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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]  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]  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]  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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Kudos [?]: 55 [2] , given: 36

Re: Inequality problem [#permalink]  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.

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Re: Inequality problem [#permalink]  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]  29 Oct 2012, 03:18
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Expert's post
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.

Similar questions to practice:
is-x-10-10-1-x-2-34-2-x-127881.html
is-5-k-less-than-1-000-1-5-k-128055.html
if-x-is-an-integer-and-4-x-100-what-is-x-1-4-x-106353.html
is-4-x-5-3x-1-1-x-is-an-integer-86765.html
is-5-x-134898.html
is-3-x-134968.html

Hope it helps.
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Re: If x is an integer, is 3^x less than 500? [#permalink]  27 Jan 2014, 13:18
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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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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

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

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