Match the following : Column-I Column-II (P) If 213 x 27 is divisible by 9 , then x = ( i ) 2 (Q) If 2415 x is divisible by 6 , then x = ( i i ) 8 (R) If 23245 x is divisible by 4 and 3 then x = ( i i i ) 3 (S) If 7251 x 93 is divisible by 11 , then x = i v 6

A number be divisible by 9 only if the sum of the digits of the number will be divisible by 9 Consider 213 x 27 , 2 + 1 + 3 + x + 2 + 7 = 1 5 + x Hence, the least value of x can be 3 so that the number will be divisible by 9 . A number will be divisible by 6 if the number is even and if the sum of digits of the number is a multiple of 3 Consider 2415 x ⇒ 2 + 4 + 1 + 5 + x = 3 y and it should be even 12 + x = 3 y and it should be even Hence x = 6 A number is divisible by 3 if the sum of the digits of the number is a multiple of 3 . A number is divisible by 4 if the last two digits of the number is divisible by 4 . Consider 23245 x ⇒ 2 + 3 + 2 + 4 + 5 + x = 1 6 + x Hence, x = 2 So, the last two digits will be 52 which is a multiple of 4 . A number will be divisible by 11 only if the difference between the sum of digits at even places and sum of digits at odd places will be either 0 or multiple of 11 . Consider 7251 x 93 , take the digits at odd place = 7 + 5 + x + 3 Take the digits at even place = 2 + 1 + 9 Difference between the digits at odd place and the digits at even place 15 + x - 12 = 1 1 y 3 + x = 11 y Put y = 0 , x = - 3 Put y = 1 , x = 8 Hence x = 8 Hence, the correct match is P – ( i ) , Q - ( i v ) , R – ( i ) , S – ( i i )

E M B I B E

IMO Olympiad Work Book 8>Chapter 16 - Playing with Numbers>ACHIEVERS SECTION (HOTS)>Q 15

EASY

8th Foundation

IMPORTANT

Earn 100

In a division, a divisor is $12$ times the quotient and $5$ times the remainder. If the remainder is $48$ , then dividend is _____.

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Important Questions on Playing with Numbers

MEDIUM

8th Foundation

IMPORTANT

IMO Olympiad Work Book 8>Chapter 16 - Playing with Numbers>ACHIEVERS SECTION (HOTS)>Q 16

Which of the following statements is incorrect?

MEDIUM

8th Foundation

IMPORTANT

IMO Olympiad Work Book 8>Chapter 16 - Playing with Numbers>ACHIEVERS SECTION (HOTS)>Q 17

Fill in the blanks.

If sum of $3 -$ digit numbers $x y z$ , $y z x$ and $z x y$ is divided by $(x + y + z$ ), then quotient is $P$ .
The difference between $2$ – digit numbers $a b$ and $b a$ (where $> b$ ) is divided by $3$ . The quotient is $Q$ .
Sum of a $2 -$ digit number and the number obtained by reversing its digit is always divisible by $R$ .

MEDIUM

8th Foundation

IMPORTANT

IMO Olympiad Work Book 8>Chapter 16 - Playing with Numbers>ACHIEVERS SECTION (HOTS)>Q 18

Match the following :

Column-I	Column-II
(P) If $213 x 27$ is divisible by $9$ , then $x =$	$(i) 2$
(Q) If $2415 x$ is divisible by $6$ , then $x =$	$(i i) 8$
(R) If $23245 x$ is divisible by $4$ and $3$ then $x =$	$(i i i) 3$
(S) If $7251 x 93$ is divisible by $11$ , then $x =$	$(i v) 6$