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# If x and y are positive, what is x+y

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If x and y are positive, what is x+y  [#permalink]

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Updated on: 09 Oct 2013, 01:04
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14
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Difficulty:

95% (hard)

Question Stats:

29% (01:25) correct 71% (01:30) wrong based on 261 sessions

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If x and y are positive, what is x+y?

(1) 2^x*3^y = 72
(2) 2^x*2^y = 32

Originally posted by imhimanshu on 08 Oct 2013, 08:44.
Last edited by Bunuel on 09 Oct 2013, 01:04, edited 1 time in total.
Edited the question.
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Joined: 02 Sep 2009
Posts: 49430
Re: If x and y are positive, what is x+y  [#permalink]

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09 Oct 2013, 01:27
6
4
mikemcgarry wrote:
imhimanshu wrote:
If $$x$$ and $$y$$ are positive, what is $$x+y$$?
a) $$2^x*3^y = 72$$
b) $$2^x*2^y = 32$$

Dear Himanshu,
The decimal points don't make sense in this context --- those are not the appropriate symbols for multiplication, which is, I assume, what is meant here. The asterisk (shift=8) is a standard plaintext symbol for multiplication.
Furthermore, I don't think the OA given is correct.

You see,
72 = 8*9 = (2^3)*(3^2), so it must be true that x = 3 and y = 2, which means x + y = 5. That makes statement #1 sufficient.

For statement #2,
(2^x)*(2^y) = 2^(x + y) --- that's a standard law of exponents:
http://magoosh.com/gmat/2012/exponent-p ... -the-gmat/
Since 32 = 2^5, we know x + y = 5, although we couldn't find x and y individually from this statement. Nevertheless, this statement is also sufficient to answer the prompt.

I believe the correct answer should be (D), not (B).

Does all this make sense?
Mike

I have to respectfully disagree. The correct answer must be B, not D.

If x and y are positive, what is x+y?

Notice that we are not told that x and y are integers.

(1) 2^x*3^y = 72. Now, if were told that x and y are positive integers, then yes, from 2^x*3^y = 2^3*3^2, it would follow that x=3 and y=2. But we are not given that, thus it's possible that x is say 1 and y is some irrational number (satisfying 3^y=36 --> y=~3.26...). Not sufficient.

(2) 2^x*2^y = 32 --> 2^(x+y) = 2^5 --> x+y = 5. Sufficient.

Answer: B.

Similar questions to practice:
if-3-a-4-b-c-what-is-the-value-of-b-1-5-a-25-2-c-106047.html
if-x-2y-3-200-what-is-xy-92486.html

Hope it helps.
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Posts: 4664
Re: If x and y are positive, what is x+y  [#permalink]

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08 Oct 2013, 11:51
3
imhimanshu wrote:
If $$x$$ and $$y$$ are positive, what is $$x+y$$?
a) $$2^x*3^y = 72$$
b) $$2^x*2^y = 32$$

Dear Himanshu,
The decimal points don't make sense in this context --- those are not the appropriate symbols for multiplication, which is, I assume, what is meant here. The asterisk (shift=8) is a standard plaintext symbol for multiplication.
Furthermore, I don't think the OA given is correct.

You see,
72 = 8*9 = (2^3)*(3^2), so it must be true that x = 3 and y = 2, which means x + y = 5. That makes statement #1 sufficient.

For statement #2,
(2^x)*(2^y) = 2^(x + y) --- that's a standard law of exponents:
http://magoosh.com/gmat/2012/exponent-p ... -the-gmat/
Since 32 = 2^5, we know x + y = 5, although we couldn't find x and y individually from this statement. Nevertheless, this statement is also sufficient to answer the prompt.

I believe the correct answer should be (D), not (B).

Does all this make sense?
Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Manager
Joined: 26 Sep 2013
Posts: 197
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: If x and y are positive, what is x+y  [#permalink]

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08 Oct 2013, 16:59
mikemcgarry wrote:
imhimanshu wrote:
If $$x$$ and $$y$$ are positive, what is $$x+y$$?
a) $$2^x*3^y = 72$$
b) $$2^x*2^y = 32$$

Dear Himanshu,
The decimal points don't make sense in this context --- those are not the appropriate symbols for multiplication, which is, I assume, what is meant here. The asterisk (shift=8) is a standard plaintext symbol for multiplication.
Furthermore, I don't think the OA given is correct.

You see,
72 = 8*9 = (2^3)*(3^2), so it must be true that x = 3 and y = 2, which means x + y = 5. That makes statement #1 sufficient.

