$$Is\ a\ +\ a^{-1}\ >\ 2\ ?$$
(1) a > 0
(2) a < 1
Number Properties
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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 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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Timer
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Your Answer
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C
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Global Stats
The error is highlighted above in blue.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
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