If the sum of five consecutive positive integers is A, then the sum of

Question

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

VeritasPrepDennis · Accepted Answer

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.

ENGRTOMBA2018 · Answer

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.

GMATinsight · Answer

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

Answer: option C

GMATnavigator · Answer

To correct here, fourth integer should be A/5 +1 (not A/5+2)

Bunuel · Answer

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

Answer: C.

KrishnakumarKA1 · Answer

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

JeffTargetTestPrep · Answer

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 =   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.
 
Answer: C

Aparna05 · Answer

Since the sum of 5 consecutive integers is A, then next 5 terms will be sum of 5+1,5+2,5+3,5+4,5+5 respectively.
Hence sum of the next five consecutive integers in terms of A is 5*5 + (1+2+3+4+5)=25+A

IMO C is the correct answer.

BrushMyQuant · Answer

The sum of five consecutive positive integers is A

Let the consecutive numbers be x, x+1, x+2, x+3, x+4
=> Their sum = A

The sum of the next five consecutive integers in terms of A is:

Now, each of the next five consecutive numbers will be 5 more than the previous 5 numbers

Ex: x + 5 is 5 more than x and so on

=> Sum of next 5 numbers = A + 5*5 = A + 25

So,  Answer will be C 
Hope it helps!

Watch the following video to learn How to Sequence problems

https://www.youtube.com/watch?v=EfNT2JoE5CM

Rohanx9 · Answer

Its easy to plugin numbers.

1+2+3+4+5 = 15

6+7+8+9+10 = 40

Difference = 25.

If the sum of five consecutive positive integers is A, then the sum of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If the sum of five consecutive positive integers is A, then the sum of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards