Is the product of two positive integers x

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jjjinapinch: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Mon Jul 24, 2017 8:16 amFollowed by: 1 member

by jjjinapinch » Wed Aug 02, 2017 11:14 am

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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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Source: Beat The GMAT — Data Sufficiency | Wed Aug 02, 2017 11:14 am

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » 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.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8147; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Mar 27, 2018 3:09 pm

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

Contact Rich at [email protected]

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GmatPeak: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Mar 20, 2018 9:59 am

by GmatPeak » Thu Mar 29, 2018 1:00 am

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?

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GmatPeak: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Mar 20, 2018 9:59 am

by GmatPeak » Thu Mar 29, 2018 1:40 am

GmatPeak wrote: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

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