of 2840) × (last digit of 2492) × (last digit of 6032) = 0 × 2 × 2 = 0, which = 0.

### Question 4

The sum of three consecutive odd integer numbers is -2211. The middle among the three is?

A

-737.

B

-736.

C

-734.

D

-735.

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 = -2211, ⇒ middle = \$-2211/3\$, i.e., middle = -737.

### Question 5

The sum of two numbers is 14. Their product is 45. One of the two numbers is?

A

9.

B

10.

C

8.

D

11.

Soln.
Ans: a

Let the numbers be \$a\$ and \$14 - a\$. We are given their product as a × (14 - a) = 45, which is a quadratic expression that can be simplified to \$(a - 9) × (5 - a) = 0\$. So the numbers could be 9 and 5.