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

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

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

The answer should be (E) in my opinion.

chetan2u can you please help.

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.

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

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:)

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

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