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25 May 2021, 03:15
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Difficulty:
25%
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74% (02:06) correct
26%
(02:20)
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based on 70
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If the sum of 9 consecutive integers is 90, what is the sum of the following 9 consecutive integers?
A. 99
B. 135
C. 145
D. 171
E. 180
A. 99
B. 135
C. 145
D. 171
E. 180
25 May 2021, 05:37
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Asked: If the sum of 9 consecutive integers is 90, what is the sum of the following 9 consecutive integers?
The sum of 9 consecutive integers is 90
S_n = n/2 (2a + (n-1)d) = 9/2 (2a + 8) = 90
2a + 8 = 20
a = 6
The sum of the following 9 consecutive integers
a' = 6 + 9 = 15
S_9 = 9/2(2*15 + 8) = 9/2 (38) = 9*19 = 171
IMO D
The sum of 9 consecutive integers is 90
S_n = n/2 (2a + (n-1)d) = 9/2 (2a + 8) = 90
2a + 8 = 20
a = 6
The sum of the following 9 consecutive integers
a' = 6 + 9 = 15
S_9 = 9/2(2*15 + 8) = 9/2 (38) = 9*19 = 171
IMO D
25 May 2021, 06:02
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Solution:
Let the numbers be x,x+1,x+2,...x+8
=> x + x+1 + x+2+....x+8 = 90
=>9x + 36 = 90
=> x = 6 =>We were given the sum of 6,7,8,..14(9 terms)
We are to now find the sum of 15-23 (!5+16+17+....23)
=> Sum of (1 to 23) - Sum (1 to 14)
=23*24/2 - 14*15/2
=23*12 - 15*7
=276 -105
=171 (option d)
Devmitra Sen
GMAT SME
Let the numbers be x,x+1,x+2,...x+8
=> x + x+1 + x+2+....x+8 = 90
=>9x + 36 = 90
=> x = 6 =>We were given the sum of 6,7,8,..14(9 terms)
We are to now find the sum of 15-23 (!5+16+17+....23)
=> Sum of (1 to 23) - Sum (1 to 14)
=23*24/2 - 14*15/2
=23*12 - 15*7
=276 -105
=171 (option d)
Devmitra Sen
GMAT SME
