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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] New post 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 27 Feb 2014, 04:26, edited 2 times in total.
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Re: if 9 [#permalink] New post 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] New post 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] New post 06 Jul 2008, 17:22
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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)

E
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Re: if 9 [#permalink] New post 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.
Please help to correct my wrong concept as the OA is E.
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Re: if 9 [#permalink] New post 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.
Please help to correct my wrong concept as the OA is E.


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}.

Answer: E.

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

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Re: if 9 [#permalink] New post 23 Jan 2012, 01:15
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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.
Please help to correct my wrong concept as the OA is E.


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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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink] New post 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
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink] New post 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
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink] New post 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.
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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink] New post 25 Jun 2013, 04:55
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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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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

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Re: If 9x=27^y, which of the following expresses x in terms of y [#permalink] New post 25 Jun 2013, 07:51
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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] New post 26 Feb 2014, 22:26
27 can be written as 9^ 3/2

So x = 9^(3y/2-1)

x = 3^(3y-2) = Answer = E
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Re: If 9x=27^y, which of the following expresses x in terms of y   [#permalink] 26 Feb 2014, 22:26
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