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Set A has consecutive integers from 1 to n
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31 Jul 2021, 10:51
31 Jul 2021, 10:51
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Set A has consecutive integers from 1 to n. If all integers in the set A are squared and then added, the result will be 2,470. How many integers are in the set A?
(A) 23
(B) 22
(C) 21
(D) 20
(E) 19
(A) 23
(B) 22
(C) 21
(D) 20
(E) 19
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Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Location: India
WE:Education (Education)
Re: Set A has consecutive integers from 1 to n
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31 Jul 2021, 19:56
31 Jul 2021, 19:56
motion2020 wrote:
Set A has consecutive integers from 1 to n. If all integers in the set A are squared and then added, the result will be 2,470. How many integers are in the set A?
(A) 23
(B) 22
(C) 21
(D) 20
(E) 19
(A) 23
(B) 22
(C) 21
(D) 20
(E) 19
Sum of squares of first \(n\) consecutive numbers = \(\frac{n(n+1)(2n+1)}{6}\)
Check the option choices;
A. \(\frac{23(24)(47)}{6} = 4324\)
B. \(\frac{22(23)(45)}{6} = 3795\)
C. \(\frac{21(22)(43)}{6} = 3311\)
D. \(\frac{20(21)(41)}{6} = 2870\)
E. \(\frac{19(20)(39)}{6} = 2470\)
Hence, option E
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I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, India
https://www.instagram.com/prepster_education/
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, India
https://www.instagram.com/prepster_education/
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