If x + y^2 = (x + y ^2)^2, what is the value of y?

This topic has expert replies
Legendary Member
Posts: 2276
Joined: Sat Oct 14, 2017 6:10 am
Followed by:3 members
If $$x+y^2=(x+y^2)^2,$$ what is the value of y?

(1) x = y ^2
(2) xy ^2 = 0

The OA is C.

I don't understand why is not sufficient the statement (1). Experts, may you give me some help here, please? Thanks.

User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members
VJesus12 wrote:If $$x+y^2=(x+y^2)^2,$$ what is the value of y?

(1) x = y ^2
(2) xy ^2 = 0

The OA is C.

I don't understand why is not sufficient the statement (1). Experts, may you give me some help here, please? Thanks.
If $$x+y^2=(x+y^2)^2,$$

then x+y^2 = 1 or 0


Question : y = ?

Statement 1: x = y ^2
@x+y^2 = 1, y ^2 = 1/2 i.e. y = 1/√2
@x+y^2 = 0, y ^2 = 0 i.e. y = 0
NOT SUFFICIENT

Statement 2: x*y ^2 = 0
@x+y^2 = 1, y ^2 = 0 or y^2=1 i.e. y = 0 or 1
NOT SUFFICIENT

Combining the two statements
x = y ^2 and x*y ^2 =
i.e. x = y = 0
SUFFICIENT

Answer: Option C
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour