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If x is an integer, how many leading zeros...

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by BTGmoderatorLU » Tue Oct 24, 2017 1:25 pm
If x is an integer, how many leading zeros (zeros to the right of the decimal point but before the first nonzero digit of a decimal) are in the decimal representation of 1/x?

(1) 90 < x < 101
(2) 96 < x < 99

The OA is D.

I need help with this DS question. Can any expert explain it please? Thanks.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Oct 24, 2017 10:09 pm
LUANDATO wrote:If x is an integer, how many leading zeros (zeros to the right of the decimal point but before the first nonzero digit of a decimal) are in the decimal representation of 1/x?

(1) 90 < x < 101
(2) 96 < x < 99

The OA is D.

I need help with this DS question. Can any expert explain it please? Thanks.
(1) 90 < x < 101

Let's take two extreme cases.

Case 1: Say x = 90 (easier to handle)

Maximum value of 1/x = ~1/90 = ~(1/9)*(1/10) = ~0.11*0.1 = ~0.011. There is only one leading zero.

Case 2: Say x = 100

Minimum value of 1/x = 1/100 = 0.01. There is only one leading zero.

The answer is that there is only one leading zero. Sufficient.

(2) 96 < x < 99

Since the range 90 < x < 101 encompasses 96 < x < 99 and answers the question in yes, the range 96< x < 99 would also answer in Yes. Sufficient.

The correct answer: D

Hope this helps!

-Jay

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