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Number Properties

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Source: — Data Sufficiency |
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by harsh8686 » Sun Jan 06, 2019 2:58 am
Can anyone please tell me what wrong with my approach:

=> the given equation can be written as a + 1/a > 2
=> (a^2+ 1)/a > 2
=> (a^2 + 1 - 2a)/a > 0
=> (a-1)^2/a > 0

since (a-1)^2 will always be positive therefore if a>0 we will have the answer as YES, and if a<0 then the answer is NO

STATEMENT 1
(1) a>0: SUFFICIENT

STATEMENT 2
(2) a<1: INSUFFICIENT


However, the official answer is C
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by Brent@GMATPrepNow » Sun Jan 06, 2019 7:26 am
harsh8686 wrote:Can anyone please tell me what wrong with my approach:

=> the given equation can be written as a + 1/a > 2
=> (a^2+ 1)/a > 2
=> (a^2 + 1 - 2a)/a > 0
=> (a-1)^2/a > 0

since (a-1)^2 will always be positive therefore if a>0 we will have the answer as YES, and if a<0 then the answer is NO

STATEMENT 1
(1) a>0: SUFFICIENT

STATEMENT 2
(2) a<1: INSUFFICIENT


However, the official answer is C
The error is highlighted above in blue.
if a>0 we will have the answer as YES is ALMOST true.
The only time it's not true is when a = 1

If a = 1, then the answer is NO.
We can verify this using either the original inequality or the rephrased inequality.
Take "Is a + 1/a > 2?" and replace a with 1 to get: "Is 1 + 1/1 > 2?", which becomes "Is 2 > 2?" Answer = NO
Take "Is (a-1)^2/a > 0?" and replace a with 1 to get: "(1-1)^2/1 > 0", which becomes "Is 0 > 0?" Answer = NO

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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