If n is an integer and k = 9.87 X 10^n, what is the value of

Question

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

mau5 · Accepted Answer

Firstly, for any value of n, K will always be a positive entity.

From F.S 1, we have  10^{-4} < K < 10^{-3}  , multiply across by  10^4 	o   10^{-4+4} < K *10^4< 10^{-3+4}  	o   1< 9.87*10^{n+4} < 10  	o  Thus, the only value which n can assume is n =-4.Sufficient.

F.S 2 can be re-written as the same as F.S 1, Thus Sufficient.

D.

Bunuel · Answer

Similar question to practice: if-k-is-a-positive-integer-and-n-7-049-10-k-what-is-the-val-131649.html Hope it helps.

fozzzy · Answer

Great Method... I would have never thought of that to multiply  10^4  that step made the problem really easy... would there be any other alternative?

bluecatie1 · Answer

Hi Bunuel, I really do not understand how to solve the second part of data sufficiency. Can you please explain?

Bunuel · Answer

Consider this: 10<20<100 can be rewritten as 1/100<1/20<1/10.

The same way: 10^3<1/k<10^4 can be rewritten as 1/10^4<k<1/10^3 --> the same equation as in the first statement.

Hope it's clear.

SKTRain · Answer

thank you, but why is there a change in the order of the inequality. I though u only change the algebraic sign if you multiply with a negative number. but here u merely multiply with a fraction.

Bunuel · Answer

Simplest way to understand to consider an example: 2<3<4 --> 1/4<1/3<1/2.

bluecatie1 · Answer

Bunuel, thank you for your valuable feedback :-)

EMPOWERgmatRichC · Answer

Hi All,

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

GMAT assassins aren't born, they're made, 
Rich

AnirudhaS · Answer

(1)  10^{−4}<K<10^{−3} 
(2)  10^3<K^{−1}<10^4 
Are basically the same expressions, so answer can be D or E,

(1)
 10^{−4}<K<10^{−3} 
 10^{−4}<9.87*10^x<10^{−3} 
therefore, x=-4
Sufficient

(2) is basically the same as (1) and we proved (1) is sufficient to (2) must be sufficient

Answer:  D

Fish181 · Answer

am I wrong in my assumption that if you multiply the multiple inequality in 2) it would be the same as 1)?

Bunuel · Answer

Check this: https://gmatclub.com/forum/if-n-is-an-i ... l#p1260443

If n is an integer and k = 9.87 X 10^n, what is the value of

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GMAT Data Sufficiency (DS) Questions

If n is an integer and k = 9.87 X 10^n, what is the value of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards