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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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New post Updated on: 09 Oct 2013, 01:04
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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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Re: If x and y are positive, what is x+y  [#permalink]

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New post 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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Re: If x and y are positive, what is x+y  [#permalink]

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New post 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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Re: If x and y are positive, what is x+y  [#permalink]

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New post 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
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Re: If x and y are positive, what is x+y  [#permalink]

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New post 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.
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Re: If x and y are positive, what is x+y  [#permalink]

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New post 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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Re: If x and y are positive, what is x+y  [#permalink]

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New post 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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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 19 Aug 2018, 09:54
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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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Re: If x and y are positive, what is x+y &nbs [#permalink] 19 Aug 2018, 09:54
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