# Problems on Numbers Quiz Set 009

### Question 1

The sum of three consecutive even integer numbers is -2274. The middle among the three is?

A

-758.

B

-757.

C

-755.

D

-756.

Soln.
Ans: a

Let the numbers be 2n - 2, 2n and 2n + 2. The sum is 6n = 3 x 2n = 3 x middle. We are given 3 x middle = -2274, ⇒ middle = \$-2274/3\$, i.e., middle = -758.

### Question 2

12 times the middle of three consecutive even numbers is 152 more than 8 times the smallest of the three numbers. What is the middle number?

A

34.

B

35.

C

33.

D

36.

Soln.
Ans: a

This is the general solution. Let the numbers be 2n - 2, 2n and 2n + 2. We are given 12 × 2n = 152 + 8 × (2n - 2).
⇒ 12 × 2n = 152 + 8 × 2n - 8 × 2.
⇒ 2n × (12 - 8) = 152 - 8 × 2, so 2n = \${152 - 8 × 2}/{12 - 8} = 34\$

### Question 3

How many odd numbers are there between -1714 and 2242?

A

1978.

B

1979.

C

1977.

D

1980.

Soln.
Ans: a

Odd numbers are in an AP. First term \$a = -1713\$, common difference \$d = 2\$, the last term \$t_n\$ is given as 2241. By the AP formula, \$2241 = -1713 + (n - 1) × 2\$ ⇒ \$n = 1 + {{2241 - (-1713)}/2} = 1978\$.

### Question 4

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.

### Question 5

If \$6/17\$ of a number is 24, what is the number?

A

68.

B

69.

C

67.

D

70.

Soln.
Ans: a

Let the number be N. Then \${6/17}\$ x N = 24. ⇒ N = 24 x \${17/6}\$ = 68