DS (Number System)

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DS (Number System)

by rintoo22 » Sat Mar 23, 2013 8:00 am
In the decimal representation of x, where 0 < x < 1, is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

X could be any of the following values 0.1, 0.01, 0.001 .... etc
To be absolutely sure that tenth value is non-zero the 2nd statement should hold true for X (0.01).
So the answer should be B.However QA the answer is A.
Please assist.
Source: — Data Sufficiency |

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by Anju@Gurome » Sat Mar 23, 2013 8:21 am
rintoo22 wrote:In the decimal representation of x, where 0 < x < 1, is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.
Any positive decimal with nonzero tenths digit will be greater than a positive decimal with tenths digit equal to zero. For example, 0.1 is greater than 0.09, 0.08 etc.

Statement 1: Let us assume 16x = I (some integer)
Hence, x = I/16
Now, minimum possible value of I is 1.
So, minimum possible value of x is 1/16 = 0.0625
So, x can be equal to 0.0625 or 0.625

Not sufficient

Statement 2: Let us assume 8x = I (some integer)
Hence, x = I/8
Now, minimum possible value of I is 1.
So, minimum possible value of x is 1/8 = 0.125
So, tenths digit of x will be always greater than or equal to 1, i.e. nonzero.

Sufficient

The correct answer is B.
Anju Agarwal
Quant Expert, Gurome

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