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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Question of the Week - 36 (If xy < 0, what is the value of x?)  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 31% (02:41) correct 69% (02:32) wrong based on 67 sessions

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Question of the Week #36

If x and y are integers, and xy < 0, what is the value of x?

Statement 1: Five times the value of x is 17 more than 3 times the value of y
Statement 2. x is a perfect square

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Originally posted by EgmatQuantExpert on 15 Feb 2019, 02:16.
Last edited by EgmatQuantExpert on 28 Feb 2019, 00:48, edited 1 time in total.
Manager  G
Joined: 07 Aug 2017
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Re: Question of the Week - 36 (If xy < 0, what is the value of x?)  [#permalink]

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1
IMO A

xy<0.... either of x or y is negative.

Statement 1:
5x=3y+17
x=(3y+17)/5
From this it is clear that, for xy<0 to be true, y should have negative value and only for y=-4, x will be an integer.
Therefore, x = 1

Statement 2:
x is a perfect square.
x can be 4, 16, 64 and still satisfy xy<0 when y = -1, -2, -3.....
Therefore, not sufficient.

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Re: Question of the Week - 36 (If xy < 0, what is the value of x?)  [#permalink]

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given
x*y<0
so either of x & y has to be -ve integer

#1
5x=17+3y
now to get either of x & y -ve
at x = 1 ; y = -4
sufficient

#2
x is a perfect square does not help in determing whether x*y<0 ; because x can be +/- ( 4,9,16....)
in sufficeint

IMO A

EgmatQuantExpert wrote:
If x and y are integers, and xy < 0, what is the value of x?

Statement 1: Five times the value of x is 17 more than 3 times the value of y
Statement 2. x is a perfect square

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Question of the Week - 36 (If xy < 0, what is the value of x?)  [#permalink]

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Solution

Given:
In this question, we are given:
• The numbers x and y are integers
• Also, xy < 0

To find:
We need to determine
• The value of x

Approach & Working
As it is given that xy < 0 and both of them are integers, we can say that
• None of x and y can be individually 0.
• If x is greater than 0 or a positive integer, then y is less than zero or negative integer.
• Alternatively, if x is less than 0 or a negative integer, then y is greater than 0 or positive integer.

With this understanding, let us now analyse the individual statements.

Analyse Statement 1
As per the information given in statement 1, five times the value of x is 17 more than 3 times the value of y.
• 5x = 17 + 3y
Or, x = 1/5 (17 + 3y)

As both x and y are integers, we can have multiple possible values of x and y:
• x = -5 and y = -14
• x = -2 and y = -9
• x = 1 and y = -4
• x = 4 and y = 1
• x = 7 and y = 6
• x = 10 and y = 11
• x = 13 and y = 16 and so on…

Now, observing the values of x and y, we can see that there is only one specific case where x and y are of opposite signs (when x = 1 and y = -4).

Therefore, from statement 1 we can determine the unique value of x.

Hence, statement 1 is sufficient to answer the question.

Analyse Statement 2
As per the information given in statement 2, x is a perfect square.
• From this statement, we can only say that x is a positive integer, and therefore, y is a negative integer.
• However, we cannot conclude the exact value of x.

Hence, statement 2 is not sufficient to answer the question.

Hence the correct answer is Option A.

_________________ Question of the Week - 36 (If xy < 0, what is the value of x?)   [#permalink] 18 Feb 2019, 19:50
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