For a DS question that gives you few constraints in the question stem, the best strategy is to TEST NUMBERS.
Start by testing easy numbers that fit the statement, and see if you get a "yes" or "no" answer to the question. Then test another case to try to get the opposite answer.
Is the product of two positive integers x and y divisible by the sum of x and of y ?
(1) x = y
Case 1:
x = 1
y = 1
xy = 1
x + y = 2
No, the product xy is not divisible by (x + y). Let's see if we can think of a case that would give us a "yes" answer.
Case 2:
x = 2
y = 2
xy = 4
x + y = 4
Yes, the product xy is divisible by the sum x + y. If one case gives us a "no" and the other gives us a "yes," it's insufficient.
(2) x = 2
Case 1:
x = 2
y = 2
We can recycle a test we used above - we know that this gives us a "yes" answer. Now try another case to see if we can get a "no."
Case 2:
x = 2
y = 3
xy = 6
x + y = 5
Since 6 is not divisible by 5, then answer is "no." Insufficient.
(1) & (2) together:
If x = 2 and x = y, then y = 2. We know that xy = 4 and x+ y = 4, so we have sufficient information.
The answer is C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
