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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the difference between the sum of all even integers tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 1 member reply ### GMAT/MBA Expert ## What is the difference between the sum of all even integers ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice 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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$99 for 3 month Online Course
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Max@Math Revolution wrote:
[Math Revolution GMAT math practice 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
$${S_A}\,\,\, = \,\,\,2 + 4 + 6 + \ldots + 50$$
$${S_B}\,\,\, = \,\,\,\left( {50 + 2} \right) + \left( {50 + 4} \right) + \left( {50 + 6} \right) + \ldots + \left( {50 + 50} \right)\,\,\, = \,\,\,{S_A} + 25 \cdot 50$$
$$?\,\,\, = \,\,\,{S_B} - {S_A}\,\,\, = \,\,\,25 \cdot 50\,\,\, = \,\,\,1250\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{A}} \right)$$

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

Regards,
Fabio.

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Each set has 25 even consecutive numbers, and the difference between each element is 50,
(2, 4, 6, . . . , 50)
and
(52, 54, 56, . . . , 100).

So, the difference between the two sets is 25*50 = 1250.

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( 52 + 54 + â€¦ + 100 ) - ( 2 + 4 + â€¦ + 50 ) = ( 52 - 2 ) + ( 54 - 4 ) + â€¦ + ( 100 - 50 ) = 50 + 50 + â€¦ + 50 = 50 * 25 = 1250.

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