What will be the sum of all the even numbers between 1 and 60?

Question

What will be the sum of all the even numbers between 1 and 59?

(A) 960
(B) 870 
(C) 860
(D) 840 
(E) 720

richimar98 · Answer

there are 29 even numbers between 1 and 59.

If we arrange the sum of them in pair such as ( 2+58 ), ( 4+56 )...( 28+32 ) we notice that the sum is 60 for each of them.

We take 29 numbers in pair so 14,5 and multiply it by 60. 14,5*60=870

ShahadatHJ · Answer

Since, we are supposed to calculate the sum of even numbers between 1-59, then we can say that we need to sum all the even numbers from 2-58.

Hence, the numbers: 2+4+6+8+...+58
We can re-write this sequence to: 2*(1+2+3+...+29)

And we know the sum of N numbers in a sequence is: n*(n+1)/2

So, 2*(29*(29+1))/2 = 870

Ans: B

AnujSheth · Answer

If we take 0 to 59 we have exactly 60 numbers, and 30 even numbers(including 0), so 15 pairs which make 58, 58*15 is 870

ansarose · Answer

Cant we find the result using arithmetic progressions?

Posted from my mobile device

aniruddhawarang29 · Answer

Yes we can, unless it doesn't take you more than 45 seconds for this type of calculation based Q.

hykhan · Answer

sum = average * # of terms

number of terms = ((highest instance - lowest instance)/(type of integer)) + 1

in this case, the highest even number between 1-60 is 58. the lowest is 2. the type of integer is even/odd so the value at the bottom will be 2.

(58-2)/2 - 1 = 29

average = (highest instance + lowest instance)/2 --> 58+2/2 = 30

29*30 = 870

B

gmatmonks · Answer

Note that this is an evenly spaced sequence.

Thus, the sum = No. of terms * Average

Average = (First Term + Last Term)/2 = (2 + 58)/2 = 30

No. of Terms =   + 1 =   + 1 = 29

Sum = 29 * 30 = 870

Hence  (B)  is the answer

P.S. 
Although we can directly use the formula for arithmetic progressions, one should know to handle such a sequence without the knowledge of the formula as well.

ScottTargetTestPrep · Answer

Solution:
 
The smallest even number between 1 and 59 is 2 and the largest is 58. There are (58 - 2)/2 + 1 = 29 even numbers between 1 and 59. We know that the average of these 29 (evenly-spaced) numbers is (2 + 58) / 2 = 30, We use the formula: average x number = sum to obtain: 
(2 + 58)/2 x 29 = 30 x 29 = 870

Alternate Solution:

We need to determine the value of the sum 2 + 4 + 6 + … + 58. Let’s factor the common factor of 2:

2 + 4 + 6 + … + 58 = 2(1 + 2 + 3 + … + 29)

Using the formula n(n+1)/2 for the sum of the consecutive integers between 1 and n, inclusive, we have 1 + 2 + 3 + … + 29 = (29 x 30)/2. Thus:

2(1 + 2 + 3 + … + 29) = 2 x   = 29 x 30 = 870

Answer: B

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What will be the sum of all the even numbers between 1 and 60?

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What will be the sum of all the even numbers between 1 and 60?

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