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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Tue May 26, 2009 3:41 pm

The average 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

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Source: Beat The GMAT — Problem Solving | Tue May 26, 2009 3:41 pm

gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Tue May 26, 2009 7:14 pm

Let x = 54820

so we have to find the average of x^2 and (x+2)^2

thus, [x^2 and (x+2)^2]/2
Now when you expand (x+2)^2, you get,
= 2[x^2 +2x +2]/2 = x^2 +2x +2 = (x+1)^2 +1

But x =54,820
so x+1 = 54821

thus answer is (54821)^2 + 1

IMO D

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dumb.doofus: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat Sep 27, 2008 2:02 pmFollowed by: 1 member; Location: San Jose, CA; Thanked: 43 times; GMAT Score:720

by dumb.doofus » Tue May 26, 2009 7:27 pm

Nice approach gmat740..

I thought it in this way.. almost similar to yours..

a^2 + b^2 = (a - b)^2 + 2ab ------------- (1)

Now, if x = 54821,

then a = x - 1, b = x + 1

(x+1)(x-1) = x^2 -1 --------------- (2)

so (a^2 + b^2)/2 = [4 + 2(x^2-1)]/2

= 1 + x^2
= 1 + 54821^2 i.e. D

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