Is x – y divisible by 5?

Question

(1) x is divisible by 5.
(2) y is divisible by 5

Source:   Nova GMAT  
Difficulty Level:   550

BrentGMATPrepNow · Answer

Target question :    Is x – y divisible by 5?

Statement 1 : x is divisible by 5.   
No information about y, so statement 1 is NOT SUFFICIENT

If you're not convinced, there are several values of x and y that satisfy statement 1. Here are two: 
Case a: x = 15 and y = 5, in which case x - y = 10, So,  x - y IS divisible by 5 
Case b: x = 15 and y = 7, in which case x - y = 8, So,  x - y in NOT divisible by 5 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : y is divisible by 5 
Applying the same logic as above, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
There's a nice rule that says:   If M is divisible by k and N is divisible by k, then M - N is divisible by k (likewise, M + N is divisible by k)  
So, we can be certain that  x - y IS divisible by 5 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer:  C

utkarshthapak · Answer

S1: x is divisible by 5, y can be anything and given expression may or may not be divisible by 5.
S2: Same as S1, x can be anything.

on combining, expression will always be divisible which gives us a definite answer.

Option C is correct.

Xin Cho · Answer

I understand how statements I and II lead to 5(x-y) and thus it must be divisible by 5.

However, what if both x and y are the same number. Their difference would be zero and is zero divisible by 5?

QuantMadeEasy · Answer

(1)  x is divisible by 5. 
5 is a factor of x but dont know about y. insufficient

(2) y is divisible by 5
5 is a factor of y but we dont know about factors of x. Insufficient

(1)+(2), 5 is a factor of both x and y, means 5 is a factor of x-y also. Sufficient
C is correct

TheNightKing · Answer

Statement 1:
x=5
y=1

Answer = No.

x=10
y=5

Answer = Yes.

Not Sufficient.

Statement 2:
x=11
y=5

Answer = No.

x=10
y=5

Answer = Yes.

Not Sufficient.

Combined 
Both x and y are multiple of 5 so x-y is divisible by 5. Even if they are equal 5-5 then 0 is divisible by 5.

Answer (C)

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. The question that x - y is divisible by 5 is equivalent to the statement x and y have a same remainder when they are divided by 5. Condition 1) tells x has a remainder 0 when it is divided by 5. Condition 2) tells y has a remainder 0 when it is divided by 5. When we consider both conditions together, we realize x and y have the same remainder 0 when they are divided by 5. Since both conditions together yield a unique solution, they are sufficient. Therefore, C is the answer.

Is x – y divisible by 5?

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