For statement #2,
(2^x)*(2^y) = 2^(x + y) --- that's a standard law of exponents:
http://magoosh.com/gmat/2012/exponent-p ... -the-gmat/
Since 32 = 2^5, we know x + y = 5, although we couldn't find x and y individually from this statement. Nevertheless, this statement is also sufficient to answer the prompt.

I believe the correct answer should be (D), not (B).

Does all this make sense?
Mike

I had it being D as well
Manager
Joined: 29 Aug 2013
Posts: 74
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q41 V29
GMAT 2: 540 Q44 V20
GPA: 3.5
WE: Programming (Computer Software)
Re: If x and y are positive, what is x+y  [#permalink]

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09 Oct 2013, 00:23
imhimanshu wrote:
If $$x$$ and $$y$$ are positive, what is $$x+y$$?
a) $$2^x.3^y = 72$$
b) $$2^x.2^y = 32$$

It has to be "D". Both the statements give you clear values of x + y.

Could anyone please provide an OA.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4664
Re: If x and y are positive, what is x+y  [#permalink]

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09 Oct 2013, 10:51
Bunuel wrote:
I have to respectfully disagree. The correct answer must be B, not D.

If x and y are positive, what is x+y?

Notice that we are not told that x and y are integers.

(1) 2^x*3^y = 72. Now, if were told that x and y are positive integers, then yes, from 2^x*3^y = 2^3*3^2, it would follow that x=3 and y=2. But we are not given that, thus it's possible that x is say 1 and y is some irrational number (satisfying 3^y=36 --> y=~3.26...). Not sufficient..

Bunuel,
Very interesting. You're quite right --- if x & y are not integers, then the sum could vary widely. I know the GMAT very much likes to test concepts such as prime factorization & laws of exponents, and so I was assuming this question was designed concepts such as that. Do you think that the real GMAT would expect test-takers to know facts about non-integer exponents and how they behave --- essentially, introductory logarithm ideas --- including the facts necessary to arrive at the correct OA of (B)? Have you ever seen such topics arise in official materials? I'm curious.
Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Math Expert
Joined: 02 Sep 2009
Posts: 49430
Re: If x and y are positive, what is x+y  [#permalink]

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09 Oct 2013, 10:58
1
mikemcgarry wrote:
Bunuel wrote:
I have to respectfully disagree. The correct answer must be B, not D.

If x and y are positive, what is x+y?

Notice that we are not told that x and y are integers.

(1) 2^x*3^y = 72. Now, if were told that x and y are positive integers, then yes, from 2^x*3^y = 2^3*3^2, it would follow that x=3 and y=2. But we are not given that, thus it's possible that x is say 1 and y is some irrational number (satisfying 3^y=36 --> y=~3.26...). Not sufficient..

Bunuel,
Very interesting. You're quite right --- if x & y are not integers, then the sum could vary widely. I know the GMAT very much likes to test concepts such as prime factorization & laws of exponents, and so I was assuming this question was designed concepts such as that. Do you think that the real GMAT would expect test-takers to know facts about non-integer exponents and how they behave --- essentially, introductory logarithm ideas --- including the facts necessary to arrive at the correct OA of (B)? Have you ever seen such topics arise in official materials? I'm curious.
Mike

I've seen several questions testing the same thing (links to 2 of them are in my post above), not sure though that they are from reliable sources.
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Re: If x and y are positive, what is x+y  [#permalink]

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19 Aug 2018, 09:54
1
Top Contributor
1
imhimanshu wrote:
If x and y are positive, what is x+y?

(1) 2^x*3^y = 72
(2) 2^x*2^y = 32

-------------ASIDE--------------------------------
IMPORTANT: We are not told that x and y are integers. So, they need not be integers!

ALSO IMPORTANT: There exists a value of y so that 3^y = 36.
How do we know this?
Well, 3^3 = 27 and 3^4 = 81
Since 36 is BETWEEN 27 and 81, there must be a y-value BETWEEN 3 and 4 such that 3^y = 36.
Let's say that, when y = 3.something, 3^y = 36.
------ONTO THE QUESTION!!-----------------------------

Target question: What is the value of x+y?

Statement 1: (2^x)(3^y) = 72
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 3 and y = 2. In this case, x + y = 3 + 2 = 5. So, the answer to the target question is x + y = 5
Case b: x = 1 and y = 3.something. In this case, x + y = 1 + 3.something = 4.something. So, the answer to the target question is x + y = 4.something
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (2^x)(2^y) = 32
Since we have the SAME BASE, we can rewrite this as: 2^(x + y) = 32
Replace 32 with 2^5 to get: 2^(x + y) = 2^5
So, it must be the case that x + y = 5
So, the answer to the target question is x + y = 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com

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