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What is the value of t?

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by VJesus12 » Mon Mar 19, 2018 3:42 am
What is the value of t? $$(1)\ \ \ \ \ t(t-1)^2=4t\ .$$ $$(2)\ \ \ t\ \ is\ an\ \ integer.$$ The OA is E.

Experts, using both statements is not sufficient? I think the answer should be C. Am I wrong?
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by GMATGuruNY » Mon Mar 19, 2018 3:48 am
VJesus12 wrote:What is the value of t? $$(1)\ \ \ \ \ t(t-1)^2=4t\ .$$ $$(2)\ \ \ t\ \ is\ an\ \ integer.$$ The OA is E.

Experts, using both statements is not sufficient? I think the answer should be C. Am I wrong?
Statements combined:
Test easy integer values for t (0, 1, 2, 3, etc.).
t(t-1)² = 4t is satisfied by both t=0 and t=3.
Since t can be different values, INSUFFICIENT.

The correct answer is E.
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by Jeff@TargetTestPrep » Mon Mar 26, 2018 4:53 pm
VJesus12 wrote:What is the value of t? $$(1)\ \ \ \ \ t(t-1)^2=4t\ .$$ $$(2)\ \ \ t\ \ is\ an\ \ integer.$$
We need to determine the value of t.

Statement One Alone:

t(t - 1)^2 = 4t

Simplifying we have:

t(t^2 - 2t + 1) = 4t

t^3 - 2t^2 + t = 4t

t^3 - 2t^2 - 3t = 0

t(t^2 - 2t - 3) = 0

t(t - 3)(t + 1) = 0

t = 0 or 3 or -1

Statement one alone is not sufficient to answer the question.

Statement Two Alone:

t is an integer

Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using both statements we still see that t = 0 or 3 or -1.

Answer: E

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