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# If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1

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Math Expert
Joined: 02 Sep 2009
Posts: 47037
If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1 [#permalink]

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13 Apr 2018, 02:10
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:58) correct 25% (01:22) wrong based on 93 sessions

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If y ≠ 0, is y > 0?

(1) $$|y| > 1$$

(2) $$\frac{y^2 + y}{y^2} > 1$$

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Manager
Joined: 28 Apr 2014
Posts: 52
GMAT 1: 640 Q50 V25
If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1 [#permalink]

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Updated on: 13 Apr 2018, 03:19
IMO B

St1 y>1 or y<-1
insufficient

St2 y^2+y>y^2 (sq quantity is +ve)
y>0
sufficient

Originally posted by NiharikaR on 13 Apr 2018, 02:13.
Last edited by NiharikaR on 13 Apr 2018, 03:19, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 6219
Re: If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1 [#permalink]

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13 Apr 2018, 03:15
Bunuel wrote:
If y ≠ 0, is y > 0?

(1) $$|y| > 1$$

(2) $$\frac{y^2 + y}{y^2} > 1$$

NiharikaR, ans should be B..

(1) $$|y| > 1$$
tells us that y<-1 or y>1
insuff

(2) $$\frac{y^2 + y}{y^2} > 1$$..
Cross multiply as y^2 is POSITIVE
$$y^2 + y > y^2.............y>y^2-y^2.......y>0$$..
suff

B
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Manager
Joined: 28 Apr 2014
Posts: 52
GMAT 1: 640 Q50 V25
If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1 [#permalink]

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13 Apr 2018, 03:27
Thanks. I read the question wrong. I thought its asking y>1.
Though I got y>0, I wrote insufficient.

I have to avoid such silly mistakes during exam
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Re: If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1 [#permalink]

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13 Apr 2018, 06:12
I ) |y| > 1

y>1
y <-1

not sufficient

II)
$$y^2+y/y^2$$ > 1

y^2/y^2 + y/y^2 > 1

1 + 1/y >1 ==> 1/y >0 ==> y>0

sufficient

Therefore B
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Joined: 02 Oct 2017
Posts: 596
Re: If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1 [#permalink]

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28 Apr 2018, 06:29
I) y could be 2 or -2
Insufficient

II) rewriting eqn
1+(1/y)>1

1/y>0
Y>0

So b is ANS

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Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1 [#permalink]

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30 Apr 2018, 12:39
Bunuel wrote:
If y ≠ 0, is y > 0?

(1) $$|y| > 1$$

(2) $$\frac{y^2 + y}{y^2} > 1$$

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (y) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If $$y = 1$$, then $$y > 0$$. The answer is "yes".
If $$y = -1$$, then $$y < 0$$. The answer is "no".
Since we don't have a unique solution, the condition 1) is not sufficient.

Condition 2)

$$\frac{y^2 + y}{y^2} > 1$$
$$⇔ y^2 + y > y^2$$
$$⇔ y > 1$$
Then we have $$y > 0$$.

Condition 2) is sufficient.

Therefore, B is the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1   [#permalink] 30 Apr 2018, 12:39
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# If y ≠ 0, is y > 0? (1) |y| > 1 (2) y^2 + y/y^2 > 1

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