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Source: — Data Sufficiency |

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by Anurag@Gurome » Sun Jan 22, 2012 10:12 pm
nitya20 wrote:Is 7<sqrt(n)<8?

1. n>50
2. n<60


OA: C

However, I disagree with the OA. I think it should be E as sqrt(n) could be negative.
I just wanted to make sure it wasn't just me.
Question is: Is 7<sqrt(n)<8 or Is 49 < n < 64?

(1) n > 50
If n = 60, then n lies between 49 and 64, so the answer to the question is "yes".
If n = 65, then n does not lie between 49 and 64, so the answer to the question is "no".
No definite answer; NOT sufficient.

(2) n < 60
If n = 59, then n lies between 49 and 64, so the answer to the question is "yes".
If n = 45, then n does not lie between 49 and 64, so the answer to the question is "no".
No definite answer; NOT sufficient.

Combining (1) and (2), 50 < n < 60, so the answer to the question is "yes"; SUFFICIENT.

The correct answer is C.
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by nitya20 » Sun Jan 22, 2012 11:38 pm
Anurag@Gurome wrote:
nitya20 wrote:Is 7<sqrt(n)<8?

1. n>50
2. n<60


OA: C

However, I disagree with the OA. I think it should be E as sqrt(n) could be negative.
I just wanted to make sure it wasn't just me.
Question is: Is 7<sqrt(n)<8 or Is 49 < n < 64?

(1) n > 50
If n = 60, then n lies between 49 and 64, so the answer to the question is "yes".
If n = 65, then n does not lie between 49 and 64, so the answer to the question is "no".
No definite answer; NOT sufficient.

(2) n < 60
If n = 59, then n lies between 49 and 64, so the answer to the question is "yes".
If n = 45, then n does not lie between 49 and 64, so the answer to the question is "no".
No definite answer; NOT sufficient.

Combining (1) and (2), 50 < n < 60, so the answer to the question is "yes"; SUFFICIENT.

The correct answer is C.

I agree that that would be the case if I assume sqrt(n) to be positive. However, sqrt(51) could either be -7.something or 7.something. If it is negative, then the inequality would not hold true.
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by Anurag@Gurome » Mon Jan 23, 2012 3:17 am
nitya20 wrote: I agree that that would be the case if I assume sqrt(n) to be positive. However, sqrt(51) could either be -7.something or 7.something. If it is negative, then the inequality would not hold true.
By convention, square root always refer to the principal square root, which means it will always be a positive value.
√x² = |x|
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