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If n is an integer and k= 9.87 * 10^n, what is the value o

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by vinni.k » Sat Sep 02, 2017 7:45 am
If n is an integer and k= 9.87 * 10^n, what is the value of n?

(1) 10^−4 < K < 10^−3

(2) 10^3 < K^−1 < 10^4

OA is D

I am able to get through S(1) but not able to get through S(2). Can you please let me know the easiest and quickest way to solve S(2).

Thanks
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Source: — Data Sufficiency |

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by [email protected] » Sat Sep 02, 2017 1:45 pm
Hi vinni.k,

This question is essentially about 'decimal' shifts. Since N is an integer, we know that K will the same digits (just shifted depending on the decimal). For example:

N = 1... K = 98.7
N = 2... K = 987
N = 3... K = 9870

We're NOT told that N is necessarily positive though, so we have to consider other options...

N = 0... K = 9.87
N = -1... K = 0.987
N = -2... K = 0.0987
N = -3... K = 0.00987
Etc.

We're asked for the value of N.

1) 10^-4 < K < 10^-3

With this range, we know that K is between 1/10,000 and 1/1,000. There's only one value that fits this range: K = 0.000987, so N must be -4.
Fact 1 is SUFFICIENT

2) 10^3 < K^-1 < 10^4

You might find it helpful to rewrite this range as:
10^3 < 1/K < 10^4

In that way, K would have to be between 1/1,000 and 1/10,000 (the same information we were given in Fact 1).
Fact 2 is SUFFICIENT

Final Answer: D

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by Jay@ManhattanReview » Sun Sep 03, 2017 4:15 am
vinni.k wrote:If n is an integer and k= 9.87 * 10^n, what is the value of n?

(1) 10^−4 < K < 10^−3

(2) 10^3 < K^−1 < 10^4

OA is D

I am able to get through S(1) but not able to get through S(2). Can you please let me know the easiest and quickest way to solve S(2).

Thanks
Hi vinni.k,

Since you could get through S1, let's see S2.

Statement 2 is an inverted version of statement 1. Both the statements are same. Let's see how.

Statement 2: 10^3 < K^−1 < 10^4

=> 10^3 < 1/K < 10^4

=> 1/10^(-3) < 1/K < 1/10^(-4); we can write 10^3 as 1/10^(-3)

=> 10^(-3) > K > 10^(-4); raciprocating the fractions. The signs of inequality will reverse. Bigger will become smaller and vice-versa.

Above inequality is same as that in Statement 1.

Hope this helps!

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by vinni.k » Mon Sep 04, 2017 10:36 am
Thanks,

These were some of the key steps that I was missing.

Regards
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