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# If 9x=27^y, which of the following expresses x in terms of y

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If 9x=27^y, which of the following expresses x in terms of y [#permalink]  05 Jul 2008, 10:21
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If 9x = 27^y, which of the following expresses x in terms of y?
A. 3^y
B. 3^(y-1)
C. 3^(2y-1)
D. 3^(2y-3)
E. 3^(3y-2)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Jan 2012, 07:03, edited 1 time in total.
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Re: if 9 [#permalink]  05 Jul 2008, 10:27
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9x = 27^y
=> 3^2*x = 3^3y
=> dividing both sides by 3^2

=> x = 3^3y-2

Hence E
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Re: if 9 [#permalink]  05 Jul 2008, 13:03
TheBigCheese wrote:
If 9x = 27^y, which of the following expresses x in terms of y?

a) 3^y
b) 3^y-1
c) 3^2y-1
d) 3^2y-3
e) 3^3y-2

9x = 27^y
x = (3^3)^y/3^2
x = 3^(3y-2)
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Re: if 9 [#permalink]  06 Jul 2008, 17:22
1
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TheBigCheese wrote:
If 9x = 27^y, which of the following expresses x in terms of y?

a) 3^y
b) 3^y-1
c) 3^2y-1
d) 3^2y-3
e) 3^3y-2

9x = 27^y
x = 27^y/9
= 3^3y/3^2
= 3^(3y-2)

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Re: if 9 [#permalink]  22 Jan 2012, 06:37
What's wrong if i solve the problem as follows:
3*3x=3*9^y
3x = 9^y [Dividing both side by 3]
x = 3^(2y-1)
Ans. C.
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Re: if 9 [#permalink]  22 Jan 2012, 06:57
Expert's post
Baten80 wrote:
What's wrong if i solve the problem as follows:
3*3x=3*9^y
3x = 9^y [Dividing both side by 3]
x = 3^(2y-1)
Ans. C.

The point is that 3*9^y does not equal to 27^y: 3*9^y=3*3^{2y}=3^{2y+1} on the other hand 27^y=(3^3)^y=3^{3y}.

Solution:
If 9x = 27^y, which of the following expresses x in terms of y?
A. 3^y
B. 3^(y-1)
C. 3^(2y-1)
D. 3^(2y-3)
E. 3^(3y-2)

9x=3^2*x and 27^y=(3^3)^y=3^{3y} --> 3^2*x=3^{3y} --> x=\frac{3^{3y}}{3^2} --> x=3^{3y-2}.

For theory on exponents check: math-number-theory-88376.html

Tough DS questions on exponents with solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough PS questions on exponents with solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Hope it helps.
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Re: if 9 [#permalink]  23 Jan 2012, 01:15
1
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Expert's post
Baten80 wrote:
What's wrong if i solve the problem as follows:
3*3x=3*9^y
3x = 9^y [Dividing both side by 3]
x = 3^(2y-1)
Ans. C.

Bunuel has already pointed out your error so I will not repeat it.

Let me give you another method of working out the solution here (though you should ensure that you understand the theory of exponents well)

If 9x = 27^y, which of the following expresses x in terms of y?
A. 3^y
B. 3^(y-1)
C. 3^(2y-1)
D. 3^(2y-3)
E. 3^(3y-2)

We need x in terms of y.
In 9x = (27)^y, put y = 0. You get x = 1/9

Now see which option will give you 1/9 when you put y = 0. I hope you can quickly see that only option (E) will give you x = 1/9 when y = 0. Answer is (E). Such methods work well when you have variables in the options.

Note: If more than one options had given 1/9, you could have tried some other values to choose the right answer out of those options.
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Senior Manager Status: D-Day is on February 10th. and I am not stressed Affiliations: American Management association, American Association of financial accountants Joined: 12 Apr 2011 Posts: 275 Location: Kuwait Schools: Columbia university Followers: 4 Kudos [?]: 19 [0], given: 52 Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink] 23 Jan 2012, 07:06 9x=27^y 3^2x=3^3y devide both sides by 3^2 x=3^3y-2. note, you need to make both sides have equale exponent, and remember when you simplify exponents through division, you subtract them _________________ Sky is the limit Intern Joined: 03 Dec 2010 Posts: 22 Followers: 0 Kudos [?]: 1 [0], given: 0 Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink] 08 Apr 2012, 21:41 To Karishma, I'm glad you used the same approach as I've used, but I used y=1, which makes, 9x = 27^y 9x = 27 x = 3. Look for options which give ans. as x=3, I marked A (option E also gives x=3), which gives x=3 which is wrong ans. Can u explain where I'm wrong Thnx, Priyal Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 3780 Location: Pune, India Followers: 812 Kudos [?]: 3237 [0], given: 138 Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink] 09 Apr 2012, 04:28 Expert's post priyalr wrote: To Karishma, I'm glad you used the same approach as I've used, but I used y=1, which makes, 9x = 27^y 9x = 27 x = 3. Look for options which give ans. as x=3, I marked A (option E also gives x=3), which gives x=3 which is wrong ans. Can u explain where I'm wrong Thnx, Priyal When you put y = 1, three of the five options give you x = 3 (options A, C and E). Any one of these 3 could be the correct answer. You now need to try out some other values of y to get the answer out of these 3 options. You need to check all the options to ensure that no other options gives you the same value. When I put y = 0, I try it in all the options and only option E gives me 1/9 so I can directly mark that as the answer. This is the reason I mentioned the note in the post above: "Note: If more than one options had given 1/9, you could have tried some other values to choose the right answer out of those options." So now your next step is to put y = 0 and out of the 3 options, only E will satisfy x = 1/9. Try and put the easiest value first. Easiest value is generally 0, if allowed. Putting y = 2/3/4... will make it cumbersome. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]  25 Jun 2013, 04:55
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink]  25 Jun 2013, 07:51
1
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Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

9x=27^y
3^2 x = 3^3y

Clearly, x=1 an y=2/3 will satisfy

Now we have the values of x given in the options, substitute y=2/3 , wherever we get value =1, is the answer

which is clearly E since only that has 3 multiplied with y which conveniently cancels our denominator and results in 3^0 =1

Ans=>E
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Re: If 9x=27^y, which of the following expresses x in terms of y   [#permalink] 25 Jun 2013, 07:51
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