Official GMAT DS # 151

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Official GMAT DS # 151

by skhanna » Sun Jan 09, 2011 9:35 am
If n is a positive integer and k = 5.1 * 10^n, what is the value of k?

(1) 6000 < k < 500,000
(2) k^2 = 2.601 * 10^9

-----------------------------

I know statement (1) is sufficient to get the value that k = 51,000

But statement (2) should get 2 values (5.1 * 10^4) and (-5.1 * 10^4) as square of both these numbers will give 2.601 * 10^9.

Question tells about positivity of n but not k. Hence, I believe the answer should be just (A) for this DS question. But the officia guide suggests (D)...please advise?
Source: — Data Sufficiency |

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by anshumishra » Sun Jan 09, 2011 9:39 am
skhanna wrote:If n is a positive integer and k = 5.1 * 10^n, what is the value of k?

(1) 6000 < k < 500,000
(2) k^2 = 2.601 * 10^9

-----------------------------

I know statement (1) is sufficient to get the value that k = 51,000

But statement (2) should get 2 values (5.1 * 10^4) and (-5.1 * 10^4) as square of both these numbers will give 2.601 * 10^9.

Question tells about positivity of n but not k. Hence, I believe the answer should be just (A) for this DS question. But the officia guide suggests (D)...please advise?
As per question : k= 5.1*10^n = Always positive.

Hence, D.
Thanks
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by Anurag@Gurome » Sun Jan 09, 2011 10:16 am
If n is a positive integer and k = 5.1 * 10^n, what is the value of k?

(1) 6000 < k < 500,000
(2) k^2 = 2.601 * 10^9
k = 5.1*(10^n), n is positive integer.

For n = 1, k = 5.1
For n = 2, k = 51
For n = 3, k = 510 etc...

Statement 1: 6000 < k < 500,000
Only one possible value of k lies in this range, which is 51,000

Sufficient

Statement 2: k^2 = 2.601 * 10^9
Two possible values of k. But one of them is negative and as per the question stem, value of k can never be negative. Hence a single value of k can be determined.

Sufficient

The correct answer is D.
Anurag Mairal, Ph.D., MBA
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