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If (48 + 40 + 56)^(1/2)/(2^t + 2^(t + 1)) = 4, what is the v
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13 Apr 2020, 09:39
13 Apr 2020, 09:39
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Question Stats:
70% (01:45) correct
29% (03:07) wrong based on 24 sessions
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If \(\frac{\sqrt{48 + 40 + 56}}{2^t + 2^{(t + 1)}} = 4\), what is the value of t ?
A) –2
B) –1
C) 0
D) 1/2
E) 2
Kudos for the right answer and explanation
A) –2
B) –1
C) 0
D) 1/2
E) 2
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If (48 + 40 + 56)^(1/2)/(2^t + 2^(t + 1)) = 4, what is the v
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13 Apr 2020, 10:56
13 Apr 2020, 10:56
Carcass wrote:
If \(\frac{\sqrt{48 + 40 + 56}}{2^t + 2^{(t + 1)}} = 4\), what is the value of t ?
A) –2
B) –1
C) 0
D) 1/2
E) 2
Kudos for the right answer and explanation
A) –2
B) –1
C) 0
D) 1/2
E) 2
Kudos for the right answer and explanation
Take: \(\frac{\sqrt{48 + 40 + 56}}{2^t + 2^{(t + 1)}} = 4\)
Simplify: \(\frac{\sqrt{144}}{2^t + 2^{(t + 1)}} = 4\)
Simplify: \(\frac{12}{2^t + 2^{(t + 1)}} = 4\)
Since 12/3 = 4, we know that \(2^t + 2^{(t + 1)} =\) 3
At this point, we can EITHER test the answer choices to see which one satisfies the simplified equation above, OR solve the equation algebraically.
Let's solve it algebraically....
Take: \(2^t + 2^{(t + 1)} =3\)
Factor to get: \(2^t(1 + 2^1) =3\)
Evaluate to get: \((2^t)(3) =3\)
Divide both sides by \(3\) to get: \(2^t =1\)
So it must be the case that \(t=0\)
Answer: C
Cheers,
Brent
gmatclubot
Re: If (48 + 40 + 56)^(1/2)/(2^t + 2^(t + 1)) = 4, what is the v [#permalink]
13 Apr 2020, 10:56
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