Number System Practice Questions for SSC CGL, CPO, CHSL, GD, Bank and other Competitive Exams. Important question answer with solution from the previous year exam question papers.

### Number System : Question Answer

**Q.1:** What is the greatest five-digit number that is completely divisible by 8, 15, 16, 21 and 5 ?

(A) 95760

(B) 98320

(C) 99120

(D) 92680

###### Show Answer

LCM of 8, 15, 16, 21, 5 = 1680

greatest five-digit number = 99999

99999/1680 = 879 Remainder

= 99999 – 879 = 99120

**Q.2:** When (2^{24} – 1) is divided by 7 , the remainder is:

(A) 4

(B) 2

(C) 1

(D) 0

###### Show Answer

Remanent

**Q.3:** If the five-digit number 672 xy is divisible by 3, 7 and 11, then what is the value of (6x + 5y) ?

(A) 16

(B) 23

(C) 17

(D) 24

###### Show Answer

672 xy

put x = 2, y = 1

It is divisible by 3, 7, 11

(6x + 5y)

6 x 2+5 x 1 = 12+5 = 17

**Q.4:** If a nine-digit number 489 x 6378 y is divisible by 72, then the value of will be:

(A) 10

(B) 6

(C) 8

(D) 4

###### Show Answer

489 x 6378 y, is divisible by 72

72 = is also divisible 9 x 8

x = 5, y = 4 satisfy

so

**Q.5:** If the nine-digit number 87605x31y is divisible by 72, then the value of 2x-3y is:

(A) -1

(B) 0

(C) 1

(D) 2

###### Show Answer

87605 x 31 y

is divisible by 72

Will also be divisible by 9 x 8 = 72

x = 4, y = 2 satisfy

2x – 3y

2 x 4 – 3 x 2 = 8 – 6 = 2

**Q.6:** When a positive integer ‘n’ is divided by 12, the remainder is 5. What will be the remainder if 8n^{2} + 7 is divided by 12 ?

(A) 5

(B) 3

(C) 2

(D) 4

###### Show Answer

remainder

remainder = n = 5

8n

^{2}+ 7

8 x 5

^{2}+ 7 = 207

remainder

**Q.7:** If 71^{83} +73^{83} is divided by 36, the remainder is:

(A) 13

(B) 9

(C) 0

(D) 8

###### Show Answer

71

^{83}+73

^{83}factor

(71 + 73) = 144

(a

^{n}+b

^{n}) = (a+b)

if n=odd No.

remainder

**Q.8:** If 31^{47} +43^{47} is divided by 37, the remainder is:

(A) 0

(B) 2

(C) 1

(D) 3

###### Show Answer

31

^{47}+43

^{47}

(a

^{n}+b

^{n}) = (a+b)

if n=odd No.

31+43 = 74

remainder

**Q.9:** If the number 4A306768B2 is divisible by both 8 and 11, then the smallest possible values of A and B will be:

(A) A = 3, B = 5

(B) A = 5, B = 4

(C) A = 5, B = 2

(D) A = 5, B = 3

###### Show Answer

4 A 3 0 6 7 6 8 B 2

B = 3 is divisible by 8 [divisible by ]

The whole number is divisible by 11

A = 5

so A = 5, B = 3

**Q.10:** If the 11 digit number 4y6884805x6 is divisible by 72, and , then the value of is:

(A)

(B)

(C)

(D)

###### Show Answer

4 y 6 8 8 4 8 0 5 x 6

72 = 9×8, is divisible by 9 and 8

if x = 3 is divisible

The whole number 4 y 6 8 8 4 8 0 5 3 6 is divisible by 9.

y = 2 Keeping

The Sum of the digits will be divisible by 9

**Q.11:** When a number is divided by 3, the remainder is 2. Again, when the quotient is divided by 7, the remainder is 5. What will be the remainder when the original number is divided by 21?

(A) 14

(B) 16

(C) 13

(D) 17

###### Show Answer

divisor 3 7

remainder 2 5

Number (7 + 5) x 3 + 2 = 38

According of question remainder

**Q.12:** The largest six-digit number exactly divisible by 243 is:

(A) 999947

(B) 999945

(C) 999949

(D) 999943

###### Show Answer

Largest six digit number = 999999

999999/243 = 54 remainder

= 999999 – 54 = 999945

**Q.13:** If the nine-digit number 259876p05 is completely divisible by 11, then what is the value of (p^{2} + 5) ?

(A) 48

(B) 45

(C) 54

(D) 50

###### Show Answer

2 5 9 8 7 6 p 0 5

is divisible by 11

Sum of digits at even places – Sum of digits at odd places = 0

(23+P) – 19 = 0 or 11

P = 7 satisfy

P

^{2}+5

7

^{2}+5 = 54

**Q.14:** If the nine-digit number ‘8475639AB’ is divisible by 99, then what is the value of A and B ?

(A) A = 4, B = 6

(B) A = 4, B = 8

(C) A = 3, B = 9

(D) A = 5, B = 3

###### Show Answer

8 4 7 5 6 3 9 A B,

is divisible by 99

Will also be divisible by 99 = 11 x 9

so A = 4, B = 8 satisfy

A = 4, B = 8

Thanks for attempt Number System Practice Questions for SSC CGL, CPO, CHSL, GD, Bank and other Competitive Exams.

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