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practice inequality

by sana.noor » Tue Jan 15, 2013 6:52 am
3) Is it true that a > b ?

(1) a2 > b2
(2) a > b - 2

E

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Jan 15, 2013 7:13 am
sana.noor wrote:3) Is it true that a > b ?

(1) a^2 > b^2
(2) a > b - 2
Target question: Is a > b ?

Statement 1: a^2 > b^2
There are several pairs of values that meet this condition. Here are two:
Case a: a = 1 and b = 0, in which case a is greater than b
Case b: a = -1 and b = 0, in which case a is not greater than b
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a > b - 2
There are several pairs of values that meet this condition. Here are two:
Case a: a = 1 and b = 0, in which case a is greater than b
Case b: a = -1 and b = 0, in which case a is not greater than b
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
There are still several pairs of values that meet this condition. Here are two:
Case a: a = 1 and b = 0, in which case a is greater than b
Case b: a = -1 and b = 0, in which case a is not greater than b
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

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by GMATGuruNY » Tue Jan 15, 2013 7:59 am
sana.noor wrote:3) Is it true that a > b ?

(1) a2 > b2
(2) a > b - 2

E
Question stem, rephrased: Is a-b > 0?

Statement 1, rephrased:
a² - b² > 0
(a+b)(a-b) > 0.

Statement 2, rephrased:
a-b > -2.

Both statements are satisfied if a+b = 1 and a-b = 3, in which case a-b > 0.
Both statements are satisfied if a+b = -3 and a-b = -1, in which case a-b < 0.
Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.
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