What is the value of t?

[BTGmoderatorDC]

What is the value of t?

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

(2) t is an integer.


OA E

Source: Manhattan Prep

[Jay@ManhattanReview]

What is the value of t?

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

(2) t is an integer.

OA E

Source: Manhattan Prep

Let's take each statement one by one.

(1) t(t – 1)^2 = 4t

=> t(t – 1)^2 – 4t = 0

t[(t – 1)^2 – 4] = 0

=> t = 0 or (t – 1)^2 – 4 = 0

Taking (t – 1)^2 – 4 = 0, we have t = –1 or 3.

So, there are three values of t: –1, 0, and 3. No unique value. Insufficient.

(2) t is an integer.

Certainly insufficient.

Even both statements together are insufficient as we can't get the unique value of t.

Correct answer: E

Hope this helps!

-Jay
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[swerve]

What is the value of t?

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

(2) t is an integer.


OA E

Source: Manhattan Prep

Statement 1:

\begin{align*}
t(t-1)^2&=4t\\
(t-1)^2 &=4 \\
(t-1)^2 - 2^2 &= 0\\
(t-1+2)(t-1-2) &= 0\\
(t+1)(t-3) &= 0\\
t&= -1, 3
\end{align*}

Statement 2:

Already known in Statement 1. Insufficient

Combining 1 & 2, also insufficient

Therefore, E