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# If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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06 Oct 2015, 04:55
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:47) correct 30% (01:34) wrong based on 221 sessions

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If x ≠ 0, is y greater than 0?

(1) xy = 24
(2) x – y = 5

Kudos for a correct solution.

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Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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06 Oct 2015, 05:36
Bunuel wrote:
If x ≠ 0, is y greater than 0?

(1) xy = 24
(2) x – y = 5

Kudos for a correct solution.

Question : Is y > 0?

Statement 1: xy = 24
Case 1: x = 2, y = 12 Positive
Case 2: x = -2, y = -12 Negative
NOT SUFFICIENT

Statement 2: x – y = 5
Case 1: x = 7, y = 2 Positive
Case 2: x = 3, y = -2 Negative
NOT SUFFICIENT

Combining the two statements
From Statement 1: x = 24/y

i.e. (24/y) - y = 5
i.e. y^2 + 5y - 24 = 0
i.e. y = 8 or -3
NOT SUFFICIENT

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Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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07 Oct 2015, 08:07
1
Bunuel wrote:
If x ≠ 0, is y greater than 0?

(1) xy = 24
(2) x – y = 5

Kudos for a correct solution.

We need to find out if y is positive that is y is not negative and not zero.

1) xy = 24
=> y ≠ 0
=> x and y can have both positive and negative values (6, 4) and (-6, -4) to give 24.
Hence, NOT SUFFICIENT

2) x - y = 5
=> Again, x and y can have multiple values: (-3, -8), (5, 0), (8, 3)
Hence, NOT SUFFICIENT

(1) + (2)
xy = 24 && x - y =5
This can again take multiple values, both positive and negative: (-3, -8) and (8, 3)
Hence, NOT SUFFICIENT

Ans: E
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If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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07 Oct 2015, 09:28
From Option A :
xy=24
since x <> 0 y <0 or >0
if x=3 y =8 if x=-4 ,y=-6 So y can be either <0 or >0
A is not sufficient

From Option b:
x-y=5
So x=7 y=2 or x=3 y=-2 .Y can be either <0 or >0 .Not sufficient

combining both A and B
equation can be written (y+5)y=24 --> $$y^2+5y-24=0$$
solving for y : $$y=-8$$ or $$y=3$$
Y can be <0 or >0

Correct answer is Option E
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Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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08 Oct 2015, 03:34
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x ≠ 0, is y greater than 0?

(1) xy = 24
(2) x – y = 5

There are two variables (x,y) from the original condition, and we need 2 equations in order to match the numbers. The 2 conditions provide the 2 equations, so there is high chance that (C) is going to be the answer.
Looking at the conditions together,
If we substitute y=x-5 into the first condition, xy=x(x-5)=24, x^2-5x-24=0, (x-8)(x+3)=0
The answer to the question is ‘yes’ for x=8 y=3, but ‘no’ for x=-3 y=-8, so the conditions are insufficient and the answer becomes (E).

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Posts: 52906
Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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11 Oct 2015, 06:29
Bunuel wrote:
If x ≠ 0, is y greater than 0?

(1) xy = 24
(2) x – y = 5

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No “Is y greater than 0?” Or, in other words, “Is y positive?”

Given information from the question stem: x does not equal 0.

Statement 1: xy = 24. In order to get a positive result from multiplication you either need two positive or two negative numbers. It is possible for both x and y to be positive (giving you a “yes”) and for both to be negative (giving you a “no”). This statement allows both yes and no and is not consistent and not sufficient. The answer will be choice B, C, or E.

Statement 2: x – y = 5. This can be restated as “x = y + 5.” This is not sufficient alone since y could be a negative number. For example, x = -5 and y = -10. This statement allows x to be positive as well as negative so it is not sufficient. Eliminate choice B.

Together: Taken together the statements tell you that “x is 5 greater than y” and that “xy = 24.” The question is, can you Play Devil’s Advocate and find both positive and negative values for y that work with both statements. First x and y can be positive. Let x = 8 and y = 3. This satisfies both statements and yields a “yes, y is positive.” Simply making x = -3 and y = -8 also works with both statements and gives you a “no, y is not positive.” Even taken together these statements are not sufficient. The correct answer is E.
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Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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22 Dec 2015, 01:54
Is this one really a 700 question ??
Feels like 600-700 or 600
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Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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22 Dec 2015, 22:54
3
manishkhare wrote:
From Option A :
xy=24
since x <> 0 y <0 or >0
if x=3 y =8 if x=-4 ,y=-6 So y can be either <0 or >0
A is not sufficient

From Option b:
x-y=5
So x=7 y=2 or x=3 y=-2 .Y can be either <0 or >0 .Not sufficient

combining both A and B
equation can be written (y+5)y=24 --> $$y^2+5y-24=0$$
solving for y : $$y=-8$$ or $$y=3$$
Y can be <0 or >0

Correct answer is Option E

As a sidenote, note that you don't really need to solve $$y^2+5y-24=0$$ to get values of y. The product of the roots (-24) is negative so one root is positive and the other negative. So you already know that both statements together are not sufficient. It may not save a ton of time in this question but in case of non-integer roots, this observation could really help.
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Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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31 May 2016, 06:37
Before we start looking at the conditions, it is important to note there are no restrictions on x or y outside of the fact x cannot equal 0.

1.) xy = 24
x = 3 ---> y = 6
x = -3 ---> y = -6
Y could be greater or less than 0 so NS

2.) x-y = 5
y = x -5
x = 7 ---> y = 2
x = 2 ---> y = -3
Y could be greater or less than 0 so NS

1&2 Combined.)
x = y+5 from statement 2
Plug this into statement 1 to get y(y+5) = 24
---> y^2+5y-24=0
(y+8)(y-3) = 0
Y could be greater or less than 0 so NS
---> E as the correct answer
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Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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26 Jul 2017, 23:31
Bunuel wrote:
If x ≠ 0, is y greater than 0?

(1) xy = 24
(2) x – y = 5

Kudos for a correct solution.

Given : x ≠ 0
DS : y>0?

Statement 1: xy = 24
So, if x<0, y <0
if x>0, y >0
NOT SUFFICIENT

Statement 2: x - y = 5
-> x = y +5
if x>5, y >0
if x<5, y<0
NOT SUFFICIENT

Combined :
(y+5)y = 24
y^2 + 5y -24 = 0
y^2 + 8y - 3y -24 = 0
(y+8)(y-3) = 0
y = -8, 3
NOT SUFFICIENT

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Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5  [#permalink]

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Re: If x ≠ 0, is y greater than 0? (1) xy = 24 (2) x – y = 5   [#permalink] 06 Sep 2018, 07:56
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