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anmolmakkarz17
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If 0 < x < 1 and m=(1/2^n) 06 Nov 2019, 04:05
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95% (hard)

Question Stats:

41% (02:29) correct 59% (02:24) wrong based on 80 sessions

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If 0 < x < 1 and m=(\(\frac{1}{2^n}\)) , where n is a positive integer, what is the thousandths digit of \(\frac{x}{m}\)?

1) The thousandths digit of x is greater than 0.
2) 1,000x is a multiple of 5.
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B
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chetan2u
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GMAT Focus 1: 735 Q90 V89 DI81
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If 0 < x < 1 and m=(1/2^n) 07 Nov 2019, 06:02
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anmolmakkarz17
If 0 < x < 1 and m=(\(\frac{1}{2^n}\)) , where n is a positive integer, what is the thousandths digit of \(\frac{x}{m}\)?

1) The thousandths digit of x is greater than 0.
2) 1,000x is a multiple of 5.
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Hi..

1) The thousandths digit of x is greater than 0.
the thousandths digit of \(\frac{x}{m}\) could be anything...

2) 1,000x is a multiple of 5.
Let \(1000x=5a.......x=\frac{5a}{1000}=\frac{a}{200}\), where a is an integer..
\(\frac{x}{m}=\frac{a}{200}*2^n\), where n is a positive integer..
Now, \(\frac{a}{200}*2^n\) is atleast \(\frac{a}{100}\)..
As we have only 100 or a factor of 100 in denominator, if a is a multiple of 2 or 5 or n>1..
Hence we will not have more than 2 decimal places in \(\frac{x}{m}\).
This means, the number is abc.rs000000, or the thousandths digit is 0
Suff

B
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ManjariMishra
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If 0 < x < 1 and m=(1/2^n) Updated on: 07 Nov 2019, 00:23
Originally posted by ManjariMishra on 06 Nov 2019, 05:06.
Last edited by ManjariMishra on 07 Nov 2019, 00:23, edited 2 times in total.
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can anybody please explain B chetan2u , Bunuel
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If 0 < x < 1 and m=(1/2^n) 06 Nov 2019, 22:38
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Hi! Can someone explain this problem?
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adstudy
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If 0 < x < 1 and m=(1/2^n) 07 Nov 2019, 05:22
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anmolmakkarz17
If 0 < x < 1 and m=(\(\frac{1}{2^n}\)) , where n is a positive integer, what is the thousandths digit of \(\frac{x}{m}\)?

1) The thousandths digit of x is greater than 0.
2) 1,000x is a multiple of 5.
Show more

x is of the form 0.abc...

and m is of the form \(\frac{1}{2^n}\) where n = 1,2,3,....

we need \(\frac{x}{m}\) which is equal to \(0.abc...* 2^n\)

Hence we need the value of \(c*2^n\)

From Statement 1 - The thousandths digit of x is greater than 0.

Not much info we get from this statement. This means that c is not equal to zero, except zero it can anything from 1 to 9.

Not Sufficient

From Statement 2 - 1,000x is a multiple of 5

This means that the new number after multiplying with 1000 becomes 'ab5.000'

That is we now know the value of c and after decimal no value will exist at it will not be a multiple then. Only integers are multiple of integers.

hence we now know that x would be something like this -> '0.ab5'.

When multiplied by any positive integer power of 2 will give us 0 in the thousandth place.

Hence Sufficient.

Hence answer B
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If 0 < x < 1 and m=(1/2^n) 25 May 2023, 00:38
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Hi chetan2u

Isn't this question wrong? Since option A is giving wrong info, it's not data sufficiency anymore.
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