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Joined: 19 Nov 2020
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GRE 1: Q160 V152
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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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
gmatclubot
Re: Set A has consecutive integers from 1 to n [#permalink]
31 Jul 2021, 19:56
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