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X, Y>0, If X^3 = Y, is Y a fraction? (1) X^2 is a

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X, Y>0, If X^3 = Y, is Y a fraction? (1) X^2 is a [#permalink] New post 15 Nov 2004, 13:44
X, Y>0, If X^3 = Y, is Y a fraction?

(1) X^2 is a fraction.

(2) X > Y.
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 [#permalink] New post 15 Nov 2004, 14:07
This one is tricky.

First from the stem Y>0 so X>0

Statement 1 : X^2 is a fraction

if X^2 is a fraction, X is a fraction as well as Y

Statement 2 : X > X^3 > 0 so X <1 : Y is a fraction

So I choose D
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 [#permalink] New post 15 Nov 2004, 14:40
What if.. X=2^(1/3) ?
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 [#permalink] New post 15 Nov 2004, 14:57
I thought about this ^(1/3) point.

My reasoning was x^1/3 is not necessarily a fraction - I was wondering whether every number could be described as a ratio of 2 relative numbers ??
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 [#permalink] New post 15 Nov 2004, 15:19
I think B is the answer.

If X^2 is a fraction, we cann't say for certainity that X^3 is a fraction. So, (1) is insufficient
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 [#permalink] New post 16 Nov 2004, 00:09
I'll go with B.

Statement 1--- when we take x=5^(1/3) or 4(1/3) etc... then x^2 is a fraction but x^3 is not, hence in this case y is not a fraction.

but if x^2=1/4, x^3=1/8, hence y is a fraction.

so statement 1 is insufficient.

statement 2----

suppose x^3=1/125, y is a fraction. (x=1/5)> y is satisfied.

x^3= 27/8000, y is a fraction. x=3/20 which is greater than y.

hence statement 2 is sufficient.
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 [#permalink] New post 16 Nov 2004, 00:14
Anonymous wrote:
I'll go with B.

Statement 1--- when we take x=5^(1/3) or 4^(1/3) etc... then x^2 is a fraction but x^3 is not, hence in this case y is not a fraction.

but if x^2=1/4, x^3=1/8, hence y is a fraction.

so statement 1 is insufficient.

statement 2----

suppose x^3=1/125, y is a fraction. (x=1/5)> y is satisfied.

x^3= 27/8000, y is a fraction. x=3/20 which is greater than y.

hence statement 2 is sufficient.


sorry that was me :roll:
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is Y a fraction? [#permalink] New post 16 Nov 2004, 03:43
I think it is B, but I also think that we are discussing semantics here.

Plugging in:
x^2= 1/2 , x = 1/ sqrt (2) , x^3= sqrt(2) / 4 This is not a fraction.
x^2= 9/4 , x = 3/ 2 , x^3= 27/8. This is a fraction.

Sqrt(2) / 4 is not a fraction because is not a rational number. Sqrt (2) is irrational, not an integer.

Rational numbers are those that can be written as a fraction of two integers (it will not be defined if the denominator =0) and rational numbers can be integers or fractions.

If x=n^(1/3), I think that x^2 can only be a fraction for those cases where n is a fraction where numerator and denominator are perfect cubes, and for these cases, x^3 will always be a fraction. All other values of n will give x^2 either integers or irrationals.

So could be D, depending on semantics. If we call sqrt (2) / 4 a fraction, then answer is B. But if we say that sqrt (2) / 4 is an irrational number and therefore not a fraction, then answer is B. So we just need to find out what’s ETS definition of fractional and irrational. :?
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 [#permalink] New post 16 Nov 2004, 05:28
Hello, everybody!

I'm a newcomer here.
Could anyone please clarify if there were any varants of answers in this subject.
Because I've not seen A) B) C) D) there and can't understand if sonmeone says "I think it's D" for example.

Thank you in advance,
Serzh
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Re: is Y a fraction? [#permalink] New post 16 Nov 2004, 05:44
artabro wrote:
I think it is B, but I also think that we are discussing semantics here.

Plugging in:
x^2= 1/2 , x = 1/ sqrt (2) , x^3= sqrt(2) / 4 This is not a fraction.
x^2= 9/4 , x = 3/ 2 , x^3= 27/8. This is a fraction.

Sqrt(2) / 4 is not a fraction because is not a rational number. Sqrt (2) is irrational, not an integer.

Rational numbers are those that can be written as a fraction of two integers (it will not be defined if the denominator =0) and rational numbers can be integers or fractions.

If x=n^(1/3), I think that x^2 can only be a fraction for those cases where n is a fraction where numerator and denominator are perfect cubes, and for these cases, x^3 will always be a fraction. All other values of n will give x^2 either integers or irrationals.

So could be D, depending on semantics. If we call sqrt (2) / 4 a fraction, then answer is B. But if we say that sqrt (2) / 4 is an irrational number and therefore not a fraction, then answer is B. So we just need to find out what’s ETS definition of fractional and irrational. :?



Thank you Artabro for adding your opinion. Maybe we are over reading the question but this kind of point deserves to be understood.


I know that not every number can be described as a ratio of integers ; I do think sqrt can not be described in this manner as well. I was wondering if every number can result from a ratio of 2 relative numbers ?

What is your opinion on these points ?
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 [#permalink] New post 16 Nov 2004, 05:49
I vote for B as well.

Serzh: Data sufficiency questions always have the same answer choices and they are

A) statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

B) statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;

D) EACH statement ALONE is sufficient to answer the question asked;

E) statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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 [#permalink] New post 16 Nov 2004, 07:15
gayathri:

Thanks a lot!
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 [#permalink] New post 16 Nov 2004, 07:29
Guest Posted: Tue Nov 16, 2004 7:15 am Post subject:

--------------------------------------------------------------------------------

gayathri:

Thanks a lot!


That was me :-D
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 [#permalink] New post 16 Nov 2004, 09:00
Great discussion.

Anyway, a "Fraction" is a ratio between two whole numbers.
Roots, like sqrt(2) or 2^(1/3) are Irrational numbers.
They can not be described as a ratio between two numbers.

So the answer is D.
It is true that we are talking semantics here, but ETS assumes that we are familiar with those definitions.

I guess we all learned something from this question :)
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 [#permalink] New post 16 Nov 2004, 14:23
Right Dookie, thanks for posting this one, we all learnt something !

One more ?! :wink:
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 [#permalink] New post 17 Nov 2004, 13:58
I just checked what ETS says about the numbers it uses.
It says "All numbers used are real".
So that'd mean they can be rational or irrational (square root 2, sqrt 3 etc).
So that means the ans to the original question would be B and not D.

Does everyone agree?
I think this is an important discussion because we need to be clear about this issue, esp. in DS where we can not assume ANYTHING!
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 [#permalink] New post 17 Nov 2004, 13:59
Sorry, that was me!
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 [#permalink] New post 17 Nov 2004, 14:18
Fractions and Irrational numbers are both "Real" numbers.

Numbers that are not real numbers are called "Complex numbers", and they are out of scope.
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 [#permalink] New post 17 Nov 2004, 17:31
I agree with Dookie. Real numbers can be rational or irrational. Check this link

http://en.wikipedia.org/wiki/Real_number

Dookie - Do you know that OA?
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  [#permalink] 17 Nov 2004, 17:31
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