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M02-36

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M02-36  [#permalink]

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New post 16 Sep 2014, 00:19
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A
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E

Difficulty:

  45% (medium)

Question Stats:

55% (00:47) correct 45% (01:01) wrong based on 210 sessions

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If \(x\) is an integer, what is the value of \(x\)?


(1) \(x^2 = x^3\)

(2) \(x\) is both a perfect square and a perfect cube. (Note: a perfect square, is an integer that can be written as the square of an integer. For example \(16=4^2\), is a perfect square. Similarly a perfect cube, is an integer that can be written as the cube of an integer. For example \(27=3^3\), is a perfect cube.)

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Re M02-36  [#permalink]

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New post 16 Sep 2014, 00:19
Official Solution:


Statement (1) by itself is insufficient. \(x\) can be 0 or 1.

Statement (2) by itself is insufficient. Perfect squares are integers 0, 1, 4, 9, 16, and so on. Similarly, perfect cubes are: 0, 1, 8, 27, 64... Thus \(x\) can be 0 or 1.

Statements (1) and (2) combined are insufficient. For example: \(x\) can still be 0 or 1.


Answer: E
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Re: M02-36  [#permalink]

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New post 07 Nov 2014, 11:02
the hint in the question seems misleading especially when it is read very literally

hint says: Similarly a perfect cube, is an integer that can be written as the cube of some other integer-----------> this implies that 1 cannot be a perfect cube because 1 cannot be written as a cube of "some other integer" but yes it can be written as a cube of 1 itself !! , according to this hint numbers like 125 ( for 125 can be written as 5^3 ---->other integer 5 ) will fall into this definition .
however , if one does not look at the hint then it is oki because as per common knowledge 1 does qualify as perfect cube
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Re: M02-36  [#permalink]

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New post 27 Dec 2014, 05:27
aditya8062 wrote:
the hint in the question seems misleading especially when it is read very literally

hint says: Similarly a perfect cube, is an integer that can be written as the cube of some other integer-----------> this implies that 1 cannot be a perfect cube because 1 cannot be written as a cube of "some other integer" but yes it can be written as a cube of 1 itself !! , according to this hint numbers like 125 ( for 125 can be written as 5^3 ---->other integer 5 ) will fall into this definition .
however , if one does not look at the hint then it is oki because as per common knowledge 1 does qualify as perfect cube


i agree with you,
this definition confused me
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Re: M02-36  [#permalink]

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New post 29 Apr 2015, 18:12
It's a quite controversial problem.
Hope I won't face similar one on the GMAT.

http://mathforum.org/library/drmath/view/52368.html
http://www.ask.com/math/zero-perfect-sq ... 33a2cfecf1
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Re: M02-36  [#permalink]

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New post 24 Sep 2015, 12:19
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient. \(x\) can be 0 or 1.

Statement (2) by itself is insufficient. Perfect squares are integers 0, 1, 4, 9, 16, and so on. Similarly, perfect cubes are: 0, 1, 8, 27, 64... Thus \(x\) can be 0 or 1.

Statements (1) and (2) combined are insufficient. For example: \(x\) can still be 0 or 1.


Answer: E


I think for stmnt 2) 0,1,64,729 are there but i ignored 0 and 1 becoz u said cube and square of "other" number
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Re: M02-36  [#permalink]

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New post 17 Nov 2015, 16:37
I agree. The hint in (2) is really confusing. However, I don't know why I thought 1, but not 0, satisfy this condition and thus chose B as the correct answer :).
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Re: M02-36  [#permalink]

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New post 14 Dec 2015, 04:39
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I think this is a high-quality question and I agree with explanation. Please change the definition containing "of some other integer" to " of any integer" ; then the question is right; else 0 and 1 cannot be answers to option 2, thanks.
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Re: M02-36  [#permalink]

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New post 19 Jan 2016, 10:43
joyandbliss wrote:
I think this is a high-quality question and I agree with explanation. Please change the definition containing "of some other integer" to " of any integer" ; then the question is right; else 0 and 1 cannot be answers to option 2, thanks.


Updated the question.
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M02-36  [#permalink]

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New post Updated on: 13 May 2018, 11:42
NOTE THIS PLEASE ... the question clearly states that x is an INTEGER so x^2 = x^3 should be sufficient as 0 does not qualify as an integer and x can only take the value 1.THE question starts as if x is an INTEGER.
give me kudos if you think iam right:)

Originally posted by Vibhav10 on 13 May 2018, 11:35.
Last edited by Vibhav10 on 13 May 2018, 11:42, edited 1 time in total.
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M02-36  [#permalink]

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New post 13 May 2018, 11:40
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient. \(x\) can be 0 or 1.

Statement (2) by itself is insufficient. Perfect squares are integers 0, 1, 4, 9, 16, and so on. Similarly, perfect cubes are: 0, 1, 8, 27, 64... Thus \(x\) can be 0 or 1.

Statements (1) and (2) combined are insufficient. For example: \(x\) can still be 0 or 1.


Answer: E

NOTE THIS PLEASE ... the question clearly states that x is an INTEGER so x^2 = x^3 should be sufficient as 0 does not qualify as an integer and x can only take the value 1.THE question starts as if x is an INTEGER. i may be wrong somewhere though.
give me kudos if you think iam right:)
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Re: M02-36  [#permalink]

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New post 13 May 2018, 12:36
Vibhav10 wrote:
Bunuel wrote:
Official Solution:


Statement (1) by itself is insufficient. \(x\) can be 0 or 1.

Statement (2) by itself is insufficient. Perfect squares are integers 0, 1, 4, 9, 16, and so on. Similarly, perfect cubes are: 0, 1, 8, 27, 64... Thus \(x\) can be 0 or 1.

Statements (1) and (2) combined are insufficient. For example: \(x\) can still be 0 or 1.


Answer: E

NOTE THIS PLEASE ... the question clearly states that x is an INTEGER so x^2 = x^3 should be sufficient as 0 does not qualify as an integer and x can only take the value 1.THE question starts as if x is an INTEGER. i may be wrong somewhere though.
give me kudos if you think iam right:)


That's wrong.

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

You should brush-up fundamentals before practising questions:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread

Hope it helps.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M02-36 &nbs [#permalink] 13 May 2018, 12:36
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