The equation 5^x - 3/a = a, where a is a real non-zero number, is possible only if:
A) a > 0
B) a = 0
C) a < 0
D) a > 3^1/2
E) a < - 3^1/2
OA: A
Thank you.
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A little help with this one, please
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Brent@GMATPrepNow
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Given: 5^x - 3/a = afambrini wrote:The equation 5^x - 3/a = a, where a is a real non-zero number, is possible only if:
A) a > 0
B) a = 0
C) a < 0
D) a > 3^1/2
E) a < - 3^1/2
OA: A
Multiply both sides by a to get: a(5^x) - 3 = a²
Add 3 to both sides: a(5^x) = a² + 3
Let's look at the RIGHT side of this equation. Since a² must be a positive value, we can be certain that a² + 3 is POSITIVE
So, for this equation to be solvable, the LEFT side of the equation, a(5^x), must be POSITIVE
Since 5^x is always positive, we need a to be positive (i.e., a > 0)
Answer: A
What is the source of this question?
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Brent
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Matt@VeritasPrep
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5Ë£ - 3/a = a
5Ë£ is always positive. If 0 > a, then -3/a is also positive, so the left side = Pos + Pos, and the right side = Neg.
This is impossible, so we can't have any negative a.
We also can't have a = 0, since -3/a wouldn't work.
That leaves us with A and D. Now shoot for a small value. Say that x = 1. Then we've got 5 - 3/a = a. This is a quadratic, a² - 5a + 3 = 0. Eyeballing it, we should have one answer ≈ 1/2 and one ≈ 4, so D is out.
Since we found a root less than √3, whatever that root is, we know the answer is A.
5Ë£ is always positive. If 0 > a, then -3/a is also positive, so the left side = Pos + Pos, and the right side = Neg.
This is impossible, so we can't have any negative a.
We also can't have a = 0, since -3/a wouldn't work.
That leaves us with A and D. Now shoot for a small value. Say that x = 1. Then we've got 5 - 3/a = a. This is a quadratic, a² - 5a + 3 = 0. Eyeballing it, we should have one answer ≈ 1/2 and one ≈ 4, so D is out.
Since we found a root less than √3, whatever that root is, we know the answer is A.
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Matt@VeritasPrep
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Not one very familiar with the GMAT, I reckon. A little too technical and proofy for the GMAC, and not a question that really tests what the GMAT seeks to.Brent@GMATPrepNow wrote: What is the source of this question?
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Brent@GMATPrepNow
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Agreed!Matt@VeritasPrep wrote:Not one very familiar with the GMAT, I reckon. A little too technical and proofy for the GMAC, and not a question that really tests what the GMAT seeks to.Brent@GMATPrepNow wrote: What is the source of this question?
Brent Hanneson - Creator of GMATPrepNow.com
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Matt@VeritasPrep
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- Joined: Wed Sep 12, 2012 3:32 pm
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We are getting a lot of beyond-the-GMAT questions this week ... I guess that's flattering, right?Brent@GMATPrepNow wrote:Agreed!Matt@VeritasPrep wrote:Not one very familiar with the GMAT, I reckon. A little too technical and proofy for the GMAC, and not a question that really tests what the GMAT seeks to.Brent@GMATPrepNow wrote: What is the source of this question?
GMAT/MBA Expert
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Brent@GMATPrepNow
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And flustering!Matt@VeritasPrep wrote:We are getting a lot of beyond-the-GMAT questions this week ... I guess that's flattering, right?Brent@GMATPrepNow wrote:Agreed!Matt@VeritasPrep wrote:Not one very familiar with the GMAT, I reckon. A little too technical and proofy for the GMAC, and not a question that really tests what the GMAT seeks to.Brent@GMATPrepNow wrote: What is the source of this question?
Brent Hanneson - Creator of GMATPrepNow.com
