Given that $1^{2}+2^{2}+\dots+8^{2}=204$, what is ... | Free GMAT Practice Question | GMAT Panda

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Given that 1^{2} + 2^{2} + \dots + 8^{2} = 204, what is the value of 6^{2} + 1 2^{2} + 1 8^{2} + \dots + 4 8^{2} ?

Explanation	Calculations	Help
$We first name the sum we want to find.$	$S = 6^{2} + 1 2^{2} + 1 8^{2} + 2 4^{2} + 3 0^{2} + 3 6^{2} + 4 2^{2} + 4 8^{2}$
$We then note that each term can be written as (6 k)^{2} where k runs from 1 to 8.$	$S = (6 \times 1)^{2} + (6 \times 2)^{2} + (6 \times 3)^{2} + (6 \times 4)^{2} + (6 \times 5)^{2} + (6 \times 6)^{2} + (6 \times 7)^{2} + (6 \times 8)^{2}$
$We then factor out the common factor 36 from each squared term.$	$S = 36 \times (1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2} + 7^{2} + 8^{2})$
$We then substitute the given value and multiply.$	$S = 36 \times 204 = 36 \times (200 + 4) = 36 \times 200 + 36 \times 4 = 7200 + 144 = 7344$	Theory & Tactics Method Card CALC2-D Click to view full details

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B

Given that 1^{2} + 2^{2} + \dots + 8^{2} = 204, what is the value of 6^{2} + 1 2^{2} + 1 8^{2} + \dots + 4 8^{2} ?

Explanation	Calculations	Help
$We first name the sum we want to find.$	$S = 6^{2} + 1 2^{2} + 1 8^{2} + 2 4^{2} + 3 0^{2} + 3 6^{2} + 4 2^{2} + 4 8^{2}$
$We then note that each term can be written as (6 k)^{2} where k runs from 1 to 8.$	$S = (6 \times 1)^{2} + (6 \times 2)^{2} + (6 \times 3)^{2} + (6 \times 4)^{2} + (6 \times 5)^{2} + (6 \times 6)^{2} + (6 \times 7)^{2} + (6 \times 8)^{2}$
$We then factor out the common factor 36 from each squared term.$	$S = 36 \times (1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2} + 7^{2} + 8^{2})$
$We then substitute the given value and multiply.$	$S = 36 \times 204 = 36 \times (200 + 4) = 36 \times 200 + 36 \times 4 = 7200 + 144 = 7344$	Theory & Tactics Method Card CALC2-D Click to view full details

Scroll horizontally to view all columns

B