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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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