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

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Intern
Joined: 29 Aug 2012
Posts: 25
Schools: Babson '14
GMAT Date: 02-28-2013
If x is an integer, is 3^x less than 500?  [#permalink]

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Updated on: 29 Oct 2012, 03:18
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95% (hard)

Question Stats:

50% (02:36) correct 50% (02:30) wrong based on 185 sessions

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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

Originally posted by himanshuhpr on 28 Oct 2012, 14:31.
Last edited by Bunuel on 29 Oct 2012, 03:18, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 61189
If x is an integer, is 3^x less than 500?  [#permalink]

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29 Oct 2012, 03:18
5
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 ??

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.

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Hope it helps.
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Joined: 02 Jul 2012
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Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
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WE: Engineering (Energy and Utilities)

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28 Oct 2012, 21:21
2
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.

Kudos Please... If my post helped.
Senior Manager
Joined: 06 Aug 2011
Posts: 316

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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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29 Oct 2012, 00:59
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.

VP
Joined: 02 Jul 2012
Posts: 1093
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)

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29 Oct 2012, 01:34
1
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

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

Kudos Please... If my post helped.
SVP
Joined: 06 Sep 2013
Posts: 1515
Concentration: Finance
Re: If x is an integer, is 3^x less than 500?  [#permalink]

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28 May 2014, 05:07
1
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
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If x is an integer, is 3^x less than 500?  [#permalink]

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04 Jun 2019, 22:22
for both the value of x in statement 2 i.e -6 and 6, statement 3x<500 is yes. Then why isnt the answer b?

I see. we are interpreting the question differently. The main statement is 3x in the question not 3 RAISED TO THE POWER X.

If 3x, in that case answer is b otherwise its c.
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Posts: 61189
Re: If x is an integer, is 3^x less than 500?  [#permalink]

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04 Jun 2019, 22:45
1
for both the value of x in statement 2 i.e -6 and 6, statement 3x<500 is yes. Then why isnt the answer b?

I see. we are interpreting the question differently. The main statement is 3x in the question not 3 RAISED TO THE POWER X.

If 3x, in that case answer is b otherwise its c.

It's $$3^x$$, NOT $$3x$$. That's what the first post says as well as my solution above.
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Re: If x is an integer, is 3^x less than 500?  [#permalink]

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06 Jun 2019, 06:43
Bunuel wrote:
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 ??

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:
http://gmatclub.com/forum/is-x-10-10-1- ... 27881.html
http://gmatclub.com/forum/is-5-k-less-t ... 28055.html
http://gmatclub.com/forum/if-x-is-an-in ... 06353.html
http://gmatclub.com/forum/is-4-x-5-3x-1 ... 86765.html
http://gmatclub.com/forum/is-5-x-134898.html
http://gmatclub.com/forum/is-3-x-134968.html

Hope it helps.

Can you please elaborate the steps for statement 1?
Math Expert
Joined: 02 Sep 2009
Posts: 61189
Re: If x is an integer, is 3^x less than 500?  [#permalink]

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06 Jun 2019, 06:56
AmanMatta wrote:
Bunuel wrote:
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 ??

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:
http://gmatclub.com/forum/is-x-10-10-1- ... 27881.html
http://gmatclub.com/forum/is-5-k-less-t ... 28055.html
http://gmatclub.com/forum/if-x-is-an-in ... 06353.html
http://gmatclub.com/forum/is-4-x-5-3x-1 ... 86765.html
http://gmatclub.com/forum/is-5-x-134898.html
http://gmatclub.com/forum/is-3-x-134968.html

Hope it helps.

Can you please elaborate the steps for statement 1?

$$4^{(x–1)} < 4^x – 120$$;

$$\frac{4^x}{4}<4^x-120$$;

Add 120 to both sides: $$\frac{4^x}{4}+120<4^x$$;

Subtract 4^x/4 from both sides: $$20<4^x-\frac{4^x}{4}$$;

$$120<\frac{3}{4}*4^x$$;

Multiply by 4/3: $$160<4^x$$;

x is an integer greater than 3: 4, 5, 6, 7, ... Not sufficient.
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Re: If x is an integer, is 3^x less than 500? (1) 4^(x 1) <  [#permalink]

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Re: If x is an integer, is 3^x less than 500? (1) 4^(x 1) <   [#permalink] 17 Jan 2020, 18:57
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