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If x is an integer, is 3^x less than 500?
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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
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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?
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29 Oct 2012, 03:18
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; \(\frac{4^x}{4}<4^x120\); \(120<\frac{3}{4}*4^x\); \(160<4^x\); 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/isx10101 ... 27881.htmlhttp://gmatclub.com/forum/is5klesst ... 28055.htmlhttp://gmatclub.com/forum/ifxisanin ... 06353.htmlhttp://gmatclub.com/forum/is4x53x1 ... 86765.htmlhttp://gmatclub.com/forum/is5x134898.htmlhttp://gmatclub.com/forum/is3x134968.htmlHope it helps.
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Re: Inequality problem
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28 Oct 2012, 21:21
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
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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^x4^x1=120..how to get comon ..i did it.. but i tuk me more than one mint
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Re: Inequality problem
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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.
Answer : B



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Re: Inequality problem
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29 Oct 2012, 01:34
sanjoo wrote: yup. i also got B..
Lets C..wat experts r replying !!
can anyone tell me trick for this thing..
4^x4^x1=120..how to get comon ..i did it.. but i tuk me more than one mint \(4^x\) \(\)\(4^(x1)\) \(= 120\) \(4^x  \frac{4^x}{4} = 120\) \(\frac{3}{4}*4^x = 120\) Kudos Please... If my post helped.



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Re: If x is an integer, is 3^x less than 500?
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28 May 2014, 05:07
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?
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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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Re: If x is an integer, is 3^x less than 500?
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04 Jun 2019, 22:45
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?
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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 ?? 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 > \(\frac{4^x}{4}<4^x120\) > \(120<\frac{3}{4}*4^x\) > \(160<4^x\) > 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/isx10101 ... 27881.htmlhttp://gmatclub.com/forum/is5klesst ... 28055.htmlhttp://gmatclub.com/forum/ifxisanin ... 06353.htmlhttp://gmatclub.com/forum/is4x53x1 ... 86765.htmlhttp://gmatclub.com/forum/is5x134898.htmlhttp://gmatclub.com/forum/is3x134968.htmlHope 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?
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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 ?? 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 > \(\frac{4^x}{4}<4^x120\) > \(120<\frac{3}{4}*4^x\) > \(160<4^x\) > 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/isx10101 ... 27881.htmlhttp://gmatclub.com/forum/is5klesst ... 28055.htmlhttp://gmatclub.com/forum/ifxisanin ... 06353.htmlhttp://gmatclub.com/forum/is4x53x1 ... 86765.htmlhttp://gmatclub.com/forum/is5x134898.htmlhttp://gmatclub.com/forum/is3x134968.htmlHope it helps. Can you please elaborate the steps for statement 1? \(4^{(x–1)} < 4^x – 120\); \(\frac{4^x}{4}<4^x120\); 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) <
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Re: If x is an integer, is 3^x less than 500? (1) 4^(x 1) <
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