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# What is the value of x?

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What is the value of x?  [#permalink]

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01 Jan 2011, 01:32
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26% (01:42) correct 74% (01:28) wrong based on 507 sessions

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What is the value of x?

(1) x^3 is a 2-digit positive odd integer.
(2) x^4 is a 2-digit positive odd integer.
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Re: Value of X  [#permalink]

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01 Jan 2011, 04:14
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shan123 wrote:
What is the value of x?
(1) X3 is a 2-digit positive odd integer. (2) X4 is a 2-digit positive odd integer.

I don't know whether the answer is correct. I got a different one.

What is the value of x?

Note that we are not told that x is an integer

(1) x^3 is a 2-digit positive odd integer --> now, if $$x$$ is an integer then $$x=3$$ as $$x^3=27$$ is the only odd 2-digit positive cube of an integer (1^3=1 and 5^3=125) but if $$x$$ is not an integer then it can be cube root of any 2-digit positive odd integer, for example if $$x=\sqrt[3]{11}$$ then $$x^3=11$$. Not sufficient.

(2) x^4 is a 2-digit positive odd integer --> basically the same here: if $$x$$ is an integer then $$x=3$$ or $$x=-3$$ as $$x^4=81$$ is the only odd 2-digit positive integer which is in fourth power of an integer (1^4=1 and 5^4=625) (so even if $$x$$ is an integer this statement is still insufficient as it gives two values for $$x$$: 3 and -3). $$x$$ also can be non-integer as above: it can be fourth root from any 2-digit positive odd integer, for example if $$x=\sqrt[4]{11}$$ then $$x^4=11$$. Not sufficient.

(1)+(2) $$x$$ cannot be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient.

Answer: C.
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Re: Value of X  [#permalink]

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23 May 2014, 10:41
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2
MensaNumber wrote:
Bunuel wrote:
shan123 wrote:

(1)+(2) $$x$$ cannot be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient.

Answer: C.

Hi Bunuel: Just like others, I also have a hard time visualizing that there does not exist an irrational number whose 3rd and 4th power both result in an odd digit integer. I mean integer is a smaller set compared to irrational numbers and we still have 3 (an integer) whose 3rd and 4th power both result in an odd 2-digit integer. On the other hand in terms of irrational numbers we have tremendous possibilities even between two integers we have infinite irrational numbers and we cannot have such a number. It some how feels odd to me. I have no doubt what you are saying is right but I have hard time imagining it. Maybe my understanding of irrational numbers and their powers is still primordial.

Say x IS an irrational number and x*x*x=x^3=integer. In this case x*x*x*x=x^3*x=integer*irrational=irrational.

If x is an irrational number and x*x*x*x=x^4=integer, then x^3=x^4/x=integer/irrational=irrational.

So, as you can see if x is an irrational number, then both x^3 and x^4 cannot be rational.

Does this make sense?
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Re: What is the value of x?  [#permalink]

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05 Jan 2013, 23:42
3
Glad that helped.

