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The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is

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The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is  [#permalink]

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New post 30 Jun 2019, 22:41
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

8% (02:07) correct 92% (02:43) wrong based on 12 sessions

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The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is

A. 80707
B. 80773
C. 80730
D. 80751
E. 80734
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Re: The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is  [#permalink]

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New post 30 Jun 2019, 23:04
The nth term of this sequence is given by (4n + 3)(4n + 7) = 16n^2 + 40n + 21n
Here the minimum value of n is 1 and the maximum is 23.
Sum of squares is given by n(n + 1)(2n + 1)/6. Here, the sum is 23(24)(47)/6 = 4324
Sum of first n natural numbers is given by n(n + 1)/2. Here, the sum is 23(24)/2 = 276
Hence, the sum of the sequence is (16*4324) + (40*276) + 21*23 = 69184 + 11040 + 483 = 80707

Note: This is definitely not a GMAT Question
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Re: The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is  [#permalink]

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New post 30 Jun 2019, 23:04
raghavrf wrote:
The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is

A. 80707
B. 80773
C. 80730
D. 80751
E. 80734


Let us write generic term Tn = (4n+3)(4n+7) = (4n+3)(4n+7) [(4n+11) - (4n-1)]/12 = (4n+3)(4n+7)(4n+11)/12 - (4n-1)(4n+3)(4n+7)/12
If we try to add Tn, all term cancel out, except largest term and negative smallest term. Sn= (4n+3)(4n+7)(4n+11)/12 - 3*7*11/12 = 95*99*103/12 - 3*7*11/12 = 80707

IMO A (A is correct)
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Re: The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is   [#permalink] 30 Jun 2019, 23:04
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