model 2 divisibility, multiples, add and subtract based number system Practice Questions Answers Test with Solutions & More Shortcuts

Question : 31 [SSC CGL 2000]

$1/0.04$ is equal to :

a) $2/5$

b) $1/40$

c) 25

d) $5/2$

Answer: (c)

$1/0.04$ = $100/4$ = 25

Question : 32 [SSC CGL Prelim 2004]

A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when the number is divided by 6?

a) 4

b) 3

c) 2

d) 5

Answer: (a)

The least number (dividend) x is obtained as follows :

3X  
2Y-1
 1-1

y = 2 × 1 + 1 = 3

x = 3 × 3 + 1 = 10

When we divide 10 by 6, the remainder = 4

Question : 33 [SSC CGL Prelim 2002]

A student was asked to multiply a number by $3/2$ but he divided that number by $3/2$. His result was 10 less than the correct answer. The number was :

a) 12

b) 10

c) 20

d) 15

Answer: (a)

Let the given number be x. Then,

(X x $3/2$)-(X ÷ $3/2$) = 10

⇒ $3/2$x - $2/3$ x = 10

⇒ = ${9x – 4x}/6$ = 10

⇒ 5x = 60 ⇒ x = 12

Question : 34

The expression $2^{6n} – 4^{2n}$, where n is a natural number is always divisible by

a) 18

b) 15

c) 48

d) 36

Answer: (c)

$2^{6n} – 4^{2n}$ = $(2^6)^n - (4^2)^n $

= $64^n – 16^n$

which is divisible by 64 –16= 48

Question : 35 [SSC CGL Prelim 2005]

A number divided by 68 gives the quotient 269 and remainder zero. If the same number is divided by 67, the remainder is :

a) 1

b) 0

c) 3

d) 2

Answer: (a)

Number = 269 × 68

= 269 × (67 + 1)

= 269 × 67 + 269

Clearly, remainder is obtained on dividing 269 by 67 that is 1.

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