Always watch out for ZIP trap (assuming Zero, Integer, Positive) -> (Make sure to check for 0, factions and negatives)
Especially for inequalities, algebraic, number/fraction problems.
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Finance your Student loan through SoFi and get $100 referral bonus : Click here Senior Manager Status: Up again. Joined: 31 Oct 2010 Posts: 454 Concentration: Strategy, Operations GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42 Re: Value of X [#permalink] ### Show Tags 17 Feb 2011, 23:29 1 Carelessly, I overlooked the possibility that x could be negative. Thanks Bunuel! _________________ My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html Intern Joined: 23 Nov 2010 Posts: 5 Location: India Re: Value of X [#permalink] ### Show Tags 01 Jan 2011, 04:48 Bunuel wrote: shan123 wrote: What is the value of x? (1) X3 is a 2-digit positive odd integer. (2) X4 is a 2-digit positive odd integer. I don't know whether the answer is correct. I got a different one. What is the value of x? Note that we are not told that x is an integer (1) x^3 is a 2-digit positive odd integer --> now, if $$x$$ is an integer then $$x=3$$ as $$x^3=27$$ is the only odd 2-digit positive cube of an integer (1^3=1 and 5^3=125) but if $$x$$ is not an integer then it can be cube root of any 2-digit positive odd integer, for example if $$x=\sqrt[3]{11}$$ then $$x^3=11$$. Not sufficient. (2) x^4 is a 2-digit positive odd integer --> basically the same here: if $$x$$ is an integer then $$x=3$$ or $$x=-3$$ as $$x^4=81$$ is the only odd 2-digit positive integer which is in fourth power of an integer (1^4=1 and 5^4=625) (so even if $$x$$ is an integer this statement is still insufficient as it gives two values for $$x$$: 3 and -3). $$x$$ also can be non-integer as above: it can be fourth root from any 2-digit positive odd integer, for example if $$x=\sqrt[4]{11}$$ then $$x^4=11$$. Not sufficient. (1)+(2) $$x$$ can not be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient. Answer: C. Thanks for the answer and detailed explanation. Manager Joined: 17 Feb 2011 Posts: 143 Concentration: Real Estate, Finance Schools: MIT (Sloan) - Class of 2014 GMAT 1: 760 Q50 V44 Re: Value of X [#permalink] ### Show Tags 18 Feb 2011, 10:25 Tricky one, I considered the integer constraint that didn't exist. Must take care with this. Bunuel wrote: shan123 wrote: What is the value of x? (1) X3 is a 2-digit positive odd integer. (2) X4 is a 2-digit positive odd integer. I don't know whether the answer is correct. I got a different one. What is the value of x? Note that we are not told that x is an integer (1) x^3 is a 2-digit positive odd integer --> now, if $$x$$ is an integer then $$x=3$$ as $$x^3=27$$ is the only odd 2-digit positive cube of an integer (1^3=1 and 5^3=125) but if $$x$$ is not an integer then it can be cube root of any 2-digit positive odd integer, for example if $$x=\sqrt[3]{11}$$ then $$x^3=11$$. Not sufficient. (2) x^4 is a 2-digit positive odd integer --> basically the same here: if $$x$$ is an integer then $$x=3$$ or $$x=-3$$ as $$x^4=81$$ is the only odd 2-digit positive integer which is in fourth power of an integer (1^4=1 and 5^4=625) (so even if $$x$$ is an integer this statement is still insufficient as it gives two values for $$x$$: 3 and -3). $$x$$ also can be non-integer as above: it can be fourth root from any 2-digit positive odd integer, for example if $$x=\sqrt[4]{11}$$ then $$x^4=11$$. Not sufficient. (1)+(2) $$x$$ can not be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient. Answer: C. VP Status: Current Student Joined: 24 Aug 2010 Posts: 1337 Location: United States GMAT 1: 710 Q48 V40 WE: Sales (Consumer Products) Re: Value of X [#permalink] ### Show Tags 18 Feb 2011, 13:13 1 I always forget about radical roots. Thanks for the explanation Bunnel. _________________ The Brain Dump - From Low GPA to Top MBA (Updated September 1, 2013) - A Few of My Favorite Things--> http://cheetarah1980.blogspot.com Manager Joined: 04 Oct 2011 Posts: 165 Location: India Concentration: Entrepreneurship, International Business GMAT 1: 440 Q33 V13 GPA: 3 Re: What is the value of x? [#permalink] ### Show Tags 05 Jan 2013, 22:47 carcass wrote: What is the value of$$x$$ ? (1) $$X^3$$ is a 2-digit positive odd integer. (2)$$X^4$$ is a 2-digit positive odd integer. Hi carcass, Stat 1 : Only 2 digit positive integers for S1 are : $$x$$-------- 3 ------ 4 $$x^3$$ ----27-----64 Here odd integer is x=3 and x^3 = 27 SUFFICIENT Stat 2 : Only 2 digit positive integers for S2 are : $$x$$----------+/-2-------------+/-3 $$x^3$$----------16----------81 Here odd integer is x=+/-3 and x^3 = 81 INSUFFICIENT (two values for x) IMO A. But how come C? did i missed out anything? Senior Manager Joined: 27 Jun 2012 Posts: 347 Concentration: Strategy, Finance Schools: Haas EWMBA '17 Re: What is the value of x? [#permalink] ### Show Tags 05 Jan 2013, 22:55 Shanmugam, the problem doesnt explicitly state that x is an integer. It can be fraction. e.g. Choice (A), x can be fraction -> $$x^3 = 35$$ i.e. x = $$\sqrt[3]{35}$$ Similarly Choice (B) alone is not sufficient. Hence (C) is the answer. _________________ Thanks, Prashant Ponde Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here Finance your Student loan through SoFi and get$100 referral bonus : Click here
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Re: What is the value of x?  [#permalink]

