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Is the product of two positive integers x

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Is the product of two positive integers x

Post Wed Aug 02, 2017 11:14 am
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

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Post Fri Nov 17, 2017 12:02 pm
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

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Post Wed Aug 02, 2017 11:31 am
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.

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