What is the value of t?
(1) t(t - 1)^2 = 4t
(2) t is an integer.
OA E
Source: Manhattan Prep
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What is the value of t?
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BTGmoderatorDC
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Let's take each statement one by one.BTGmoderatorDC wrote: ↑Sun Jul 26, 2020 6:59 pmWhat is the value of t?
(1) t(t - 1)^2 = 4t
(2) t is an integer.
OA E
Source: Manhattan Prep
(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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Statement 1:BTGmoderatorDC wrote: ↑Sun Jul 26, 2020 6:59 pmWhat is the value of t?
(1) t(t - 1)^2 = 4t
(2) t is an integer.
OA E
Source: Manhattan Prep
\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
