In a series of twenty consecutive integers, the sum of the first two

Question

In a series of twenty consecutive integers, the sum of the first two integers is 37. What is the sum of the last three integers in the set?

A 107

B 108

C 109

D 110

E 111

Archit3110 · Answer

given 
2x+1 = 37
x= 18

last three digits
3x+17+18+19 
54+54 = 108
IMO B

generis · Answer

In a set of consecutive integers, the sum of the first two is 37

(1)  First integer,  x ?
 x + (x+1)=37 
 2x+1=37 
 x=18

(2)  Last integer?
If  x  is the first integer, and there are 20 integers total, then there are 19 more
Add 19 to  x=18  (Consecutive = +1 for each integer in the set.) 
 18+19=37

If not sure, use a simpler example: There are 4 consecutive integers in the set. 
 x=18 . List them. 18, 19, 20, 21
There are  4  integers, but we need only  +3  added to  x=18  to find the last integer.

20 integers in this set, but add only 19 to the first integer.  18+19=37

(3)  Sum of last three integers?

Last three integers: 37, 36, 35
Mentally add the units digits. 
Units digit = 8
(Or, 37 + 36 + 35 = 108)

Answer B

gracie · Answer

let x=first integer
x+(x+1)=37
x=18
19th integer=18+18=36
because 19th integer is mean of last three integers,
sum of last three integers=3*36=108
B

ScottTargetTestPrep · Answer

Letting x = the first number in the set, we can create the equation:

x + x + 1 = 37

2x = 36

x = 18

The first integer is 18, and the second integer is 19. Note that the position number of the integer + 17 = the value of the integer. We see that for the 1st integer (position 1), we have 1 + 17 = 18. For the 2nd integer (position 2), we have 2 + 17 = 19. Thus, the 18th integer in the set is (18 + 17) = 35. The 19th integer in the set is (19 + 17) = 36, and the 20th integer in the set is (20 + 17) = 37.

We want the sum of the 18th, 19th, and 20th integers in the set. 
Thus, the sum of the last three integers is:

35 + 36 + 37 = 108

Answer: B

ScottTargetTestPrep · Answer

Solution:

We can let x = the first integer, then x + 1 = the second integer, x + 17 = the 18th integer, x + 18 = the 19th integer, and x + 19 = the 20th (or the last) integer. We can create the equation:

x + x + 1 = 37

2x = 36

x = 18

So the sum of the last three integers is x + 17 + x + 18 + x + 19 = 3x + 54 = 3(18) + 54 = 108.

Answer: B

Abhibarua · Answer

Suppose, First term X 
Second term X+1

2X+1 = 37 
X = 18

((Last term - First term)/ Increment) + 1 = Number of Terms 
((Last term - 18)/ 1)) + 1 = 20  
Last term = 37

37+36+35 = 108 (Option: B)

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In a series of twenty consecutive integers, the sum of the first two

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In a series of twenty consecutive integers, the sum of the first two

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