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GMAT Diagnostic Test Question 9

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Re: GMAT Diagnostic Test Question 9 [#permalink] New post 05 Nov 2012, 11:05
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] New post 05 Nov 2012, 12:30
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.

Answer: B



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] New post 06 Nov 2012, 06:18
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.

Answer: B



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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Re: GMAT Diagnostic Test Question 9 [#permalink] New post 06 Nov 2012, 07:06
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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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. NEW!!!

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Re: GMAT Diagnostic Test Question 9   [#permalink] 06 Nov 2012, 07:06
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