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22 Jul 2019, 14:18
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Difficulty:
55%
(hard)
Question Stats:
57% (02:01) correct
43%
(02:05)
wrong
based on 162
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If n ≠ 2, is \(\frac{n^2-1}{n-2}≥8\) ?
(1) n is an odd number
(2) n > 1
(1) n is an odd number
(2) n > 1
22 Jul 2019, 18:02
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\(\frac{n^2-1}{n-2}\)≥8
When n≤2
n^2-8n+15≤0
n=[3,5]
Not possible
When n≥2
n^2-8n+15≥0
n=[2,3]∪[5,∞ ]
Statement 1
n is odd number
When n>1, \(\frac{n^2-1}{n-2}\)≥8
When n≤1, \(\frac{n^2-1}{n-2}\)≤8
Statement 2- n>1
if n=[1,2)∪(3,5), \(\frac{n^2-1}{n-2}\)≤8
if n=[2,3]∪[5,∞), \(\frac{n^2-1}{n-2}\)≥8
Combining both equations
n is odd number and greater than 1
\(\frac{n^2-1}{n-2}\)≥8 is always true.
Sufficient.
When n≤2
n^2-8n+15≤0
n=[3,5]
Not possible
When n≥2
n^2-8n+15≥0
n=[2,3]∪[5,∞ ]
Statement 1
n is odd number
When n>1, \(\frac{n^2-1}{n-2}\)≥8
When n≤1, \(\frac{n^2-1}{n-2}\)≤8
Statement 2- n>1
if n=[1,2)∪(3,5), \(\frac{n^2-1}{n-2}\)≤8
if n=[2,3]∪[5,∞), \(\frac{n^2-1}{n-2}\)≥8
Combining both equations
n is odd number and greater than 1
\(\frac{n^2-1}{n-2}\)≥8 is always true.
Sufficient.
shridhar786
24 Jul 2019, 03:41
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Since the denominator is (n-2), n cannot be equal to 2; otherwise, the denominator will become ZERO and division by ZERO is not a concept tested on the GMAT. That’s why the question gives us the data about n≠2.
The plugging in approach works just fine with this question.
From statement I alone, we know that n is an odd number.
If n = 1, the expression on the LHS yields ZERO which is less than 8. We get a NO as an answer to the main question.
If n = 3, the expression on the LHS yields 8 which is equal to 8. We get a YES as an answer to the main question.
If n = 5, the expression on the LHS yields 8 which is equal to 8. We get a YES as an answer to the main question.
If n = 7, the expression on the LHS yields 48/5 which is more than 8. We get a YES as answer to the main question.
Clearly statement I alone is insufficient since it’s not giving us a definite YES or NO.
Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, just knowing that n>1 is not sufficient to say that the LHS is always more than or equal to 8.
Answer option B can be eliminated. Possible answer options at this stage are C or E.
Combining statements I and II, for all values of n which are odd numbers more than 1, the expression always yields a value more than or equal to 8.
The answer option has to be C.
Hope this helps!
The plugging in approach works just fine with this question.
From statement I alone, we know that n is an odd number.
If n = 1, the expression on the LHS yields ZERO which is less than 8. We get a NO as an answer to the main question.
If n = 3, the expression on the LHS yields 8 which is equal to 8. We get a YES as an answer to the main question.
If n = 5, the expression on the LHS yields 8 which is equal to 8. We get a YES as an answer to the main question.
If n = 7, the expression on the LHS yields 48/5 which is more than 8. We get a YES as answer to the main question.
Clearly statement I alone is insufficient since it’s not giving us a definite YES or NO.
Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, just knowing that n>1 is not sufficient to say that the LHS is always more than or equal to 8.
Answer option B can be eliminated. Possible answer options at this stage are C or E.
Combining statements I and II, for all values of n which are odd numbers more than 1, the expression always yields a value more than or equal to 8.
The answer option has to be C.
Hope this helps!
