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OG #12 DS 151 Explanation !!!!!

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OG #12 DS 151 Explanation !!!!!

by rockeyb » Thu Dec 24, 2009 9:13 pm
If n is a +ve integer and k = 5.1x10^n , what is the value of k ?

1. 6,000 < k < 500,000

2. k^2 = 2.601 x 10^9

Now here since we know n is a + ve and an integer option 1 clearly suggests that n = 4 .

In option 2 what I don't understand is why is k = root of (2.601 x 10^9) and since in GMAT roots give only +ve values we have only 1 value for K .

But in a similar example lets say if x^2 = 16 what is X ?

you would be tempted to say that its + 4 OR -4 and that is correct you will get two values .

SO my question is why in case of k^2 = 2.601 x 10^9 are we not taking two values . IF we look at it more deeply effectively we are taking square roots both the side in case of X and in case of K as well , so why different approaches?

Can any one explain?
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by papgust » Thu Dec 24, 2009 10:05 pm
Maybe its because the question itself says that k is +ve (If n is a +ve integer, then k = 5.1 x 10^n will also be +ve). So we are ignoring the fact that k would be -ve here.
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by Stuart@KaplanGMAT » Thu Dec 24, 2009 10:35 pm
papgust wrote:Maybe its because the question itself says that k is +ve (If n is a +ve integer, then k = 5.1 x 10^n will also be +ve). So we are ignoring the fact that k would be -ve here.
Bingo!
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by rockeyb » Fri Dec 25, 2009 12:27 am
Thanks papgust and stuart for your replies .

But I would like you guys to read the question again it very clearly says that " If n is a + ve integer and K = 5.1x10^n, what is the value of K?

No were in the question dose it specify that K is +ve , it only says n is + ve . And more over n being +ve or - ve dose not make K + ve Or - ve .

I hope this explains my confusion better.
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by papgust » Fri Dec 25, 2009 1:19 am
rockeyb,

Nowhere it is mentioned that k is a +ve. Agreed. But it is an unstated assumption that k is a +ve just like we find an assumption in CR's. So, we the test takers, have to be careful in identifying these assumptions.

Just try to substitute values of n in k. You know that n is +ve. Try calculating K

If n=1, K = 5.1 * 10^1 = 51 (+ve)
If n=2, K = 5.1 * 10^2 = 510 (+ve)
If n=3, K = 5.1 * 10^3 = 5100 (+ve)
If n=4, K = 5.1 * 10^4 = 51000 (+ve)
.
.
you can keep calculating this if you wish to. But it will only be +ve.

Remember that this equation (K) is stated or given explicitly to you. If you try to assume -ve values of k, you are actually trying to contradict the question itself, for which GMAT will ultimately hit back at you saying that your answer is wrong.

So, we should be watchful about it. This is a nice lesson to learn!
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by rockeyb » Fri Dec 25, 2009 3:45 am
papgust wrote:rockeyb,

Nowhere it is mentioned that k is a +ve. Agreed. But it is an unstated assumption that k is a +ve just like we find an assumption in CR's. So, we the test takers, have to be careful in identifying these assumptions.

Just try to substitute values of n in k. You know that n is +ve. Try calculating K

If n=1, K = 5.1 * 10^1 = 51 (+ve)
If n=2, K = 5.1 * 10^2 = 510 (+ve)
If n=3, K = 5.1 * 10^3 = 5100 (+ve)
If n=4, K = 5.1 * 10^4 = 51000 (+ve)
.
.
you can keep calculating this if you wish to. But it will only be +ve.

Remember that this equation (K) is stated or given explicitly to you. If you try to assume -ve values of k, you are actually trying to contradict the question itself, for which GMAT will ultimately hit back at you saying that your answer is wrong.

So, we should be watchful about it. This is a nice lesson to learn!

OK agreed .

So by saying K = 5.1x10 ^n where n is +ve and option (2) stating K^2 = 2.601 x 10^9 what they actually are saying is this :

Ex : X is a + ve number and X^2 = 16 so what is the value of X. No doubt that X^2 will still give two roots that is + 4 and - 4 since X is + ve we will only consider the +ve root .

This is why K has only 1 root .

Is this correct ?
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by papgust » Fri Dec 25, 2009 4:11 am
Yes, you are right.
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by pranali » Sun Dec 27, 2009 10:41 am
Hi papgust,
How to solve the above problem? Is the answer B?
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by papgust » Sun Dec 27, 2009 6:13 pm
I think it's D

Statement I says that 6000 < k < 5,00,000. If k = 5.1 * 10^n, then k can take only 1 value (51,000 or 5.1 * 10^4). So, its sufficient.

We have already seen that statement II is also sufficient because here we are considering only positive root.
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by ying » Tue Jun 08, 2010 9:58 pm
papgust wrote:Maybe its because the question itself says that k is +ve (If n is a +ve integer, then k = 5.1 x 10^n will also be +ve). So we are ignoring the fact that k would be -ve here.
Even if n<0, k is always > 0.
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by tyronetan82 » Wed Jun 23, 2010 8:49 am
I still cannot figure out why we only take the positive root value, the given info says that n is a positive integer and not k...

The value of n in this problem is an exponent....
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by Stuart@KaplanGMAT » Wed Jun 23, 2010 1:31 pm
tyronetan82 wrote:I still cannot figure out why we only take the positive root value, the given info says that n is a positive integer and not k...

The value of n in this problem is an exponent....
Hi,

k = 5.1 * 10^n (from the question stem). Since 5.1 is positive, and 10^(anything) is positive, k must also be positive.

We know that k is positive from the question stem itself, so we never have to worry about non-positive values of k.

Here's a simplified variation:

If k > 0, what's the value of k?

1) k = -5 or +5

Statement (1) is sufficient alone, since the question stem itself invalidates the solution k = -5.
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by tyronetan82 » Wed Jun 23, 2010 6:36 pm
Thanks for that, but I actually understood statement 1.

I got stuck on statement 2, can you give me a simplified version of that? Why can't the negative root be the answer?
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by sreak1089 » Wed Jun 23, 2010 11:27 pm
It is given that k = 5.1x10^n.

So for any value of 'n', k can never be a negative number. Hence, only the positive square root is the solution.


tyronetan82 wrote:Thanks for that, but I actually understood statement 1.

I got stuck on statement 2, can you give me a simplified version of that? Why can't the negative root be the answer?
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by Stuart@KaplanGMAT » Thu Jun 24, 2010 1:03 pm
tyronetan82 wrote:Thanks for that, but I actually understood statement 1.

I got stuck on statement 2, can you give me a simplified version of that? Why can't the negative root be the answer?
My reply has nothing to do with statement (1) - it's all derived from the question stem.

The information given in the question stem governs both statements.
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