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# Is x/3 < x?

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Senior SC Moderator
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21 Mar 2017, 19:02
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15% (low)

Question Stats:

79% (00:58) correct 21% (01:14) wrong based on 72 sessions

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Is $$\frac{x}{3} < x$$ ?

(1) $$x < 0$$
(2) x does not equal -1

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Re: Is x/3 < x?  [#permalink]

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22 Mar 2017, 01:43
ziyuen wrote:
Is $$\frac{x}{3} < x$$ ?

(1) $$x < 0$$
(2) x does not equal -1

St 1: for x<0, x/3>x. ANSWER
St 2: INSUFFICIENT..will show different nature of equation for x<0,x=0 and x>0

option A
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Re: Is x/3 < x?  [#permalink]

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23 Nov 2017, 14:45
1
Hi All,

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

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Re: Is x/3 < x?  [#permalink]

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23 Nov 2017, 22:41
Is x/3 < x.
Or Is x < 3x which can also be written as 3x-x>0 or 2x >0 or x > 0. So basically the question is asking whether x>0 or not.

(1) x<0. We get our answer as NO. Sufficient.

(2) x is not equal to -1. But we dont know whether x is positive or negative. Insufficient.

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Re: Is x/3 < x?  [#permalink]

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23 Nov 2017, 22:59
Any reason why -1/3 is not considered as a possible value for x ? It does not mention that x is an integer.

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Re: Is x/3 < x?  [#permalink]

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23 Nov 2017, 23:22
1
mm78582 wrote:
Any reason why -1/3 is not considered as a possible value for x ? It does not mention that x is an integer.

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Hi

Yes, x is not an integer and thus it can take any value. But the question is specifically asking "Is x/3 < x"

As I have tried to explain in my post on this, x/3 will be < x if x >0. Thus for all values of x > 0 (whether they be fractions or integers) we can answer as YES for the question asked.
And for all values of x < 0, x/3 will not be < x but x/3 will be greater than x (whether these values be fractions or integers). For all such values we can answer as NO for the question asked.

In first statement, we are given that x < 0. So that means x/3 will not be less than x. our answer becomes NO (to the question asked) and thus the statement 1 is sufficient to answer the question.
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Re: Is x/3 < x?  [#permalink]

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31 Dec 2017, 13:43
hazelnut wrote:
Is $$\frac{x}{3} < x$$ ?

(1) $$x < 0$$
(2) x does not equal -1

VERITAS PREP OFFICIAL SOLUTION:

Explanation:

(1) There are three possibilities for what can happen when you divide a number by three. If the number is positive, it will reduce in value (example: 9 --> when 9 is divided by 3 it reduces to 3). If the number is 0, it will not change (0/3 = 0). And if the number is negative, it will become "less negative" so to speak. (example: -6 --> -6/3 is -2, which is greater than -6). Because statement 1 guarantees that x is negative, we know that x/3 will be greater than x. Note that this also holds for fractions: -1/2, when divided by 3, becomes -1/6. And since -1/6 is closer to 0 than -1/2, -1/6 is greater.

(2) This only rules out one number, leaving infinite possibilities for the value of x. x could be 2 or -2, giving us answers of NO and YES, respectively. This statement is thus, insufficient. Accordingly the correct answer is A.
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Re: Is x/3 < x? &nbs [#permalink] 31 Dec 2017, 13:43
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