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 ..
Manhattan Challenge question
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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
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
Regards
Samir
Samir
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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.
(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
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Nice thinking Naren!!naren_nayak wrote: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.
regards
niks...
niks...