# Problems on Numbers Quiz Set 004

### 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 \$1{19/x}\$ × \$5{12/17}\$ = \$5{11/14}\$?

A

1358.

B

1359.

C

1357.

D

1360.

Soln.
Ans: a

We can see that \$1{19/x}\$ = \${81/14}\$ × \${17/97}\$. ⇒ \${1x + 19}/x\$ = \${1377/1358}\$ ⇒ x = 1358.

### Question 3

x should be replaced by which minimum number so that 936219x862 is completely divisible by 3?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

If the above number has to be divisible by 3, the sum of the digits, i.e., 9 + 3 + 6 + 2 + 1 + 9 + x + 8 + 6 + 2, should be divisible by 3. So we can see that \$x + 46\$ should be divisible by 3. By inspection, x = 2.

### Question 4

How many odd numbers are there between -1270 and 1358?

A

1314.

B

1315.

C

1313.

D

1316.

Soln.
Ans: a

Odd numbers are in an AP. First term \$a = -1269\$, common difference \$d = 2\$, the last term \$t_n\$ is given as 1357. By the AP formula, \$1357 = -1269 + (n - 1) × 2\$ ⇒ \$n = 1 + {{1357 - (-1269)}/2} = 1314\$.

### Question 5

Which term of this arithmetic series is zero: 70, 63, 56 ...?

A

11.

B

12.

C

10.

D

13.

Soln.
Ans: a

The first term is 70, common difference is d = -7, n-th term is 0. So \$0 = 70 + (n - 1) × -7\$ which gives \$n = 1 + {70/7} = 11\$.