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If X is the sum of first 50 positive even integers and Y is

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Manager
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Joined: 31 Jul 2017
Posts: 134
Location: Tajikistan
Concentration: Finance, Economics
Schools: Booth '21, CBS '21
GMAT 1: 690 Q48 V35
GRE 1: Q164 V162
GPA: 3.85
WE: Accounting (Investment Banking)
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Re: If X is the sum of first 50 positive even integers and Y is  [#permalink]

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New post 12 Jun 2018, 05:55
1
I used the following method.
The sum of first 50 even integers is nu of terms* av or 50/2+1=26* 25 (is av)
The sum of first 50 odd integers is nu of terms*av 50/2-1=24*25.
So we have 26*25-24*25=25(26-24)=25*2=50
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Re: If X is the sum of first 50 positive even integers and Y is  [#permalink]

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New post 04 Aug 2018, 04:04
First all the answer-choices are non-negative, so figured x would must be equal or bigger to y. Helped in my thinking.

Started with taking 2 (first even integer) + 100 (50th even integer)/2, average=51. Then multiple the number by the amount of even integers=50
51*50.

Then first odd and 50th odd--> 1+99/2=50, 50*50(amount of odd integer)

So (51*50)-(50*50), you dont have to do the calculation, you simply see its gonna be 50 left when (50*50) is subtracted.

Hence, we got our answer :D
Thumbs up if you thought it was a good explanation :-) :thumbup:
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Re: If X is the sum of first 50 positive even integers and Y is  [#permalink]

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New post 31 Aug 2018, 23:07
Hi,

well there are several super explanations given by experts which we must internalize to better our qunat score. However, just an alternate approach.

If we look at set of numbers which we get in x { 2,4,6,8,10,12.......100} and similarly set of numbers y {1,3,5,7,9...99)

now x-y would be {2 -1 + 4-3 + 6-5+ 8-7+....... 100-99}
if we just see the set performs for first 5 even odd we can then infer about the reaming set
So in first 5 even -odd it would be { 2 -1 + 4-3 + 6-5+ 8-7 +10-1}= 5

Now since we have for first 5 (even -odd) the result is 5 , so there are 10 such sets , so the answer must be 10 *5= 50


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Re: If X is the sum of first 50 positive even integers and Y is  [#permalink]

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New post 20 Sep 2018, 22:17
Sum of first 50 odd numbers: 1+3+....+97+99=100x25=2500
(bunch the numbers together, 99+1=100, 97+3=100 and there are 25 such pairs)

Sum of first 50 even numbers: 2+4+...+98+100=102x25=2550
(bunch the numbers together, 100+2=102, 98+4=102 and there are 25 such pairs)

so 2550-2500=50
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+1 Kudos if this helped :)

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Re: If X is the sum of first 50 positive even integers and Y is &nbs [#permalink] 20 Sep 2018, 22:17

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