Max@Math Revolution wrote:[GMAT math practice question]
$$If\ \ 2^n+2^{n-2}=5120,\ then\ n=?$$
A. 8
B. 9
C. 10
D. 11
E. 12
We can PLUG IN THE ANSWERS, which represent the value of n.
When the correct answer is plugged in, the given expression will be equal to 5120.
D: n=11
Plugging n=11 into the given expression, we get:
2¹¹ + 2¹¹¯² = 2¹¹ + 2� = 2�(2² + 1) = 512(5) = 2560.
Since the result is too small, the value of n must be GREATER than 11.
The correct answer is
D.
To solve algebraically, factor out the SMALLER EXPONENT.
Here, the smaller exponent is n-2:
$$\\2^n+2^{n-2}=5120\\$$
$$\\2^{n-2}(2^2 + 1)=5120\\$$
$$\\2^{n-2}(5)=5120\\$$
$$\\2^{n-2}=1024\\$$
$$\\2^{n-2}=2^{10}\\$$
$$\\n-2=10\\$$
$$\\n=12\\$$
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