If x and y are integers and 2*x^(1/2) + y^2

Question

If x and y are integers and  2\sqrt{x} + y^2 < 5 , then x*y can take how many different values ?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Are You Up For the Challenge: 700 Level Questions

SaquibHGMATWhiz · Answer

We have  2\sqrt{x}+y^2<5

Best way here could be to take scenarios using some calculations.

First of all, x has to be non-negative and the same for  y^2 .  However, y can be negative here.  
If x = 0, y can be 0, 1, 2, - 1, - 2. However xy = 0 for all the cases.
If x = 1, y can be 0, 1, -1 so possible value of xy = 0, 1, - 1
If x = 2, y can be 0, 1, - 1 so xy = 0, 2, - 2
If x= 3, y can be 0, 1, - 1 so xy = 0, 3, - 3
If x = 4, y can be 0 xy =0

Thus possible values are -3, -2, - 1, 0, 1, 2, 3

The answer is option D.

AryaSwagat · Answer

But it is stated at many places that in GAMT unless specifically stated negative integers are not taken in to consideration, So should we follow the no negative numbers method ?

SaquibHGMATWhiz · Answer

Hey, there is nothing like that. We can and in fact we should consider negative numbers if it is feasible and in line with the constraints given in the question. Could you please share the source of the above info. There could be some misinterpretation and that's why we would prefer to know the source.

Kinshook · Answer

Asked: If x and y are integers and 2\sqrt{x} + y^2 < 5 , then x*y can take how many different values ? 2\sqrt{x} + y^2 < 5 2\sqrt{x} < 5-y^2 Since 2\sqrt{x} > 0 0<=2\sqrt{x} < 5-y^2 If x=0; 5-y^2>0; y={-2,-1,0,1,2}; x*y=0 If x=1; 5-y^2 > 2; y^2<3; y={-1,0,1}; x*y={-1,0,1} If x=2; ; y={-1,0,1}; x*y={-2,0,2} If x=3; ; y={-1,0,1}; x*y={-3,0,3} If x=4; ; 5-y^2> 4; y^2< 1; y=0; x*y=0 x*y = {-3,-2,-1,0,1,2,3} : 7 values IMO D

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 2x^(1/2) + y^2 < 5, then xy can take how

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

GMAT Problem Solving (PS) Questions

If x and y are integers and 2*x^(1/2) + y^2 < 5, then x*y can take how