If x^2 + y^2 = 10x, is x

Question

If x^2 + y^2 = 10x, is x < y ?

(1) y = 3
(2) (x - 5)^2 = 16

chetan2u · Answer

If x^2 + y^2 = 10x, is x < y ?

(1) y = 3
 x^2+9=10x……..x^2-10x+9=0…….(x-1)(x-9)=0 
Thus x can be 1 or 9
Insufficient

(2) (x - 5)^2 = 16
  (x - 5)^2 = 16=4^2……|x-5|=4 
So x can be 1 or 9
Insufficient

Combined 
x could be 1 or 9
Insufficient

E

gmatophobia · Answer

Given x^2 + y^2 = 10x Statement 1 y = 3 x^2 + 9 = 10x x^2 - 10x + 9 (x-1)(x-9) = 0 x = 1 or x = 9 As we are getting two possible values of x, one in which x > y and one in which x < y, Statement 1 is not sufficient and we can eliminate A and D. Statement 2 (x-5)^2 = 16 Taking square root on both sides |x-5| = 4 x = 1 or x = 9 As we are getting two possible values of x, one in which x > y and one in which x < y, Statement 1 is not sufficient and we can eliminate B. Combined Statement 1 and Statement 2 give the same information. Hence combining both the statement we do not have any new information. Eliminate C. Option E

If x^2 + y^2 = 10x, is x < y ? (1) y = 3 (2) (x - 5)^2 = 16

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