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# If y ≠ 0, is 10/y > 5?

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Joined: 08 Oct 2011
Posts: 36
If y ≠ 0, is 10/y > 5?  [#permalink]

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15 Nov 2013, 01:39
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Difficulty:

55% (hard)

Question Stats:

59% (01:27) correct 41% (01:10) wrong based on 174 sessions

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If y ≠ 0, is 10/y > 5?

(1) 10 > 5y
(2) y is a positive number smaller than the smallest prime number
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Joined: 02 Sep 2009
Posts: 52255
Re: If y ≠ 0, is 10/y > 5?  [#permalink]

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15 Nov 2013, 01:46
If y ≠ 0, is 10/y > 5?

Is $$\frac{10}{y} > 5$$? --> is $$\frac{2}{y} > 1$$? Note that this cannot be rephrased as "is $$y<2$$?", because we don't know the sign of y and thus cannot multiply both sides by it.

(1) 10 > 5y --> $$y<2$$. If y=1, then the answer is YES but if y is any negative number, then the answer is NO. Not sufficient.

(2) y is a positive number smaller than the smallest prime number. The smallest prime is 2, thus we are given that $$0<y<2$$. For any y from this range $$\frac{2}{y} > 1$$. Sufficient.

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Re: If y ≠ 0, is 10/y > 5?  [#permalink]

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27 Dec 2014, 10:45
If y ≠ 0, is 10/y > 5?

(1) 10 > 5y
(2) y is a positive number smaller than the smallest prime number
(10/y)>5 ==> lets divide both sides by 5 ==>(2/y)>1
Statement 1. 10>5y ==> divide both sides by 5 ==> y<2. If 0<y<2 then the answer is Yes. But if y<0 then answer is No.
Statement 2. The smallest prime number is 2 ==> 0<y<2. As one can see from Statement 1 this is sufficient condition.
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If y ≠ 0, is 10/y > 5?  [#permalink]

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07 Jan 2016, 13:01
First, let's take a look at what the question is asking:

Is $$\frac{10}{y} > 5?$$

When manipulating inequalities, remember that positives and negatives affect the direction of the inequality. So let's consider both cases.

• y>0. Multiply both sides by y, and divide by 5. $$\frac{10}{5} > y$$. y<2. Thus, if y is positive, the question is asking if 0<y<2.
• y<0. Multiply both sides by y, and divide by 5 (and change the direction of the inequality). $$\frac{10}{5} < y$$. y>2. Note that since we assumed y is negative, this can't happen. Therefore, the question is asking if y is positive and between 0 and 2.

1) Manipulating this tells us that y<2. This satisfies one part of our inequality, but we still don't know if y is positive. If y is negative this isn't true. Insufficient.

2) This tells us exactly what we want: that y is positive (>0) and less than 2. Sufficient.

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Re: If y ≠ 0, is 10/y > 5?  [#permalink]

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17 Apr 2018, 19:55
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Re: If y ≠ 0, is 10/y > 5? &nbs [#permalink] 17 Apr 2018, 19:55
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