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What is the difference between the sum of elements of sets

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by Musicat » Thu May 12, 2016 10:24 pm
Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?

A 2500
B 5050
C 11325
D 6275
E 2550

OA: A
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by MartyMurray » Thu May 12, 2016 11:07 pm
Notice, there are 25 even numbers between 2 and 50 inclusive and there are 25 even numbers between 102 and 150 inclusive.

Further the difference between 102 and 2 is 100, and between each of the successive even numbers in the pairs after 102 and 2, there will a difference of 100.

So we have 25 differences of 100 for a total of 2500.

The correct answer is A.

Alternate Method

There are 25 evenly spaced elements in each set.

Add the highest and lowest in each set, multiply by 25 and divide by 2.

Set A Total: (2 + 50) x 25/2 = 26 x 25 = 650

Set B Total: (102 + 150) x 25/2 = 126 x 25 = (100 x 25) + (26 x 25) = 2500 + 650

Difference between total of B and total of A = 2500.

The correct answer is A.
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by Matt@VeritasPrep » Fri May 13, 2016 2:59 pm
I'd do

(150 - 50) + (148 - 48) + (146 - 46) + ... + (102 - 2) =>

100 + 100 + ... + 100 =>

25*100 =>

2500
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