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If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y? (1) n=m+1 (2) n=2m

There will be three cases: when M is positive: option 1 is sufficient to answer. and option 2 also give answer When M is negative: Option 1 is sufficient to answer. But option 2 is not sufficient to answer. When M is Zero: option Option 1 is sufficient to answer But Option 2 is not sufficient to answer.

Try with some nos. for these three cases. If you like the post, kindly give me 1 kudos.

Re: If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink]

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13 Sep 2012, 01:32

3

This post received KUDOS

saurabhsingh24 wrote:

If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y?

(1) n=m+1 (2) n=2m

The question is in fact "is \(3^n>2\cdot{3^m}\)?"

(1) The given inequality becomes \(3^{m+1}>2\cdot{3^m}\). Dividing through by \(3^m\), which is for sure a positive number, we obtain \(3 > 2,\) obviously true. Sufficient.

(2) Now the given inequality becomes \(3^{2m}>2\cdot{3^m}\). Dividing through again by \(3^m\), we obtain \(3^m>2\). This inequality holds only for \(m>0\). Not sufficient.

Answer A. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink]

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05 Sep 2013, 08:42

saurabhsingh24 wrote:

If n and m are integers, and x=3^n, and y=3^m, is the value of x greater than the value of 2y?

(1) n=m+1 (2) n=2m

Basically the Q asks whether 3^n> 2*3^m

St 1 substituting for n we get

3^(m+1) - 2*3^m > 0 3* 3^m -2 *3^m>0 3^m>0 ------> m can be 0 or 1 or 2 and so one so n= m+1 (1 or 2 or 3 for corresponding values of m) We see that 3^n > 2*3^m

So A is sufficient so ruling out B,C and E

From st 2 we have n= 2m

We get 3^2m -2*3^m>0 9*3^m - 2*3^m> 0 or 7*3^m>0

So m =0, n=0 ---->putting in the above equation we get (3^2m -2*3^m>0) --> 1-2 =-1 not greater than zero But if m=1,n=2 then we get 3^2m -2*3^m>0 ------>9-6>0 3>0 so 2 ans choices possible so D ruled out

Ans is A _________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Re: If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink]

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18 Sep 2013, 18:35

Here is how I solved it, x = 3^n and y =3^m 1. n = m +1; therefore, x = 3^m+1 => 3 * 3^m, now 3^m = y, therefore x = 3y and hence x > 2y Sufficient 2. n =2m; x = 3^2m; x = y^2; now nothing is given about x and y; therefore for y = 0; x =0 and hence the x is not greater than 2y whereas if y =-1, x = 1 again not satisfied, if y = -2, x = 4 ; x = 2y; if y = 3, x = 9; hence NS

Therefore answer is .A.

Please let me know in case my line of reasoning is not correct, especially for the second statement.

Re: If n and m are integers, and x=3^n, and y=3^m, is the value [#permalink]

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30 Sep 2014, 23:23

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