a is a nonzero integer. Is a^a greater than 1?

Question

(1) a < -1
(2) a is even

Bunuel · Accepted Answer

a is a nonzero integer. Is a^a greater than 1?

(1) a < -1. So, a could be -2, -3, -4, ... If a is a negative even integer, then a^a will be a positive fraction less than 1 (for example, if a = -2, then a^a = (-2)^(-2) = 1/4) and if a is a negative odd integer, then a^a will be a negative fraction greater than -1 (for example, if a = -3, then a^a = (-3)^(-3) = -1/27). In any case the result is less than 1. Sufficient.

(2) a is even. If a = 2, then a^a = 4 > 1 but if a = -2, then a^a = 1/4 < 1. Not sufficient.

Answer: A.

Hope it's clear.

23a2012 · Answer

Dear Bunuel, I think that (-2)^(-2) which is -1/2^2 should be negative fraction less than 1 and equal to = (- 1/4 )

EMPOWERgmatRichC · Answer

Hi 23a2012,

Unfortunately, that's NOT how the math "works"

When dealing with a negative exponent, you have to put the entire calculation "under" the 1.

With your example, we have (-2)^(-2). This can be rewritten as....

1/  = 1/4

IF....we were dealing with (-3)^(-3) though, we'd have.....

1/  = 1/-27 = -1/27

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

23a2012 · Answer

Ok, can you tell me how write -1/4 in the form a^a

chetan2u · Answer

hi ,
-2^-2= 1/(-2)^2=1/4....

EMPOWERgmatRichC · Answer

Hi 23a2012,

If you have an EVEN exponent, then you CANNOT have a negative outcome (unless the negative "sign" is "outside" of the exponent, and thus unaffected by the exponent).

eg
(2)^2 = 4
(2)^(-2) = 1/4

(-2)^(2) = 4
(-2)^-(2) = 1/4

(-1)  = (-1)  = -1/4

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

BrentGMATPrepNow · Answer

Target question :    Is a^a greater than 1?

Given : a is a nonzero integer.

Statement 1 : a < -1   
Let's start TESTING some values of a and see if we  discover a PATTERN

a = -2. Here a^a = (-2)^(-2) = 1/(-2)^2 = 1/4
a = -3. Here a^a = (-3)^(-3) = 1/(-3)^3 = 1/(-27) = - 1/27
a = -4. Here a^a = (-4)^(-4) = 1/(-4)^4 = 1/256
a = -5. Here a^a = (-5)^(-5) = 1/(-5)^5 = 1/(some negative value) = something negative
a = -6. Here a^a = (-6)^(-6) = 1/(-6)^6 = 1/(some positive integer) = a positive fraction that's less than 1
a = -7. Here a^a = (-7)^(-7) = 1/(-7)^7 = 1/(some negative value) = something negative
.
.
.
As we can see, when a is a NEGATIVE  EVEN  number,  a^a = some positive fraction that's LESS THAN 1 
When a is a NEGATIVE  ODD  number,  a^a = some negative value that's LESS THAN 1 
So, in both possible cases,  a^a is  definitely  LESS THAN 1 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : a is even  
We already saw in statement 1 that if a is a  NEGATIVE  EVEN integer, then  a^a = some positive fraction that's LESS THAN 1 
What if a is a  POSITIVE  EVEN integer? 
Let's test some possible values:
a = 2. Here a^a = (2)^(2) = 4. Here,  a^a is GREATER THAN 1 
So, we'll stop right here. 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

FANewJersey · Answer

Hi  Bunuel , But the question is if a^a is greater than 1 (not less than 1).In such a case, don't we need both ST-1 and ST-2 to answer the question?

Bunuel · Answer

The question asks: is a^a > 1.

From (1) we get that if a < -1, (if a is -2, -3, -4, ... ) a^a < 1. So, we have a definite NO answer to the question. Recall that a definite NO to an YES/NO DS questions is sufficient the same way as a definite YES is.

GMATmronevsall · Answer

Titans are here but here are my two cents.

Is a^a greater than 1?  so your answer should be  yes or no 
now

(1) a<-1 => a can be -2,-3,-4,.... a^a for a=-2 => (-2)^(-2)=1/(-2)^2=1/4 which is less than one.for rest of the values the denominator will be even bigger so we can say  NO  hence  SUFFICIENT

(2) a is even so it can be anything 2,-2,4,-4,6,-6... we already know that statement isn't true for -ve values for positive value answer is yes =>2^2>1
SO there are 2 answers YES and NO hence  NOT SUFFICIENT

ANSWER A

Basshead · Answer

a is a nonzero integer. Is  a^a  greater than 1?

(1)  a < -1

if  a = -2

-2^{-2} = \frac{1}{4} 
 -3^{-3} = \frac{-1}{27}

a^a is not greater than 1. Sufficient.

(2) a is even

2^2  = 4. Greater than 1
 -2^{-2}  = not greater than 1.

Answer is A.

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a is a nonzero integer. Is a^a greater than 1?

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a is a nonzero integer. Is a^a greater than 1?

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