# Problems on Numbers Quiz Set 010

### Question 1

What is 0.67676767...?

A

\$67/99\$.

B

\$68/99\$.

C

\$67/100\$.

D

\$67/101\$.

Soln.
Ans: a

0.67676767... is same as \$0.\ov 67\$. Let y = \$0.\ov 67\$. Multiply by 100, 100y = 67 + \$0.\ov 67\$ which is same as 67 + y. So 99y = 67, ⇒ y = \$67/99\$. So answer = \${67/99}\$.

### Question 2

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.

### Question 3

Which term of this arithmetic series is zero: 81, 72, 63 ...?

A

10.

B

11.

C

9.

D

12.

Soln.
Ans: a

The first term is 81, common difference is d = -9, n-th term is 0. So \$0 = 81 + (n - 1) × -9\$ which gives \$n = 1 + {81/9} = 10\$.

### Question 4

When a two digit number is reversed and added to itself we get 55. The product of the digits of that number is 6. What is the number?

A

32.

B

33.

C

31.

D

34.

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 55 = 11 × (a + b) ⇒ \$a + b = 55 / 11 = 5\$, so the digits are \$a\$ and \$5 - a\$. We are given their product as a × (5 - a) = 6, which is a quadratic expression that can be simplified to \$(a - 3) × (2 - a) = 0\$. So the number could be 32 or 23.

### Question 5

The sum of three consecutive even integer numbers is 672. The middle among the three is?

A

224.

B

225.

C

223.

D

226.

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 = 672, ⇒ middle = \$672/3\$, i.e., middle = 224. 