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is x/3 < x ?

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by BTGmoderatorLU » Sat Nov 04, 2017 6:53 am
$$Is\ \ \frac{x}{3}<x\ ?$$

$$\left(1\right)\ \ x<\ 0$$

$$(2)\ \ x\ \ does\ \ not\ \ equal\ -1.$$

The OA is A.

I need help to solve this DS question. Please, can any expert explain it for me? Thanks.
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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Sun Nov 05, 2017 8:48 am
LUANDATO wrote:$$Is\ \ \frac{x}{3}<x\ ?$$

$$\left(1\right)\ \ x<\ 0$$

$$(2)\ \ x\ \ does\ \ not\ \ equal\ -1.$$

The OA is A.

I need help to solve this DS question. Please, can any expert explain it for me? Thanks.
A rephrase is helpful here.

Start by multiplying both sides of the inequality in question by 3. " Is x/3 < x?", becomes
Is x < 3x?
Subtract 'x' from both sides
Is 0 < 2x?
Divide both sides by 2
Is 0 < x?

Statement 1: Well if x < 0, we know it's not greater than 0, so this statement alone is sufficient.

Statement 2: Clearly not sufficient. x could be -10 or 10, etc.

The answer is A
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by [email protected] » Thu Nov 09, 2017 11:44 am
Hi LUANDATO,

We're asked if X/3 is less than X. This is a YES/NO question and we can solve it with a mix of Number Property Rules and by TESTing VALUES.

1) X < 0

Fact 1 tells us that X is NEGATIVE. When dividing a negative number by 3, the result is ALWAYS CLOSER to 0 than X is. For example:
IF...
X = -3, then (-3)/3 = -1 and -1 is closer to zero than -3 is... so the answer to the question is NO.
This pattern exists with ANY negative number, so the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

2) X does NOT equal -1

IF...
X = -3, then (-3)/3 = -1 and -1 is closer to 0 than -3 is... so the answer to the question is NO.
X = 3, then 3/3 = 1... so the answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

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