Manhattan Challenge question

[gabriel]

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

Solve it people .. its a easy question ... do not be intimidated by the huge numbers ..

[keepsmilinyaar]

Ans is D.

IT can be reduce to :
[(54281- 1)^2 + (54281+1)^2]/2

[kajcha]

Agree D

[samirpandeyit62]

Hi Gabriel,
I did get a little scared by seeing the big nos , so to cope with it I replaced 54820 with x

so 54822 =x+2

so it becomes

x^2 + (x+2)^2

i.e 2x^2 + 4 + 4x

divinding this by 2 we have

x^2 + 2x + 2

Now we need to represent this in terms of answer choices wherin it should be a perfect square or square +1 / -1

Now since this expression is not a perfect square by itself so we need to convert it to a perfect square with 1 added or subtracted

we have x^2 +2x +1 +1

i.e (x+1)^2 +1

i.e 54821^2 +1

so ans should be D

[gabriel]

D is my answer to .. dont know what the OA is

[naren_nayak]

One could also use the process of elimination here:
(54,820)^2 should have a 0 in the unit's position & (54,822)^2 should end with a 4. The average of these two numbers will have a 2 in the unit's position. That eliminates A, B, C & E (A ends with a 1, B & C end with a .25 and E ends with a 0).
Hence the answer is D.

[niks_01.27]

One could also use the process of elimination here:
(54,820)^2 should have a 0 in the unit's position & (54,822)^2 should end with a 4. The average of these two numbers will have a 2 in the unit's position. That eliminates A, B, C & E (A ends with a 1, B & C end with a .25 and E ends with a 0).
Hence the answer is D.

Nice thinking Naren!!

[800GMAT]

OA given is D