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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]

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New post Updated on: 29 Oct 2012, 03:18
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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.
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If x is an integer, is 3^x less than 500?  [#permalink]

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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.

Similar questions to practice:
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http://gmatclub.com/forum/is-3-x-134968.html

Hope it helps.
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Re: Inequality problem  [#permalink]

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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.

Kudos Please... If my post helped.
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Re: Inequality problem  [#permalink]

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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]

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New post 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.

Answer : B
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Re: Inequality problem  [#permalink]

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New post 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.
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Re: If x is an integer, is 3^x less than 500?  [#permalink]

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

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New post 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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Re: If x is an integer, is 3^x less than 500?  [#permalink]

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New post 04 Jun 2019, 22:45
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goeladit wrote:
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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New post 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 ??


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.

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?
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Re: If x is an integer, is 3^x less than 500?  [#permalink]

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New post 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 ??


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.

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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