Number System

Sponsor Area

Question
SSCCGLENQA12042359

a and b are irrational numbers such that a + b = q is a rational number, then a - b is

  • always rational

  • sometimes rational

  • always irrational

  • sometimes irrational

Solution

C.

always irrational

Sponsor Area

Question
SSCCGLENQA12042135

A number when divided by 2736, leaves the remainder 75. If the same number is divided by 24, then the remainder is

  • 12

  • 3

  • 0

  • 23

Solution

B.

3

Shorcut Method:
Divide the remainder 75 by 24 , then we find 3 as remainder.

Question
SSCCGLENQA12043138

A number when divided by 361 gives a remainder 47. If the same number is divided by 19, the remainder obtained is

  • 3

  • 8

  • 9

  • 1

Solution

C.

9

Shortcut Method:
Divide the remainder 47 by 19 i.e. Required remainder = 9

Question
SSCCGLENQA12042163

A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is

  • 0

  • 2

  • 1

  • 3

Solution

D.

3

As we know that,
        If a number or square of a number is divided by the same number, a remainder is same in both the conditions.
Hence, square of a number is divided by 6, we get 3 as remainder.

Question
SSCCGLENQA12042439

A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is

  • 220030

  • 22030

  • 1220

  • 1250

Solution

A.

220030

Divisor = 555 + 445 = 1000
Remainder  = 30 (given)
Quotient  = (555 - 445) x 2
 = 110 x 2 = 220
Dividend  = (Divisor x Quotient) + Remainder
               = 1000 x 220 + 30 = 220030