number system

vipulgoyal wrote:What is the remainder when the positive integer x is divided by 8 ?
1. when x is divided by 12 the remainder is 5
2. when x is divided by 18 the remainder is 11"

NOTE: srcc25anu is right - statement 2, should read "when x is divided by 18 the remainder is 11"

Target question: What is the remainder when the positive integer x is divided by 8 ?

Statement 1: When x is divided by 12 the remainder is 5
When it comes to remainders, we have a nice rule that says:
If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, for statement 1, the possible values of x are 5, 17, 29, 41, . . .
Let's examine two possible values of x:
Case a: x = 5, in which case x divided by 8 leaves remainder 5
Case b: x = 17, in which case x divided by 8 leaves remainder 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: when x is divided by 18 the remainder is 11
So, the possible values of x are 11, 29, 47, 65, . . .
Let's examine two possible values of x:
Case a: x = 11, in which case x divided by 8 leaves remainder 3
Case b: x = 29, in which case x divided by 8 leaves remainder 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
We're now looking for values of x that satisfy statement 1 AND statement 2
From statement 1, x could equal 5, 17, 29, 41, 65, 77 . . .
From statement 2, x could equal 11, 29, 47, 65, 83, . . .
As you might guess, there are several possible values of x. Let's examine two of them:
Case a: x = 29, in which case x divided by 8 leaves remainder 5
Case b: x = 65, in which case x divided by 8 leaves remainder 1
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent