udaymathapati wrote:
In the decimal representation of x, where 0 < x < 1, is the tenths digit of x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.
Target question:Is the tenths digit of x nonzero?This is a good candidate for rephrasing the target question.
Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100First recognize that the tenths digit of x will equal ZERO,
if x is LESS THAN 0.1For example, if x = 0.
04, the tenths digit is
0So, the tenths digit of x will be
NONZERO if x
> 0.1
In other words, the tenths digit of x will be
NONZERO if x
> 1/10
Since we're already told that x < 1, we can REPHRASE the target question...
REPHRASED target question: Is 1/10 < x < 1? Statement 1: 16x is an integer. Since we're told that 0 < x (i.e., x is positive), we know that 16x is positive
So, let's say that 16x = k, where k is some positive integer
Solve for x to get: x = k/16 (where k is some positive integer)
There are several values of k that satisfy statement 1. Here are two:
Case a: k = 8, in which case
x = 8/16 = 1/2, which means it IS the case that 1/10 < x < 1Case b: k = 1, in which case
x = 1/16, which means it is NOT the case that 1/10 < x < 1Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 8x is an integer. Let's say that 8x = j, where j is some positive integer
Solve for x to get: x = j/8 (where j is some positive integer)
Since j is a positive integer, then j = 1 or 2 or 3 or ....
In all of these cases, j/8 will be GREATER than 1/10
In other words, x must be GREATER than 1/10
Since we're also told that x < 1, we can be certain that
1/10 < x < 1Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer =
Cheers,
Brent
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