jjjinapinch wrote: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

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

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