1) INSUFFICIENT - you will not know if x is positive or negative.
2) INSUFFICIENT - could be any negative number and some positive numbers.

Answer C, x would equal roughly -20.5, which would mean you can calculate x^5. 1 gives you two numbers to choose from and 2 tells you it is negative.

Hi Jim, Thanks for your explanation. How did you calculate -20.5 for x? And 2) x^9 < any number less then 23 would satisfy the answer C, right? And then If 2) x^9 < 24, the answer could not be C? I am a little bit confused about 23.

dreamv wrote:What is value of X^5?

1)X^2=426
2)X^9 < 23

st(1) implies x=|sqrt(426)| which is Not Sufficient
st(2) implies x can be assigned any value to the left of 23^(5/9) Not Sufficient

Only combining st(1&2) is Sufficient and you don't need to calculate the exact values like -20.5 or -20.65 to answer this question, because this is DS type of question which requires sufficiency test only.

c

dreamv wrote:Hi Jim, Thanks for your explanation. How did you calculate -20.5 for x? And 2) x^9 < any number less then 23 would satisfy the answer C, right? And then If 2) x^9 < 24, the answer could not be C? I am a little bit confused about 23.

when two statements are combined their jointly assigned values are considered, from st(1) x=-sqrt(426) and from st(2) x^5<23^(5/9) and not x^9 < 24, because the powers are different in your doubt.

really a good sum to entertain...

hello every one,
i am confused as to how C is the answer..


can any one provide a better way

pappueshwar wrote:hello every one,
i am confused as to how C is the answer..


can any one provide a better way

This is one of those rare cases where DS actually saves us some trouble...in this case we don't actually have to calculate anything!

The key to this problem is knowing the following:

x^2 = 25 is NOT the same thing as x = sqrt(25)

This is because both 5*5 = 25 AND -5*-5 = 25, which both work for x^2 = 25

So from part (1), we are able to narrow down the answer for x to two possibilities:
+sqrt(426)
OR
-sqrt(426)

Now, if the case statement were to determine x^4 or x^6 or any other even power, the answer would be A, because any number to an even power is positive, regardless of its sign (in this case + or - sqrt(426). But the question is to find x^5, which can be two different values, based on part (1) alone.

From part (2), we are told that x^9 < 23.

Obviously the makers of the GMAT don't want us wasting time raising a number like sqrt(426) to the power of 9, so there must be another reason they are giving us this bit of info...

Clearly, part 2 alone is INSUFFICIENT, since there are infinite values of x that can give us a value for x^9 less than 23 (fractions and negative numbers especially).

Combining parts (1) and (2):

The real reason they are giving us part 2 becomes evident when joining together both parts: they are telling us that x is less than 23. From part (1), we know that the negative possibility is less than 23, but what about the possitive possibility??

Since the sqrt(426)^2 is 426, which is MUCH larger than 23, we can safely assume that x^9 is also larger than 23.

Therefore, only -sqrt(426) will work for x, which will allow for one, distinct answer for x^5. No messy calculations needed.

C