What is the value of y?

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

What is the value of y?

by M7MBA » Sat Dec 30, 2017 7:14 am

What is the value of y? $$(1)\ \ \ y^3+2y=y+2y^2$$ $$(1)\ \ \ y^3+2y=y+2y^2$$ $$(2)\ \ \ y^2=y$$ The OA is the option E.

Can not we find the value of y from statement (1)? I am confused. Experts, may you help me? Please.

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Source: Beat The GMAT — Data Sufficiency | Sat Dec 30, 2017 7:14 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Jan 15, 2018 8:45 pm

M7MBA wrote:What is the value of y? $$(1)\ \ \ y^3+2y=y+2y^2$$ $$(2)\ \ \ y^2=y$$ The OA is the option E.

Can not we find the value of y from statement (1)? I am confused. Experts, may you help me? Please.

(1) y^3 + 2y = y + 2y^2

=> y^3 -2y^2 + y = 0

y(y^2 -2y + 1) = 0

=> y = 0 or y^2 -2y + 1 = 0 => (y - 1)^2 = 0 => y = 1.

y = 0 or 1. No unique answer. insufficient.

(2) y^2 = y

=> y^2 - y = 0

y(y - 1) = 0 => y = 0 or 1. No unique answer. insufficient.

(1) and (2) together

Even after cominging the two statements, we get that y = 0 or 1. No unique answer. insufficient.

The correct answer: E

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jan 18, 2018 1:52 pm

M7MBA wrote:What is the value of y? $$(1)\ \ \ y^3+2y=y+2y^2$$ $$(1)\ \ \ y^3+2y=y+2y^2$$ $$(2)\ \ \ y^2=y$$ The OA is the option E.

We need to determine the value of y.

Statement One Alone:

y^3 + 2y = y + 2y^2

y^3 - 2y^2 + y = 0

y(y^2 - 2y + 1) = 0

y(y - 1)(y - 1) = 0

So, y = 0 or y = 1

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

y^2 = y

Simplifying we have:

y^2 - y = 0

y(y - 1) = 0

y = 0 or y = 1

Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using both statements, we still see that y = 0 or y = 1; thus, we cannot determine the value of y.

Answer: E

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