dave13 wrote:
nishtil wrote:
If X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x-y?
A. 0
B. 25
C. 50
D. 75
E. 100
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Please try to explain your answers
Hi
pushpitkc i used the formalus from my post
https://gmatclub.com/forum/arithmetic-p ... l#p2035478but somrthing went wrong:? the formula for finding sum of even numbers confiused me.... pls explain where am i wrong. thanks
HOW TO FIND THE SUM OF THE FIRST EVEN NUMBERS \(\frac{n(n+2)}{4}\)
where \(n\) is number of terms
HOW TO FIND NUMBER OF TERMS FROM A TO Z \(\frac{last..term - first..term}{2} +1\)
Number of Even Terms \(\frac{50-2}{2} +1 = 25\)
Sum of Even Terms \(\frac{25(25+2)}{4}\) ???
HOW TO FIND SUM OF ODD NUMBERS FROM A TO B Step one: \(find..the..number...of..terms\)
Step two: \(\frac{first..term+last..term}{2}\) \(* number..of.. terms\)
Number of Odd terms \(\frac{49-1}{2} +1 = 25\)
Sum of Odd numbers \(\frac{49+1}{2}*25 = 625\)
Hi
dave13Unfortunately, the formula for the sum of even numbers is wrong.
The correct formula for the sum of even numbers is \(N(N+1)\).
Also, we have another formula for the sum of odd numbers, which is \(N^2\).
Let's check this by means of an example.
If N = 3, the even numbers are 2,4, and 6. The sum of the even numbers is 12.
If the formula was \(\frac{N(N+2)}{4} = \frac{3(5)}{4} = \frac{15}{4}\), we will not get the right answer.
Coming back to our problem, we have been asked to find
the sum of the first 50 even numbers.
However, you have found the details for the first 25 numbers(till 50)
We could go about doing this problem as follows:
The sum of the first 50 even numbers is 50*(50+1) = 50*51 = 2550(which is X)
The sum of the first 50 odd numbers is 50^2 = 2500(which is Y)
Therefore, the difference between X and Y is 2550 - 2500 =
50(Option C)Hope this helps you!