If x and y are integers, and xy

Question

e-GMAT          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

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Quant-workshop_Webinar-e1533628475738.jpg

GMATMBA5 · Answer

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.

-----------------------------------------
 Kudos if helpful!

Archit3110 · Answer

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 · Answer

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.

Answer: A

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Free-Session-NP-e1533292073470.jpg

Eternal · Answer

The answer should be (E) in my opinion.

chetan2u  can you please help.

Rachit92 · Answer

As xy<0, this implies that both x and y have different signs, i.e if x is positive, then y is negative and if x is negative, then y is positive.

Per the information given in statement 1,

5x = 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 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.

Per statement 2, 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
and our answer is option A.

adstudy · Answer

xy < 0, That means either x<0 OR y<0, Also x and y are both integers. Statement 1 - Five times the value of x is 17 more than 3 times the value of y 5x = 17 + 3y For case, x>0 and y<0. when x = 1, y = -4, equation is satisfied This is also the only case possible as, If we make y<-5, x will have to be negative and both x and y cannot be negative as per prompt. Also, y>0, will only give a positive value making x positive, and as per prompt, both x and y cannot be positive. And none of the integer values of y between -4 and 0 satisfy the equation. For case, x<0 and y>0. Not possible. x will make 5x negative and 5x will be negative only when 3y is negative and less than (-17). And from prompt we know, x and y cannot be both negative Hence this statement is sufficient . Only possible value is x = 1, y = -4 Statement 2 - x is a perfect square x can be 1, 4, 9, etc. Hence not sufficient. Hence answer is A

chetan2u · Answer

xy<0 means one of the two is negative and the other negative.. I. Five times the value of x is 17 more than 3 times the value of y 5x=17+3y.....5x-3y=17 If x<0 and y>0...5x-3y will be NEGATIVE , so x>0 and y<0. 5x=17+3y.........x=\frac{17+3y}{5} .......17+3y should be a multiple of 5 and should lie between 0 and 17 possible values of 17+3y is 5, 10 and 15..... Only when y=-4, 17+3y=17+3*(-4)=5 hence y=-4, and x=5/5=1... Suff II. x is a perfect square x could be anything 1, 100, 121 etc A

satya2029 · Answer

From 1)
5X=17+3Y
Y=(5/3)X-17/3
X=0, Y=-17/3
Y=0, X=17/5
 the line passes through 3rd,4th and 1st quadrants, but we have to consider only 4th since XY<0(X+, Y-). we can't take (X- Y+) as the line does not pass through 2nd quadrant.
Integer values between X=17/5 and Y=-17/3 are X=0,1,2,3 AND Y=0,-1,-2,-3,-4,-5
But for integer X and Y
5X=17+3Y
From the given set only (1,-4) satifies the given condition
Sufficient

From 2)
X= 1,4,9..
Not sufficient
A:)

Kinshook · Answer

Asked: If x and y are integers, and xy < 0, what is the value of x? I. Five times the value of x is 17 more than 3 times the value of y 5x = 3y + 17 x >= (3y + 17)/5 xy< 0 If x>0; y<0 or if x<0; y>0 Bur since x<0 & y>0 is not possible x>0 & y<0 y = -4; x = 1 is the only solution SUFFICIENT II. x is a perfect square x>0; y<0 x can take multiple values >0 NOT SUFFICIENT IMO A

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards