Problems on Numbers Quiz Set 002

Question 1

If \$3/17\$ of a number is 9, what is the number?

A

51.

B

52.

C

50.

D

53.

Soln.
Ans: a

Let the number be N. Then \${3/17}\$ x N = 9. ⇒ N = 9 x \${17/3}\$ = 51

Question 2

The sum of two numbers is 18. Their difference is 8. They are in the ratio?

A

\$2{3/5}\$.

B

\$4{1/2}\$.

C

\$1{1/7}\$.

D

4.

Soln.
Ans: a

Let the numbers be a and b, and let their ratio be k such that \$a/b = k\$. We are given \$a + b = 18\$ ⇒ \$b(k + 1) = 18\$. Similarly, from the difference we can obtain \$b(k - 1) = 8\$. Dividing we get \${k + 1}/{k - 1} = 18/8\$. By componendo and dividendo, \$k = {18 + 8}/{18 - 8}\$ = \${13/5}\$, which is same as: \$2{3/5}\$.

Question 3

The sum of three consecutive odd integer numbers is -2445. The middle among the three is?

A

-815.

B

-814.

C

-812.

D

-813.

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 = -2445, ⇒ middle = \$-2445/3\$, i.e., middle = -815.

Question 4

x should be replaced by which minimum number so that 77x7533423 is completely divisible by 3?

A

1.

B

2.

C

4.

D

3.

Soln.
Ans: a

If the above number has to be divisible by 3, the sum of the digits, i.e., 7 + 7 + x + 7 + 5 + 3 + 3 + 4 + 2 + 3, should be divisible by 3. So we can see that \$x + 41\$ should be divisible by 3. By inspection, x = 1.

Question 5

How many odd numbers are there between -1386 and 814?

A

1100.

B

1101.

C

1099.

D

1102.

Soln.
Ans: a

Odd numbers are in an AP. First term \$a = -1385\$, common difference \$d = 2\$, the last term \$t_n\$ is given as 813. By the AP formula, \$813 = -1385 + (n - 1) × 2\$ ⇒ \$n = 1 + {{813 - (-1385)}/2} = 1100\$.