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06 Jan 2013, 05:47
Sorry Bunuel I do not "visualize" why in C $$x^3$$ and $$x^4$$cannot be rational numbers aka integers

because an irrational can't be at the same time an 2 digits odd number ?' and of course only 3 meets both conditions ?'

Can you explain me please ?'

Thanks
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Re: What is the value of x?  [#permalink]

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07 Jan 2013, 04:12
carcass wrote:
Sorry Bunuel I do not "visualize" why in C $$x^3$$ and $$x^4$$cannot be rational numbers aka integers

because an irrational can't be at the same time an 2 digits odd number ?' and of course only 3 meets both conditions ?'

Can you explain me please ?'

Thanks

Not sure I understand what you mean.

Anyway, rational numbers and integers are not the same. Also, irrational numbers are not integers, thus they can be neither odd nor even.

For more check here: math-number-theory-88376.html
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Re: What is the value of x?  [#permalink]

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07 Jan 2013, 05:29
basically 1) is insuff because we have to consider integers and non integers (so irrational numbers). Same for 2)

Bothe statements are suff because we have only 3 that mettes the criteria so we have to consider only the 3 (the integer). So sufficient

But why we C is sufficient ?' why we can not consider the irrational numbers ??

Thanks. Now I hope is more clear what I mean. I'm sorry if I have explained myself badly
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Re: What is the value of x?  [#permalink]

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07 Jan 2013, 06:11
carcass wrote:
basically 1) is insuff because we have to consider integers and non integers (so irrational numbers). Same for 2)

Bothe statements are suff because we have only 3 that mettes the criteria so we have to consider only the 3 (the integer). So sufficient

But why we C is sufficient ?' why we can not consider the irrational numbers ??

Thanks. Now I hope is more clear what I mean. I'm sorry if I have explained myself badly

If x is an irrational number then x^3 and x^4 cannot both be integers as given in the statements, so x can only be 3.
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Re: Value of X  [#permalink]

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23 May 2014, 07:25
Bunuel wrote:
shan123 wrote:

(1)+(2) $$x$$ cannot be an irrational number (so that both x^3 and x^4 to be integers), so $$x$$ must be 3. Sufficient.

Answer: C.

Hi Bunuel: Just like others, I also have a hard time visualizing that there does not exist an irrational number whose 3rd and 4th power both result in an odd digit integer. I mean integer is a smaller set compared to irrational numbers and we still have 3 (an integer) whose 3rd and 4th power both result in an odd 2-digit integer. On the other hand in terms of irrational numbers we have tremendous possibilities even between two integers we have infinite irrational numbers and we cannot have such a number. It some how feels odd to me. I have no doubt what you are saying is right but I have hard time imagining it. Maybe my understanding of irrational numbers and their powers is still primordial.
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Re: Value of X  [#permalink]

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23 May 2014, 12:38
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Bunuel wrote:
Say x IS an irrational number and x*x*x=x^3=integer. In this case x*x*x*x=x^3*x=integer*irrational=irrational.

If x is an irrational number and x*x*x*x=x^4=integer, then x^3=x^4/x=integer/irrational=irrational.

So, as you can see if x is an irrational number, then both x^3 and x^4 cannot be rational.

Does this make sense?

Wow! Makes complete sense. This explanation is superb. Thanks!
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Re: What is the value of x?  [#permalink]

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30 Apr 2017, 19:50
Innocuous looking deadly snake this one !!!
bowled me ....
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Re: What is the value of x?  [#permalink]

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01 Sep 2017, 08:36
since x can be any number than an integer, and x can have negative value, combine 2 statement will yield the answer.
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Re: What is the value of x?   [#permalink] 24 Nov 2019, 09:34
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