Is the product of two positive integers x

[jjjinapinch]

Is the product of two positive integers x and y divisible by the sum of x and of y ?
(1) x = y
(2) x = 2

Official Guide question
Answer: C

[ceilidh.erickson]

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.

[Scott@TargetTestPrep]

Is the product of two positive integers x and y divisible by the sum of x and of y ?
(1) x = y
(2) x = 2

We can write the question:

Is xy/(x + y) = integer?

Statement One Alone:

x = y

Since x = y, we have:

Is xy/(x + y) = integer?

Is (x)(x)/(x + x) = integer?

Is x^2/2x = integer?

Is x/2 = integer?

Since we don't have a value of x, we cannot determine whether x/2 is an integer. For example, if x = 2, then x/2 is an integer; however, if x = 3, then x/2 is not an integer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x = 2

Only knowing that x = 2 is not enough to determine whether xy/(x + y) = integer. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using the statements together, we see that since x is 2, we can say that 2/2 = 1, which is an integer.

Answer: C

[[email protected]]

Hi All,

We're told that X and Y are POSITIVE INTEGERS. We're asked if the product of X and Y is divisible by the sum of X and Y. This is a YES/NO question and we can solve it by TESTing VALUES.

1) X = Y

IF....
X=Y=1, then the product = (1)(1) = 1, the sum = (1+1) = 2 and the answer to the question is NO.
X=Y=2, then the product = (2)(2) = 4, the sum = (2+2) = 4 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) X = 2

Fact 2 tells us NOTHING about the value of Y
IF....
X=2 and Y=2, then the product = (2)(2) = 4, the sum = (2+2) = 4 and the answer to the question is YES.
X=2 and Y=1, then the product = (2)(1) = 2, the sum = (2+1) = 3 and the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know the exact values for X and Y (they both equal 2), so we CAN answer the question - and it happens that the answer is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[GmatPeak]

I chose E because taking X =Y=3 gives a different answer.
3x3=9
3+3=6

9 is NOT divisible by 6, right?

So, where did I miss it?

[GmatPeak]

I chose E because taking X =Y=3 gives a different answer.
3x3=9
3+3=6

9 is NOT divisible by 6, right?

So, where did I miss it?

Oops! Pls disregard. X is given as 2