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BlueDragon2010
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The full solution below is taken from the GMATFix App.
-Patrick
is 9^x + 9^-x = b?
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Source: Beat The GMAT — Data Sufficiency |
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Patrick_GMATFix
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To compare equations or integrate data from different equations, make them look as similar to each other as possible. This is particularly helpful in DS. In this case, to evaluate (1), we should isolate variable b since b is isolated in the original question.
The full solution below is taken from the GMATFix App.
-Patrick
The full solution below is taken from the GMATFix App.
-Patrick
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GMATGuruNY
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Memorize the following quadratic indentities:BlueDragon2010 wrote:If x is an integer, is 9^x + 9^-x = b?
1) 3^x + 3^-x = sq.root(b+2)
2) x > 0
(a+b)² = a² + 2ab + b²
(a-b)² = a² - 2ab + b²
(a+b)(a-b) = a² - b².
Statement 1: 3^x + 3^-x = √(b+2)
Squaring both sides, we get:
(3^x + 3^-x)² = b+2
The identity in red can serve to rephrase the lefthand side:
(a+b)² = a² + 2ab + b²
(3^x + 3^-x)² = (3^x)² + 2(3^x)(3^-x) + (3^-x)².
Simplifying further, we get:
(3^x)² + 2(3^x)(3^-x) + (3^-x)²
= 3^(2x) + 2(3^0) + 3^(2*-x)
= 9^x + 2 + 9^(-x).
Since the lefthand side can be rephrased as 9^x + 2 + 9^(-x), we get:
9^x + 2 + 9^(-x) = b+2
9^x + 9^(-x) = b.
SUFFICIENT.
Statement 2: x > 0
No information about b.
INSUFFICIENT.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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