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

Explanation:

Official Answer: B

Statement 1 is not sufficient. Both x=2 and x=-2 satisfy the inequality. If x=2, the answer is YES, if x=-2, the answer is NO.

Statement 2 is sufficient by itself. The statement can be rewritten as x^5 < x^3. This will hold true when x \in (0,1) for positive x and x \in (-\infty, -1) for negative x. In both cases x is less than 1. The answer to the question is NO.
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One last post on this thread. I see that my initial approach for the 2nd statement was not as fast as it could be. Here goes the simplified version:

Stat2
if x>0 then x^3>x^5 => x<1 => Sufficient, but I'll do x<0 for the sake of it.
if x<0 then x^3>x^5 => x<-1
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Hi dzyubam, would you please explain again why statement 2 is sufficient

Thx again

You forget that x can be any number from the range (0,\infty) in order to satisfy S1. x < -1 is not a complete solution. Both 2 and -2 satisfy S1, as stated in the OE. S1 is not sufficient.

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Not clear.Even I got x<-1.How do you solve this question without plugging in value of x?
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countdown-beginshas-ended-85483-40.html#p649902

Somehow I usually slow down when picking numbers in DS problems, so I prefer an algebraic approach whenever I spot that an easy one is possible.

This is how I did this exercise:

Stat1
if x>0 then x>-1 => x>0. Not sufficient; no need to test for x<0.

Stat2
if x>0 then x<1 and x<-1 => 0<x<1. Sufficient; x is not greater than 1; no need to test for x<0.

Of course, easier explained online than done against the clock:)

Since I didn't know about this rule:

\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.

...I simply went ahead and pluggeed-in "2" and "-2" for the the second expression (just like the first). In this way, I concluded a "NO" answer for both 1/32 > 1/8 and -1/32 > -1/8

Let me see if I understand this question correctly - and DS problems in general since they are throwing me off left and right simply because of their demand of figuring out "yes" or "no" "yes + no" for every possibility. **So please at least tell me if I have approached this question in the correct way**



#1 The question is asking if x is greater than 1. Now I have to look at each possibility individually and plug-in numbers until I can justify whether the possibility is, in itself, enough to answer the original question stem.


#2 So, the first possibility gives us \frac{1}{x} > -1

Now I have to choose two numbers ("2" for ease) and both + and - to see if this possibility will prove the stem.

For a +2: \frac{1}{2} > -1 *This holds true as +0.5 is > -1

However,

For a -2: \frac{1}{-2} > -1 *This is also a confirmation of the expression itself, but creates a conflict with the stem which is only looking for the confirmation of x being greater than 1.

Therefore, the answer "A" can be ruled out and we are left with the possibilities of B, C or E.


#2 Now if I am to look at the second possibility, \frac{1}{x^5} > \frac{1}{x^3}, and have not "simplified it" for whatever reason (i.e. I didn't know that rule)... I will plug in the same two numbers to see what happens.

For a +2: \frac{1}{2^5} > \frac{1}{2^3}

=\frac{1}{32} > \frac{1}{8} *This does not hold true as +3.125% is not > +12.5%

However, now...

For a -2: \frac{1}{-2^5} > \frac{1}{-2^3}

=\frac{1}{-32} > \frac{1}{-8} *This does hold true as -3.125% is > -12.5%


Now I am thoroughly confused, because I'm being tricked with the second possibility (#2) with a +# as "not true" and a -# as "true." This is the main reason I think that I am failing at these DS q's because I thought that any possibility that presents both a "Yes" and "No" answer is therefore "IN SUFFICIENT"...


Where have I gone wrong here?

Hi...

I feel answer to this question must by E .

Statement (1) is obvious why it is not sufficient to find the answer

About Statement (2)

i) x = 1/2
( 1/x(power 5) = 32 ) > (1/x(power3) = 8 )

ii) x = -2
(1/x(power 5) = -1/32 ) > ( 1/x(power3) = -1/8 )

iii) x = -1/2
(1/x(power 5) = -32) < (1/x(power3) = -8 )

So that statement is also not sufficient . Please respond to my reasoning !!!

Thanks