Problem Solving

REINE wrote:What is the value of k?

Hi REINE,

Statement 1: k^4=1/625

=> k^4 = 1/(5^4)

=> k = 1/5 or -1/5. No unique value of k. Insufficient.

Statement 1: k^3 < k^2

Clearly insufficient.

Say k = -1/5, then (-1/5)^3 < (-1/5)^2 => -1/625 < 1/25.

Say k = 1/5, then (1/5)^3 < (1/5)^2 => 1/625 < 1/25. No unique value of k. Insufficient.

I deliberately chose the values of k that I derived in Statement 1 so that we can test them in Statement 2.

Statement 1 & 2 combined:

Even after combining both the statements won't help as k= -1/5 and 1/5 hold true for both. Insufficient.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Number Properties Guide

-Jay
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Hi REINE,

This DS question is based around several Number Properties - so if you recognize those rules, then you can actually avoid all of the calculations in this prompt.

We're asked for the value of K.

1) K^4 = 1/625

Since K is raised to an EVEN exponent, there will be TWO solutions to this equation (one positive and one negative) and both will be specific FRACTIONS. Since there are two different values....
Fact 1 is INSUFFICIENT

2) K^3 < K^2

ANY positive fractional value of K in the range 0 < K < 1 will 'fit' this information, so there are clearly an unlimited number of values for K here.
Fact 2 is INSUFFICIENT

Combined, we know...
-K is either one specific POSITIVE FRACTION or one specific NEGATIVE FRACTION.

Raising a positive fraction to a higher exponent makes that fraction SMALLER. For example (1/2)^2 = 1/4 and (1/2)^3 = 1/8. Thus, that specific positive fractional value of K that we noted in Fact 1"fits" K^3 < K^2.

Squaring a negative fraction makes the result POSITIVE. For example (-1/2)^2 = +1/4
Cubing a negative fraction makes the result NEGATIVE. For example (-1/2)^3 = -1/8
Thus, that specific negative fractional value of K that we noted in Fact 1 "fits" K^3 < K^2.

Ultimately, K could be EITHER of the two specific values that were possible in Fact 1.
Combined, INSUFFICIENT.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich