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# Which of the following equals the average (arithmetic mean) of (a − 2)

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
Which of the following equals the average (arithmetic mean) of (a − 2)  [#permalink]

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24 Jan 2019, 23:17
00:00

Difficulty:

15% (low)

Question Stats:

88% (00:54) correct 13% (00:26) wrong based on 24 sessions

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Which of the following equals the average (arithmetic mean) of (a − 2)^2 and (a + 2)^2?

A a^2
B a^2 + 2
C a^2 + 4
D a^2 + 2x
E a^2 + 8x

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Re: Which of the following equals the average (arithmetic mean) of (a − 2)  [#permalink]

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24 Jan 2019, 23:24
Bunuel wrote:
Which of the following equals the average (arithmetic mean) of (a − 2)^2 and (a + 2)^2?

A a^2
B a^2 + 2
C a^2 + 4
D a^2 + 2x
E a^2 + 8x

IMO C

Average will be[ (a − 2)^2 + (a + 2)^2 ]/ 2

Just expand the quadratic equations to get the value as a^2 + 4
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Re: Which of the following equals the average (arithmetic mean) of (a − 2)  [#permalink]

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25 Jan 2019, 00:26
Bunuel wrote:
Which of the following equals the average (arithmetic mean) of (a − 2)^2 and (a + 2)^2?

A a^2
B a^2 + 2
C a^2 + 4
D a^2 + 2x
E a^2 + 8x

$$\frac{(a − 2)^2 + (a + 2)^2}{2}$$

=$$\frac{a^2 - 2*a*2 + 2^2 + a^2 + 2*a*2 + 2^2}{2}$$

= $$\frac{2a^2 + 8}{2}$$

= $$\frac{2(a^2 + 4)}{2}$$

= a^2 + 4

Re: Which of the following equals the average (arithmetic mean) of (a − 2)   [#permalink] 25 Jan 2019, 00:26
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