BTGmoderatorLU wrote: ↑Sat Feb 27, 2021 1:15 pm
Source: GMAT Prep
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
The OA is
B
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: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
First recognize that the tenths digit of x will equal ZERO,
if x is LESS THAN 0.1
For example, if x = 0.
04, the tenths digit is
0
So, 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 < 1
Case b: k = 1, in which case
x = 1/16, which means it is NOT the case that 1/10 < x < 1
Since 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 < 1
Since we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
