What is the difference between the sum of all even integers between 51

Question

What is the difference between the sum of all even integers between 51 and 100 (inclusive) and the sum of all even integers between 1 and 50 (inclusive)?
 
A. 1,250 
B. 2,000 
C. 2,500 
D. 3,750 
E. 5,000

MahmoudFawzy · Answer

each set has 25 even consecutive numbers,
and the difference between each element is 50,
(2, 4, 6, ... , 50)
(52, 54, 56, ... , 100)
so the difference between the two sets is 25*50 = 1250

fskilnik · Answer

{S_A}\,\,\, = \,\,\,2 + 4 + 6 + \ldots + 50

{S_B}\,\,\, = \,\,\,\left( {50 + 2} \right) + \left( {50 + 4} \right) + \left( {50 + 6} \right) + \ldots + \left( {50 + 50} \right)\,\,\, = \,\,\,{S_A} + 25 \cdot 50

?\,\,\, = \,\,\,{S_B} - {S_A}\,\,\, = \,\,\,25 \cdot 50\,\,\, = \,\,\,1250\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{A}} \right)

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

ocelot22 · Answer

Sum of all evens (52-100) - sum of all evens (2-50)

We need to find the number of terms in both groups.

Number of terms (52-100) =(100-52)/2 +1 =25. Number of terms (2-50) =(50-2)/2+1 = 25

The sum of an evenly spaced set is S=(a1+an)/2 *n

So the value we are looking for is ((52+100)/2)(25) - ((50+2)/)(25) = 25(152/2-52/2) = 25(100/2)=25*50=1250 (A)

MathRevolution · Answer

=>

( 52 + 54 + … + 100 ) – ( 2 + 4 + … + 50 ) = ( 52 – 2 ) + ( 54 – 4 ) + … + ( 100 – 50 ) = 50 + 50 + … + 50 = 50 * 25 = 1250.

Therefore, the answer is A.
Answer: A

Archit3110 · Answer

sn = n/2 * ( 2a+ (n-1) *d )

for 1-50 
even terms = 25
25/2 * ( 2* 2+ ( 24*2)) 
= 650
for 51-100
even terms = 25
25/2 * ( 2*52+ 24 * 2 )
= 1900
1900-650 
= 1250 IMO A

ScottTargetTestPrep · Answer

To find the sum of a set of numbers, we first find the arithmetic average of the set and then multiply by the number of items in the set.

The sum of the even integers from 51 to 100, which is really from 52 to 100, is:

sum = average x number of items = (100 + 52)/2 x

sum = 76 x 25 = 1,900

The sum of the even integers from 1 to 50, which is really from 2 to 50 is:

sum = average x number of items = (2 + 50)/2 x

26 x 25 = 650

Thus, the difference is 1,900 - 650 = 1,250.

Alternate solution:

(52 + 54 + … + 98 + 100) - (2 + 4 + … + 48 + 50)

= (52 - 2) + (54 - 4) + … + (98 - 48) + (100 - 50)

= 50 + 50 + … + 50 + 50 (Note: Since there are there are twenty-five pairings, there are twenty-five 50s.)

= 50 x 25

= 1,250

Answer: A

vijayram24 · Answer

Sum of the numbers is given by n/2(a+l)

n for numbers 52-100 is (100-52)/2 +1 = 25
a= 52
l =100

Don't Simplify the sum

Similarly for 2-50 
n=25
a=2
l=50

Now when we subtract both values ,we can get 25/2(100) = 1250

Posted from my mobile device

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What is the difference between the sum of all even integers between 51

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What is the difference between the sum of all even integers between 51

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