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

Question : 16 [SSC CISF ASI 2010]

Two numbers, when divided by 17, leave remainders 13 and 11 respectively. If the sum of those two numbers is divided by 17, the remainder will be

a) 11

b) 13

c) 4

d) 7

Answer: (d)

First number (X) = 17x + 13

Second number (Y) = 17y + 11

∴${X + Y}/17$ = ${17(x + y)}/17 + {13 + 11}/17$

∴Required remainder = Remainder obtained on dividing

11 + 13

i.e. 24 by 17 = 7

Question : 17 [SSC Multi-Tasking Staff 2011]

When a number is divided by 24, the remainder is 16. The remainder when the same number is divided by 12 is

a) 4

b) 3

c) 8

d) 6

Answer: (a)

Required remainder = 16 – 12 = 4

(because 24 is a multiple of 12.)

Question : 18

A number consists of two digits. If the number formed by interchanging the digits is added to the original number, the resulting number (i.e. the sum) must be divisible by

a) 9

b) 11

c) 3

d) 5

Answer: (b)

Let the number be 10x + y

After interchanging the digits, the number obtained = 10y + x

According to the question,

Resulting number

= 10x + y + 10y + x

= 11x + 11y

= 11 (x + y) which is exactly divisible by 11.

Question : 19

Each member of a picnic party contributed twice as many rupees as the total number of members and the total collection was 3042. The number of members present in the party was

a) 32

b) 2

c) 39

d) 40

Answer: (c)

Let the required number of persons be x.

According to the question, $2x^2$ = $3042$

or $x^2$ = $3042/2$ = 1521

or x = $√{1521}$ = 39

Question : 20

When a number is divided by 893, the remainder is 193. What will be the remainder when it is divided by 47 ?

a) 5

b) 3

c) 33

d) 25

Answer: (a)

Here, 893 is exactly divisible by 47.

Hence, the required remainder is obtained on dividing 193 by 47.

∴ Remainder = 5

IMPORTANT quantitative aptitude EXERCISES

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