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If x is an integer, is 3^x less than 500?

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If x is an integer, is 3^x less than 500? [#permalink] New post 28 Oct 2012, 14:31
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If x is an integer, is 3^x less than 500?

(1) 4^(x–1) < 4^x – 120

(2) x^2 = 36
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Oct 2012, 03:18, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Inequality problem [#permalink] New post 28 Oct 2012, 21:21
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himanshuhpr wrote:
If x is an integer, is 3x less than 500?

(1) 4^(x–1) < 4^x – 120

(2) x^2 = 25



OA: C

From (1) we get x>4
From (2) we get x= +5 -5

It Should be B why its C ??


The answer IS B. If OA is given as C, then it is wrong.

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Re: Inequality problem [#permalink] New post 29 Oct 2012, 00:31
yup. i also got B..

Lets C..wat experts r replying !!

can anyone tell me trick for this thing..

4^x-4^x-1=120..how to get comon ..i did it.. but i tuk me more than one mint
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Re: Inequality problem [#permalink] New post 29 Oct 2012, 00:59
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Statement 1 --> 120 < \frac{3}{4}*4^x ==> 160 < 4^x ==> therefore, x > 3 ==> Insufficient.
Statement 2 --> x = +5 or -5 ==> therefore, 3x is either +15 or -15 in both cases its less than 500 ==> Sufficient.

Answer : B
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Re: Inequality problem [#permalink] New post 29 Oct 2012, 01:34
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sanjoo wrote:
yup. i also got B..

Lets C..wat experts r replying !!

can anyone tell me trick for this thing..

4^x-4^x-1=120..how to get comon ..i did it.. but i tuk me more than one mint


4^x -4^(x-1) = 120
4^x - \frac{4^x}{4} = 120
\frac{3}{4}*4^x = 120

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Re: Inequality problem [#permalink] New post 29 Oct 2012, 03:18
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himanshuhpr wrote:
If x is an integer, is 3x less than 500?

(1) 4^(x–1) < 4^x – 120

(2) x^2 = 25



OA: C

From (1) we get x>4
From (2) we get x= +5 -5

It Should be B why its C ??


The question should read:

If x is an integer, is 3^x less than 500?

Since 3^6=729>500 and 3^5=243<500, then the question basically asks whether x is an integer less than 6 (5, 4, 3, 2, 1, 0, -1, ...).

(1) 4^(x–1) < 4^x – 120 --> \frac{4^x}{4}<4^x-120 --> 120<\frac{3}{4}*4^x --> 160<4^x --> x is an integer greater than 3: 4, 5, 6, 7, ... Not sufficient.

(2) x^2 = 36 --> x=6 or x=-6. Not sufficient.

(1)+(2) From above x=6, thus the answer to the question is NO. Sufficient.

Answer: C.

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Hope it helps.
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Re: If x is an integer, is 3^x less than 500? [#permalink] New post 27 Jan 2014, 13:18
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Re: If x is an integer, is 3^x less than 500? [#permalink] New post 28 May 2014, 05:07
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From statement 1 we get that x>=4 hence if x=4 the answer is yes, but if x10 the answer is NO. From statement 2 we get that x can be either -6 or 6, if x=6 then yes but if x = -6 then no. From both statements together we know that x = 6 so the answer is NO C

C is the answer to problems

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Re: If x is an integer, is 3^x less than 500?   [#permalink] 28 May 2014, 05:07
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