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# GMAT Diagnostic Test Question 10

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Manager
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Re: GMAT Diagnostic Test Question 9 [#permalink]  05 Nov 2012, 10:05
dzyubam wrote:
The trick to remember during solving this question is that fractions in the range $$(0,1)$$ taken to greater power get smaller, for example $$\left(\frac{1}{3}\right)^3 < \left(\frac{1}{3}\right)^2$$, etc.

$$\frac{1}{x^5} > \frac{1}{x^3}$$ is equivalent to $$x^5 < x^3$$. because if two fractions have equal numerators, the fraction with a smaller denominator is the bigger one. Now we need to find the range of values of $$x$$ in which $$x^5 < x^3$$ holds true. This is possible in $$x \in (0,1)$$ for positive $$x$$ and in $$x \in (-\infty,-1)$$ for negative $$x$$.

We can put the values of $$x$$ from these ranges to make sure it works:

positive $$x=\frac{1}{2}$$:
$$\left(\frac{1}{2}\right)^5 < \left(\frac{1}{2}\right)^3$$
$$\left(\frac{1}{32}\right) < \left(\frac{1}{8}\right)$$ -- holds true

negative $$x=-2$$:
$$(-2)^5 < (-2)^3$$
$$-32 < -8$$ -- holds true

In either range the value of $$x$$ is smaller than 1, so Statement (2) is sufficient by itself.

Hope this helps.
defoue wrote:
Hi dzyubam, would you please explain again why statement 2 is sufficient

Thx again

what if x=2 in second statement.. i guess then it will not satisfy
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Re: GMAT Diagnostic Test Question 9 [#permalink]  05 Nov 2012, 11:30
dzyubam wrote:
We should probably revise the difficulty level of the question.
I like your approach. +1. Can't see anything wrong with it.
dpgxxx wrote:
Here is my way, which worries me by its simplicity in comparison to a "750" level problem. Please let me know if there are any errors in the following approach. I am not the best with these question types and am not sure if plugging in numbers, like others did, considers an element my approach does not.

S1) 1/X > - 1 ---> 1>-X ---> (multiply by -1/turn sign)---> -1<X ..... This means X can be -.5, 0, 1, 2..insufficient

S2) 1/X^5 > 1/X^3 --->(multiply both sides by X^3)---> 1/x^2 > 1 ---> 1>X2 ---> +-1 > X ...if X is less than 1 or -1, we know its not greater than 1; sufficient.

Ok. I belive there is something which is wrong.
S1) As per comments above X>-1 but X =-2 satisfies
-1/2 > -1 True

We cannot multiply variables in inequality without knowing their signs.
1/X > -1 will be solved as

Case 1) X>0 => -X<1 or X > -1 but X>0
so X>0

Case 2) X<0 => Multiply by X and change sign -X>1 or X < -1

S2) 1/X^5 > 1/X^3

1/(X*X^4) > 1/(X*X^2)
(X^2 and X^4 are positive)

X^2/X > X^4/X
or X > X^3
X (X^2-1) < 0

0<X<1 or X<-1
Therefore Ans B

Question deserves to be at this level.
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Re: GMAT Diagnostic Test Question 9 [#permalink]  06 Nov 2012, 05:18
Expert's post
BangOn wrote:
dzyubam wrote:
We should probably revise the difficulty level of the question.
I like your approach. +1. Can't see anything wrong with it.
dpgxxx wrote:
Here is my way, which worries me by its simplicity in comparison to a "750" level problem. Please let me know if there are any errors in the following approach. I am not the best with these question types and am not sure if plugging in numbers, like others did, considers an element my approach does not.

S1) 1/X > - 1 ---> 1>-X ---> (multiply by -1/turn sign)---> -1<X ..... This means X can be -.5, 0, 1, 2..insufficient

S2) 1/X^5 > 1/X^3 --->(multiply both sides by X^3)---> 1/x^2 > 1 ---> 1>X2 ---> +-1 > X ...if X is less than 1 or -1, we know its not greater than 1; sufficient.

Ok. I belive there is something which is wrong.
S1) As per comments above X>-1 but X =-2 satisfies
-1/2 > -1 True

We cannot multiply variables in inequality without knowing their signs.
1/X > -1 will be solved as

Case 1) X>0 => -X<1 or X > -1 but X>0
so X>0

Case 2) X<0 => Multiply by X and change sign -X>1 or X < -1

S2) 1/X^5 > 1/X^3

1/(X*X^4) > 1/(X*X^2)
(X^2 and X^4 are positive)

X^2/X > X^4/X
or X > X^3
X (X^2-1) < 0

0<X<1 or X<-1
Therefore Ans B

Question deserves to be at this level.

Check here: gmat-diagnostic-test-question-79337-20.html#p678344
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Posts: 27238
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Kudos [?]: 41151 [0], given: 5672

Re: GMAT Diagnostic Test Question 9 [#permalink]  06 Nov 2012, 06:06
Expert's post
breakit wrote:
what if x=2 in second statement.. i guess then it will not satisfy

Not sure I understand. x cannot be 2 for (2), since 1/32<1/8
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GMAT Date: 09-27-2013
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WE: Information Technology (Computer Software)
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Kudos [?]: 9 [0], given: 66

Re: GMAT Diagnostic Test Question 9 [#permalink]  12 Aug 2013, 07:46
Good explanation....

+1
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Re: GMAT Diagnostic Test Question 10 [#permalink]  10 Jan 2014, 02:29
Its crazy to me how this questions was SUPERRRRRRRR EASY to me but most are difficult to me...

GMAT 490
Quant 34
Verbal 27

This is why I hate the GMAT
Re: GMAT Diagnostic Test Question 10   [#permalink] 10 Jan 2014, 02:29

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# GMAT Diagnostic Test Question 10

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