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pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

GMAT PREP I EXPONENTS

by pkw209 » Tue Dec 29, 2009 10:37 am

Hey all,

I think the answer should be B rather than D since the question stem doesn't state positive INTEGER. A brief explanation would be very much appreciated. Thanks!

78) x and y are positive, what is x + y?

a. 2x3y = 72
b. 2x2y = 32

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Source: Beat The GMAT — Data Sufficiency | Tue Dec 29, 2009 10:37 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Tue Dec 29, 2009 5:41 pm

pkw209 wrote:Hey all,

I think the answer should be B rather than D since the question stem doesn't state positive INTEGER. A brief explanation would be very much appreciated. Thanks!

78) x and y are positive, what is x + y?

a. 2x3y = 72
b. 2x2y = 32

I'm assuming that the question involves exponents (even though it doesn't appear so)
If the question is:
x and y are positive, what is x + y?
(1) (2^x)(3^y) = 72
(2) (2^x)(2^y) = 32
then you're right. The answer should be B.

(1) (2^x)(3^y) = 72
Without getting too out of scope, statement (1) can give us more than one set of values for x and y such that the sum of x and y differ.
Here are two sets:
a) x=3 and y=2 --> x+y equals 5
b) x=log(base2)9 and y=log(base3)8 --> x+y does not equal 5
Don't worry about the logs; they aren't required for the GMAT

INSUFFICIENT

(2) (2^x)(2^y) = 32
(2^x)(2^y) = 2^5
2^(x+y) = 2^5
x+y=5
SUFFICIENT

If the question had restricted x and y to positive integers, the answer would have been D.

Brent Hanneson - Creator of GMATPrepNow.com

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linkinpark: Master | Next Rank: 500 Posts; Posts: 124; Joined: Tue Dec 22, 2009 8:32 am; Location: Karjat; Thanked: 3 times

by linkinpark » Wed Dec 30, 2009 10:43 am

Hi Brent,
I'm slightly confused here regarding stmt 1, aren't x=3 and y = 2 the only values that satisfy (2^x)(3^y) = 72?

I chose D at first.

thanks

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pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Wed Dec 30, 2009 12:44 pm

Thanks guys. Yes, should be exponents. That's what I thought.

linkin-as Brent explained, because the question stem doesn't state INTEGER, there could be multiple answers (Brent provides 2).

wow I haven't logs since high school

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linkinpark: Master | Next Rank: 500 Posts; Posts: 124; Joined: Tue Dec 22, 2009 8:32 am; Location: Karjat; Thanked: 3 times

by linkinpark » Wed Dec 30, 2009 9:09 pm

I'm still not out of confusion, from my knowledge we're not tested on logarithms on GMAT.

can you tell me what other values of x and y satisfy statement 1 apart from x=3 and y = 2

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pkw209: Master | Next Rank: 500 Posts; Posts: 266; Joined: Mon Oct 19, 2009 9:46 pm; Thanked: 8 times; GMAT Score:690

by pkw209 » Fri Jan 01, 2010 1:20 pm

linkin-

no, logs are not tested. the point that brent was making is that there are other possibilities since x and y do not have to be INTEGERS. this is actually an important concept that must be understood because it's pretty pervasive throughout the gmat.

orig equation -->(2^x)(3^y) = 72

for example, x could be 1/2, then 2 ^ 1/2, which equals sqrt(2) = 1.4

...then 1.4 * 3 ^ y = 72.

Without going further, you have an equation with one variable so if you wanted to you could solve for y.

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linkinpark: Master | Next Rank: 500 Posts; Posts: 124; Joined: Tue Dec 22, 2009 8:32 am; Location: Karjat; Thanked: 3 times

by linkinpark » Fri Jan 01, 2010 9:08 pm

pkw209 wrote:linkin-

no, logs are not tested. the point that brent was making is that there are other possibilities since x and y do not have to be INTEGERS. this is actually an important concept that must be understood because it's pretty pervasive throughout the gmat.

orig equation -->(2^x)(3^y) = 72

for example, x could be 1/2, then 2 ^ 1/2, which equals sqrt(2) = 1.4

...then 1.4 * 3 ^ y = 72.

Without going further, you have an equation with one variable so if you wanted to you could solve for y.

for a moment I agree with you on this but wouldn't it be the same case with stmt 2 ?? sorry for dragging the topic but i feel uneasy until I get it down