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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  [#permalink]

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New post 09 Jan 2019, 00:22
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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

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

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New post 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
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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.
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Re: What is the difference between the sum of all even integers between 51  [#permalink]

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New post 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.

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Fabio.
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Re: What is the difference between the sum of all even integers between 51  [#permalink]

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New post 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)
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Re: What is the difference between the sum of all even integers between 51  [#permalink]

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New post 11 Jan 2019, 03:48
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=>

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

Therefore, the answer is A.
Answer: A
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Re: What is the difference between the sum of all even integers between 51  [#permalink]

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New post 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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