GMAT Club World Cup 2022 (DAY 6): If x^2 +y^2

Question

If  x^2 +y^2 \leq 25 , is  x^2 < x  ?

(1)  y^2 > 9 .
(2)  x = y + 3 .

Iotaa · Answer

First work on the question stem: x^2 < x = x(x-1)<0, S1: y^2 > 9 = y>3 or y<-3. If we substitute any eligible value within this range, it will give x(x-1)>0. Hence Sufficient S2: x = y + 3 , y=x-3. Put it in original equation, we will get Xˆ2 + (x-3)ˆ2 < or equal to 25, xˆ2-x-8< or equal to 0. After solving we will get two value of X which gives x(x-1)>0. Hence Sufficient Hence Option C is the answer

Kinshook · Answer

Asked: If x^2 +y^2 \leq 25 , is x^2 < x ? (1) y^2 > 9 . x^2 + y^2 > x^2 + 9 <= 25 x^2 < =16 -4 <=x <=4 If x = .5 ; x^2 - x = .25 - .5 = -.25 < 0 But if x =3; x^2 - x = 9 - 3 = 6 >0 NOT SUFFICIENT (2) x = y + 3 . y = x-3 x^2 + (x-3)^2 <=25 x^2 + x^2 - 6x + 9 < =25 2x^2 - 6x - 16 <=0 x^2 - 3x - 8 <=0 (x-3/2)^2 -(8+9/4) <=0 (x-3/2)^2 - 41/4 <=0 -\frac{\sqrt{41}}{2}<=x<=\frac{\sqrt{41}}{2} If x = .5 ; x^2 - x = .25 - .5 = -.25 < 0 But if x =3; x^2 - x = 9 - 3 = 6 >0 NOT SUFFICIENT (1) + (2) (1) y^2 > 9 . (2) x = y + 3 . (x-3)^2 > 9 (x-3)^2 - 3^2 > 0 x(x-6)>0 x > 6 or x<0 x^2 + 9 < x^2 + y^2 <= 25 x^2 < =16 -4 <=x <=4 -4<=x<0 x^2 - x = x(x-1) >0 SUFFICIENT IMO C

gmatophobia · Answer

Given: x^2 + y^2 \leq 25 Ques: x^2 < x x^2 - x < 0 x(x-1) < 0 In short the question is asking if 0 < x < 1 Statement 1 From this statement we know that - y^2 - 9 > 0 y > 3 or y < -3 We do not have any information on x. Hence we can eliminate this statement Statement 2 x = y + 3 Case 1 Say y = -2.5 ; x = -2.5 + 3 = 0.5 Also, (-2.5)^2 + (0.5)^2 \leq 25 Is 0 < x < 1 -- Yes Case 2 Say y = 0 ; x = 0 + 3 = 3 Also, (3)^2 + (0)^2 \leq 25 Is 0 < x < 1 -- No Combining From Statement 1, we know that y > 3 or y < -3 So y+3 > 6 or y+3 < 0. Therefore x > 6, this is not possible or x < 0, this is possible. Is 0 < x < 1 -- No IMO C

VelvetThunder · Answer

Bunuel · Answer

Could you please demonstrate fractions which would change the answer? Thank you!

GMAT Club World Cup 2022 (DAY 6): If x^2 +y^2 <= 25, is x^2 < x ?

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