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

Question

(1) 2x = y, and x^3 = y^2

(2) y - x = 4, and x^2= 2y

Bunuel · Answer

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

(1) 2x = y, and x^3 = y^2 -->  x^3 = (2x)^2  -->  x^2(x-4)=0  -->  x=0  and  y=0  OR  x=4  and  y=8 . Not sufficient.

(2) y - x = 4, and x^2= 2y -->  x^2=2(x+4)  -->  x=-2  and  y=2  OR  x=4  and  y=8 . Not sufficient.

(1)+(2) Common solutions are  x=4  and  y=8 . Sufficient.

Answer: C.

Griffins · Answer

Why statement 1 is not enough ?

as per statement 1, 2x=y i.e. x=y/2 ---1

statement 1 also says, x^3 = y^2, so if we substitute 1 here, we get  (y/2)^3 = y^2 , solving this we get y = 8.

Bunuel · Answer

If you read the solution you quote carefully you'll see that there exist two solutions for y, 0 and 8.

I think you reduced (y/2)^3 = y^2 by y^2, which is wrong.

If you divide (reduce) (y/2)^3 = y^2 by y^2 you assume, with no ground for it, that y does not equal to zero thus exclude a possible solution (notice that both y = 0 AND y = 8 satisfy the equation).

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

fireinbelly · Answer

If x and y are integers, what is the value of y ?
(1) 2x = y, and x^3 = y^2.
(2) y - x = 4, and x^2 = 2y.

masoomdon · Answer

IMO  B

Explanation :
Statement 1 : y=2x and x^3=y^2
 x^3=4x^2
 x^2(x-4)=0
 x=0,4
 y=0,8
(x,y)=(0,0) or(4,8)
we are getting two values of y so  INSUFFICIENT  (A cant be the answer )

Statement 2 : y-x=4 and x^2=2y
 x^2-2x-8=0
 (x-4)(x+2)=0
 x=4,-2
 y=8,-4
(x,y)=(4,8)or(-2,-4)
again two values of y so  INSUFFICIENT 
if we combine both statements we get (x,y)=(4,8)
y=8
Answer:  C

fireinbelly · Answer

Well I guess you want to say C and not B....because your solution (combining both statements) points towards C
Even I got C hence I have posted this question here as the answer given is A which even I feel is wrong....they have cancelled out x in option A rather than subtracting and by cancelling out x we get only one value for x which is 4....

I am waiting for some expert to reply and confirm...thanks.

masoomdon · Answer

yeah that was a mistake i meant (C)

BrainLab · Answer

If x and y are integers, what is the value of y ?
(1) 2x = y , and  x^3 = y^2 
(2)  y - x = 4 , and  x^2 = 2y

Argo · Answer

C.

Statement 1: Solving statement 1, we get x = 0 or x = 4. INSUFFICIENT.

Statement 2: Solving statement 2, we get x = 4 or x = 0. INSUFFICIENT.

1+2 : x =4. SUFFICIENT.

Donnie84 · Answer

St1:

y = 2x
y^2 = 4x^2

Plugging this in the other equation:

x^3 = y^2
x^3 = 4x^2
x^3 - 4x^2 = 0
x^2(x - 4) = 0
x can be 0 or 4 -> y can be 0 or 8.
Insufficient.

St2:

y = x + 4

Plugging this in the other equation:

x^2 = 2y
x^2 = 2x + 8
x^2 - 2x - 8 = 0
(x + 2)(x - 4) = 0
x can be -2 or 4 -> y can be 8 or 2.
Insufficient.

St1 + St2:

x = 4.
y = 8.
Sufficient.

Answer (C).

abhimahna · Answer

BrainLab  are you sure OA is A.

I also getting C.

BrainLab · Answer

Hi,

yes, the official answer is A, but I also don't agree with it. You can not cancel out a variable if you are not 100% sure that this variable is not equal to zero.

abhimahna · Answer

Yes, I never cancelled any variable. This is the Basic rule of DS which I am aware of. But my concern is how can the answer be A.

May be we need to wait for some experts to help !!

Bunuel · Answer

Merging topics. Please refer to the discussion above.

P.S. The correct answer is C, not A.

Scyzo · Answer

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

1.)  2x = y , and  x^3 = y^2

2.)  y-x = 4 , and  x^2 = 2y

Source: Jeff Sackman Algebra Challenge

Scyzo · Answer

I keep getting C. OA is A though. Plz correct me where I’m going wrong on this one.

Here is how I approach this:

From Condition 1 I get:

x^3 = (2x)^2
x^3 = 4x^2
x^3 - 4x^2 = 0

(x^2)(x-4) = 0

x could be either 0 or 4.

Plug into 2x = y, y could be either 0 or 8. Hence Insuff.

From Condition 2:

x^2 = 2(4+x)
x^2 = 8 + 2x
x^2 - 2x - 8 = 0
(x-4)(x+2) = 0

Hence x could be either -2 or 4.

Plug into y - x = 4, y could be either 2 or 8. Hence Insuff.

Taking both together y can be 8 for both conditions, so y will be 8. So C.

Bunuel · Answer

Merging topics. Please refer to the discussion above.

P.S. The correct answer is C, not A.

bumpbot · Answer

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

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