Question - In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560. What is the sum of the last 5 integers in the sequence?
(A) 585
(B) 580
(C) 575
(D) 570
(E) 565
“In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560. What is the sum of the last 5 integers in the sequence?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "Official Guide for GMAT Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.
Approach 1
It is given that the sum of first 5 increasing integer is 560.
Since the integers are increasing we need to add values and not subtract.
Let’s say that the 10 consecutive integers are x, x+1, x+2, ..., x+9
Hence, as per the problem statement:
First five:
x+(x+1)+(x+2)+(x+3)+(x+4)=560
Next five:
(x+5)+(x+6)+(x+7)+(x+8)+(x+9)=?
Notice that the 6th term is 5 more than the 1st term, the 7th term is 5 more than the 2nd term, ..., the 10th term is 5 more than the 5th term
Hence, the sum of the last 5 terms is:
5*5=25 greater than the sum of the first 5 terms.
Therefore the answer is
560+25=585
Hence, A is the correct answer.
Approach 2
It is given that the sum of first 5 increasing integer is 560.
Since the integers are increasing we need to add values and not subtract.
Let’s say that the 10 consecutive integers are x, x+1, x+2, ..., x+9
Hence, as per the problem statement:
First five:
x+(x+1)+(x+2)+(x+3)+(x+4)=560
Next five:
(x+5)+(x+6)+(x+7)+(x+8)+(x+9)=?
The sum of first 5 is 560.
Hence, x , x+1 , x+2 , x+3 , x+4 = 560
=> 5 (x+2) = 560 ............ As they are consecutive; so sum will be middle term * 5
=> x+2 = 112
=> x = 110
So next five numbers will be:
115 , 116 , 117 , 118 , 119
Therefore the sum will be:
=> 117 * 5
=> 585
Hence, A is the correct answer.
Approach 3
This is another approach by which the problem can be solved:
Considering the first 5 numbers as x, (x+1), (x+2), (x+3), (x+4)
So we get:
X+x+1+x+2+x+3+x+4=560
5x+10=560
x=110
Total sum
=10/2(2(110)+1(10-1))
=5(229)
=1145
Total sum- sum of first five terms:
=1145-560
=585
Correct Answer: A
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