banksy wrote:
If x and y are positive integers and x is a multiple of y, is y = 2?
(1) y ≠ 1
(2) x + 2 is a multiple of y.
Hi,
When x is a multiple of y, it means that when x is divided by y, it will leave 0 as remainder.
It can be written x mod y = 0.
Suppose x=6 and y = 2. Hence x is divisible by y. i.e 6 mod 2 = 0 (leaves remainder 0)
Stmt1: y ≠ 1
But you can clearly see in the number i have picked that for x=6, y can be 2,3, or 6. All the values will satisfy equation x mod y = 0. i.e 6 divided by 1,2,3,and 6 will all leave 0 as remainder. Hence y can be 2 or 3 or 6. Insufficient.
Stmt2: x+2 is a multiple of y. x+2= 6+2=8 is a multiple of 2. Hence equation x mod y = 0 is satisfied.
But pick x=6 and y=1. in this case equation x mod y = 0 is satisfied and x+2 =>6+2=8 is a multiple of 1. Hence we have different values of y for different values of x. Hence one value of y cannot be determined. Insufficient.
Take both together, from stmt1, y can be 2,3, or 6. From stmt2, y can 1,2. Together, only 2 satisfy. Hence sufficient.
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