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# If the sum of five consecutive positive integers is A

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Manager
Joined: 26 Nov 2014
Posts: 106
If the sum of five consecutive positive integers is A [#permalink]

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01 Aug 2015, 12:29
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If the sum of five consecutive positive integers is A, then the sum of the next five consecutive integers in terms of A is:

A. A+1
B. A+5
C. A+25
D. 2A
E. 5A
[Reveal] Spoiler: OA
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Re: If the sum of five consecutive positive integers is A [#permalink]

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01 Aug 2015, 12:42
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shyind wrote:
If the sum of five consecutive positive integers is A, then the sum of the next five
consecutive integers in terms of A is:

a) A+1
b) A+5
c) A+25
d) 2A
e) 5A

Let the integers be
x
x+1
x+2
x+3
x+4.... x+9

Thus, A = 5x+10

sum of last 5 terms = 5x + 35 = 5x + 10 +25 = A+25. C is the correct answer.
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Re: If the sum of five consecutive positive integers is A [#permalink]

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01 Aug 2015, 22:16
Expert's post
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shyind wrote:
If the sum of five consecutive positive integers is A, then the sum of the next five
consecutive integers in terms of A is:

a) A+1
b) A+5
c) A+25
d) 2A
e) 5A

In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median

I.e. Median = A/5 = Mean = Third Integer

First Integer = A/5 - 2
Second Integer = A/5 - 1
Third Integer = A/5
Forth Integer = A/5 + 2
Fifth Integer = A/5 + 2

i.e.
SixthInteger = A/5 + 3
Seventh Integer = A/5 + 4
Eigth Integer = A/5 + 5
Ninth Integer = A/5 + 6
Tenth Integer = A/5 + 7

Now Mean of next 5 Integers = Median = A/5 + 5

i.e. Sum of Next 5 integers = (A/5 + 5)*5 = A+25

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Re: If the sum of five consecutive positive integers is A [#permalink]

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02 Aug 2015, 20:02
2
KUDOS
Expert's post
The sum of 5 consecutive positive integers = A. Think of it this way, each of the next 5 consecutive positive integers is 5 more than the corresponding first five integers. SInce there are 5 integers, 5x5 would make the sum 25 greater than A. Thus, answer choice C A+25 is correct.
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Re: If the sum of five consecutive positive integers is A [#permalink]

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04 Aug 2015, 14:36
1
KUDOS
GMATinsight wrote:
shyind wrote:
If the sum of five consecutive positive integers is A, then the sum of the next five
consecutive integers in terms of A is:

a) A+1
b) A+5
c) A+25
d) 2A
e) 5A

In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median

I.e. Median = A/5 = Mean = Third Integer

First Integer = A/5 - 2
Second Integer = A/5 - 1
Third Integer = A/5
Forth Integer = A/5 + 2
Fifth Integer = A/5 + 2

i.e.
SixthInteger = A/5 + 3
Seventh Integer = A/5 + 4
Eigth Integer = A/5 + 5
Ninth Integer = A/5 + 6
Tenth Integer = A/5 + 7

Now Mean of next 5 Integers = Median = A/5 + 5

i.e. Sum of Next 5 integers = (A/5 + 5)*5 = A+25

To correct here, fourth integer should be A/5 +1 (not A/5+2)
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Posts: 43896
Re: If the sum of five consecutive positive integers is A [#permalink]

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16 Aug 2015, 14:05
shyind wrote:
If the sum of five consecutive positive integers is A, then the sum of the next five consecutive integers in terms of A is:

A. A+1
B. A+5
C. A+25
D. 2A
E. 5A

The sum of five consecutive positive integers is A, next 5 consecutive will gain additional 5*5 = 25, so the sum of the next five consecutive integers in terms of A is: A + 25

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Re: If the sum of five consecutive positive integers is A [#permalink]

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29 Sep 2016, 04:43
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Re: If the sum of five consecutive positive integers is A [#permalink]

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27 Feb 2017, 04:12
Let the first 5 integers be 1,2,3,4,5 (A = 15)and next 5 integers be 6,7,8,9,10 (sum = 40)
Substitute A = 15 in the option. Only option C will yield 40. ANSWER
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Re: If the sum of five consecutive positive integers is A [#permalink]

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01 Mar 2017, 17:24
1
KUDOS
Expert's post
shyind wrote:
If the sum of five consecutive positive integers is A, then the sum of the next five consecutive integers in terms of A is:

A. A+1
B. A+5
C. A+25
D. 2A
E. 5A

We can label each integer as follows:

First integer = x

Second integer = x + 1

Third integer = x + 2

Fourth integer = x + 3

Fifth integer = x + 4

Thus:

A = 5x + 10

A - 10 = 5x

(A - 10)/5 = x

A/5 - 2 = x

We see that the next 5 integers are x + 5, x + 6, x + 7, x + 8, and x + 9.

Since we have an evenly spaced set, sum = average x quantity, and since x = A/5 - 2, we have:

sum = (first term in the set + last term in the set)/2 x quantity

sum = [(A/5 - 2 + 5 + A/5 - 2 + 9)/2] x 5

sum = [(2A/5 + 10)/2] x 5

sum = (A/5 + 5) x 5

sum = A + 25

Alternate solution:

If we let the first integer be x, then the first five integers will be x, x + 1, x + 2, x + 3, and x + 4, and the next five integers will be x + 5, x + 6, x + 7, x + 8, and x + 9. We can see that each of the next five integers is 5 more than its counterpart in the first five integers. Thus, the sum of the next five integers is 5 x 5 = 25 more than the sum of the first five integers. So, if the sum of the first five integers is A, the sum of the next five integers is A + 25.

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Re: If the sum of five consecutive positive integers is A   [#permalink] 01 Mar 2017, 17:24
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