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Bunuel
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What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 10 Nov 2023, 04:32
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

72% (02:14) correct 28% (02:10) wrong based on 345 sessions

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What is the value of \(\frac{1^2+2^2+...+10^2}{1+2+...+10}\)?

(A) 7/3
(B) 7/2
(C) 5
(D) 7
(E) 14
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D
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What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 10 Nov 2023, 04:44
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Bunuel
What is the value of \(\frac{1^2+2^2+...+10^2}{1+2+...+10}\)?

(A) 7/3
(B) 7/2
(C) 5
(D) 7
(E) 14
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These are the most important formula that we must revise
Sum of squares of first n natural numbers -> [n(n+1)(2n+1)] / 6
Sum of squares of first n even numbers -> [2n(n + 1)(2n + 1)] / 3
Sum of squares of first n odd numbers -> [n(2n+1)(2n-1)] / 3

Sum of first n number = n(n+1)/2

Now to solve this
Numerator is square of first n number where n = 10
and denominator is sum of first n number where n = 10

Numerator = \(\frac{[n(n+1)(2n+1)]*2 }{ 6*n(n+1)}\) = \(\frac{2n+1 }{3}\)= 21/3 = 7
OA is D
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What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 07 Dec 2024, 09:38
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Is there an alternate solution to this if one doesn't know the formula?
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What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 07 Dec 2024, 12:55
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I did it with brut force:

1+4+9+16+25+36+49+64+81+100

Then, I tried to match numbers for easy calculations:

100
81+9= 90
36+64=100
4+16=20
49+1 = 50
25

100+100+90+50+20+25 = 385

Same with the denominator:
1+2+3+4+5+6+7+8+9+10

10
1+9=10
8+2=10
7+3=10
6+4=10
5

10*5+5=55

385/55=7



ManifestDreamMBA
Is there an alternate solution to this if one doesn't know the formula?
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What is the value of (1^2 + 2^2 + ... + 10^2)/(1 + 2 + ...+ 10)? 08 Dec 2024, 13:43
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Thanks, I followed these annoying calculations too. But was wondering if there's another approach, given a lot of GMAT questions don't need these not so common formula.

Btw, the denominator can be calculated using the mean * number of terms or n(n+1)/2 formula (this one is pretty common, don't want to contradict what i just mentioned above, :D )
Mariana_Taramona
I did it with brut force:

1+4+9+16+25+36+49+64+81+100

Then, I tried to match numbers for easy calculations:

100
81+9= 90
36+64=100
4+16=20
49+1 = 50
25

100+100+90+50+20+25 = 385

Same with the denominator:
1+2+3+4+5+6+7+8+9+10

10
1+9=10
8+2=10
7+3=10
6+4=10
5

10*5+5=55

385/55=7



ManifestDreamMBA
Is there an alternate solution to this if one doesn't know the formula?
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