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Difficulty:
45%
(medium)
Question Stats:
70% (02:03) correct
30%
(02:08)
wrong
based on 2519
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The mean of \((54,820)^2\) and \((54,822)^2 =\)
(A) \((54,821)^2\)
(B) \((54,821.5)^2\)
(C) \((54,820.5)^2\)
(D) \((54,821)^2 + 1\)
(E) \((54,821)^2 – 1\)
(A) \((54,821)^2\)
(B) \((54,821.5)^2\)
(C) \((54,820.5)^2\)
(D) \((54,821)^2 + 1\)
(E) \((54,821)^2 – 1\)
11 Sep 2012, 02:02
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The mean of \((54,820)^2\) and \((54,822)^2 =\)
(A) \((54,821)^2\)
(B) \((54,821.5)^2\)
(C) \((54,820.5)^2\)
(D) \((54,821)^2 + 1\)
(E) \((54,821)^2 – 1\)
APPROACH #1:
Test some small numbers: \(\frac{2^2+4^2}{2}=10=3^2+1\) or: \(\frac{4^2+6^2}{2}=26=5^2+1\).
APPROACH #2:
Say \(54,821=x\), then \(\frac{54,820^2+54,822^2}{2}=\frac{(x-1)^2+(x+1)^2}{2}=x^2+1=54,821^2+1\).
APPROACH #3:
The units digit of \(54,820^2+54,822^2\) is \(0+2=4\). Now, since \(54,820^2+54,822^2\) must be a multiple of 4, then \(\frac{54,820^2+54,822^2}{2}\) must have the units digit of 2. Only answer choice D fits.
Answer: D.
(A) \((54,821)^2\)
(B) \((54,821.5)^2\)
(C) \((54,820.5)^2\)
(D) \((54,821)^2 + 1\)
(E) \((54,821)^2 – 1\)
APPROACH #1:
Test some small numbers: \(\frac{2^2+4^2}{2}=10=3^2+1\) or: \(\frac{4^2+6^2}{2}=26=5^2+1\).
APPROACH #2:
Say \(54,821=x\), then \(\frac{54,820^2+54,822^2}{2}=\frac{(x-1)^2+(x+1)^2}{2}=x^2+1=54,821^2+1\).
APPROACH #3:
The units digit of \(54,820^2+54,822^2\) is \(0+2=4\). Now, since \(54,820^2+54,822^2\) must be a multiple of 4, then \(\frac{54,820^2+54,822^2}{2}\) must have the units digit of 2. Only answer choice D fits.
Answer: D.
10 Dec 2012, 03:04
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Shrink the monster technique.
The two numbers are two consecutive even numbers raised to 2. Shrink the monster and think of baby numbers such as 0 and 2.
\(mean=\frac{{0^2 + 2^2}}{2}=2\)
Substitute you baby numbers to the answer choices.
(A) \({0+1}^{2}=1\) Eliminate!
(B) \({0+1.5}^{2}=2.25\) Eliminate!
(C) \({0+0.5}^{2}=0.25\) Eliminate!
(D) \({0+1}^{2}+1=2\) Bingo!
(E) \({0+1}^{2}-1=0\) Eliminate!
Answer: D
The two numbers are two consecutive even numbers raised to 2. Shrink the monster and think of baby numbers such as 0 and 2.
\(mean=\frac{{0^2 + 2^2}}{2}=2\)
Substitute you baby numbers to the answer choices.
(A) \({0+1}^{2}=1\) Eliminate!
(B) \({0+1.5}^{2}=2.25\) Eliminate!
(C) \({0+0.5}^{2}=0.25\) Eliminate!
(D) \({0+1}^{2}+1=2\) Bingo!
(E) \({0+1}^{2}-1=0\) Eliminate!
Answer: D
