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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the difference between the sum of all even integers between 51  [#permalink]

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09 Jan 2019, 00:22
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:22) correct 41% (00:54) wrong based on 34 sessions

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[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

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Status: Manager Joined: 27 Oct 2018 Posts: 107 Location: Malaysia Concentration: Strategy, International Business GPA: 3.67 WE: Pharmaceuticals (Health Care) What is the difference between the sum of all even integers between 51 [#permalink] ### Show Tags Updated on: 09 Jan 2019, 08:26 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 _________________ ...Thanks for KUDOS Originally posted by Mahmoudfawzy83 on 09 Jan 2019, 01:28. Last edited by Mahmoudfawzy83 on 09 Jan 2019, 08:26, edited 2 times in total. GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 619 Re: What is the difference between the sum of all even integers between 51 [#permalink] ### Show Tags 09 Jan 2019, 08:00 2 MathRevolution 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. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Intern Joined: 16 Oct 2011 Posts: 49 GMAT 1: 620 Q37 V38 Re: What is the difference between the sum of all even integers between 51 [#permalink] ### Show Tags 09 Jan 2019, 09:43 MathRevolution 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 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) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the difference between the sum of all even integers between 51 [#permalink] ### Show Tags 11 Jan 2019, 03:48 1 => $$( 52 + 54 + … + 100 ) – ( 2 + 4 + … + 50 ) = ( 52 – 2 ) + ( 54 – 4 ) + … + ( 100 – 50 ) = 50 + 50 + … + 50 = 50 * 25 = 1250.$$ Therefore, the answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: What is the difference between the sum of all even integers between 51  [#permalink]

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11 Jan 2019, 04:23
1
MathRevolution 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

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
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Re: What is the difference between the sum of all even integers between 51 &nbs [#permalink] 11 Jan 2019, 04:23
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