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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2505
Given Kudos: 1055
GPA: 3.39
The mean of (54,820)^2 and (54,822)^2 =
[#permalink]
26 Nov 2022, 02:01
26 Nov 2022, 02:01
Expert Reply
00:00
Question Stats:
60% (01:42) correct
40% (00:54) wrong based on 5 sessions
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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) \((54,821)^2 – 1\)
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2505
Given Kudos: 1055
GPA: 3.39
Re: The mean of (54,820)^2 and (54,822)^2 =
[#permalink]
27 Nov 2022, 21:03
27 Nov 2022, 21:03
Expert Reply
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
Re: The mean of (54,820)^2 and (54,822)^2 =
[#permalink]
10 Dec 2022, 05:47
10 Dec 2022, 05:47
2
Let x=54821
54822²+54820²=(x-1)²+(x+1)²=
=x²-2x+1 + x²+2x+1=2x²+2
Mean= 2(x²+1)/2= x²+1
Recall that x=54821
Hence mean= 54821²+1
Posted from my mobile device
54822²+54820²=(x-1)²+(x+1)²=
=x²-2x+1 + x²+2x+1=2x²+2
Mean= 2(x²+1)/2= x²+1
Recall that x=54821
Hence mean= 54821²+1
Posted from my mobile device
