.For integer n, f(n) denotes the remainder when n is divided by integer k. Is k greater than 10?
1). f(k+32)=8
2). f(k+42)=6
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vipulgoyal
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Statement 1: (k + 32) leaves a remainder of 8 when divided by k.vipulgoyal wrote:.For integer n, f(n) denotes the remainder when n is divided by integer k. Is k greater than 10?
1). f(k+32)=8
2). f(k+42)=6
--> 32 leaves a remainder of 8 when divided by k
--> k is greater than 8 and (32 - 8) = 24 is divisible by k but 32 is not divisible by k
--> possible values of k are : 12 and 24
--> k > 10
Sufficient
Statement 2: (k + 42) leaves a remainder of 6 when divided by k.
--> 42 leaves a remainder of 6 when divided by k
--> k is greater than 6 and (42 - 6) = 36 is divisible by k but 42 is not divisible by k
--> possible values of k are : 9, 12, 18, and 36
If k = 9, k < 10
If k = 12, k > 10
Not sufficient
The correct answer is A.
Anju Agarwal
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CSASHISHPANDAY
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Look f(k+32)=8 is the remainder..so k+32-8 =k+24/k is divisible...
or can say that
(k/k)+ (k/24) is divisible by k
or can say that 24 is divisible by k......................(1)
if remainder is 8 also k must be more than 8
Now 8<K ........................(2)
from (1) k can be 1, 2, 3, 4, 6, 8, 12, 24.
from (2) k can be 9.....................24
by combining we get k= 12 &/or 24.
in each case K is bigger than 10.
sufficient..
2. with same argument..36 should be divisible by k and k>6...value satisfying these,k=9,12,18,36..hence k>10 i not true always..
Insufficient
or can say that
(k/k)+ (k/24) is divisible by k
or can say that 24 is divisible by k......................(1)
if remainder is 8 also k must be more than 8
Now 8<K ........................(2)
from (1) k can be 1, 2, 3, 4, 6, 8, 12, 24.
from (2) k can be 9.....................24
by combining we get k= 12 &/or 24.
in each case K is bigger than 10.
sufficient..
2. with same argument..36 should be divisible by k and k>6...value satisfying these,k=9,12,18,36..hence k>10 i not true always..
Insufficient
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