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a is a nonzero integer. Is a^a greater than 1?
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Updated on: 14 Aug 2014, 10:35
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a is a nonzero integer. Is a^a greater than 1? (1) a < 1 (2) a is even
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Originally posted by NoHalfMeasures on 14 Aug 2014, 10:17.
Last edited by Bunuel on 14 Aug 2014, 10:35, edited 1 time in total.
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Re: a is a nonzero integer. Is a^a greater than 1?
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14 Aug 2014, 10:45
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.
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a is a nonzero integer. Is a^a greater than 1?
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11 Feb 2015, 16:24
Bunuel wrote: 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. Dear Bunuel, I think that (2)^(2) which is 1/2^2 should be negative fraction less than 1 and equal to = ( 1/4 )
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Re: a is a nonzero integer. Is a^a greater than 1?
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11 Feb 2015, 21:57
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/[(2)^2] = 1/4 IF....we were dealing with (3)^(3) though, we'd have..... 1/[(3)^3] = 1/27 = 1/27 GMAT assassins aren't born, they're made, Rich
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a is a nonzero integer. Is a^a greater than 1?
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12 Feb 2015, 05:15
EMPOWERgmatRichC wrote: 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/[(2)^2] = 1/4
IF....we were dealing with (3)^(3) though, we'd have.....
1/[(3)^3] = 1/27 = 1/27
GMAT assassins aren't born, they're made, Rich Ok, can you tell me how write 1/4 in the form a^a
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Re: a is a nonzero integer. Is a^a greater than 1?
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12 Feb 2015, 05:27
23a2012 wrote: Bunuel wrote: 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. Dear Bunuel, I think that (2)^(2) which is 1/2^2 should be negative fraction less than 1 and equal to = ( 1/4 ) hi , 2^2= 1/(2)^2=1/4....
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Re: a is a nonzero integer. Is a^a greater than 1?
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12 Feb 2015, 11:20
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)[2^(2)] = (1)[1/4] = 1/4 GMAT assassins aren't born, they're made, Rich
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Re: a is a nonzero integer. Is a^a greater than 1?
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18 Jan 2018, 06:28
NoHalfMeasures wrote: a is a nonzero integer. Is a^a greater than 1?
(1) a < 1 (2) a is even 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 PATTERNa = 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 1When a is a NEGATIVE ODD number, a^a = some negative value that's LESS THAN 1So, in both possible cases, a^a is definitely LESS THAN 1Since 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 1What 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 1So, we'll stop right here. Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent
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Re: a is a nonzero integer. Is a^a greater than 1?
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02 Jan 2019, 14:58
Bunuel wrote: 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. 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 ST1 and ST2 to answer the question?



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Re: a is a nonzero integer. Is a^a greater than 1?
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03 Jan 2019, 02:49
FANewJersey wrote: Bunuel wrote: 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. 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 ST1 and ST2 to answer the question? 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.
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