This question has tedious calculation but I am 100% positive that my calculation is correct (verified using Excel spread sheet and small computer program) . So my concept is wrong and I will present my logic vs the correct logic . An explanation will be appreciated. So here goes the question..
Q If x is the sum of first 50 positive even integers 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
My solution
Using formula n(n+1)/2 for sum of first n numbers.
Sum of all 50 numbers comes to 25(51) --> Lets call it as t (for total)
Sum of first 50 positive even integers 25(26) which is x
So sum of first 50 positive odd integers will be y=t-x=25(51)-25(26)=25(25)
Now x-y
=25(26)-25(25)=25 My answer is B
GMAT Solution
x-y
(2+4+6+8....100)-(1+3+5...+99)
(2-1)+(4-3)+(6-5)+....(100-99)
50(1) So answer is 50 Correct answer is C
What I don't understand why is it x is (2+4+6+8....100) and not (2+4+6+8....50) or y is (1+3+5...+99) and not (1+3+5...+49)
Even if i use GMAT solution and use (2+4+6+8....50) similarly calculate y I get answer B
Q If x is the sum of first 50 positive even integers 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
My solution
Using formula n(n+1)/2 for sum of first n numbers.
Sum of all 50 numbers comes to 25(51) --> Lets call it as t (for total)
Sum of first 50 positive even integers 25(26) which is x
So sum of first 50 positive odd integers will be y=t-x=25(51)-25(26)=25(25)
Now x-y
=25(26)-25(25)=25 My answer is B
GMAT Solution
x-y
(2+4+6+8....100)-(1+3+5...+99)
(2-1)+(4-3)+(6-5)+....(100-99)
50(1) So answer is 50 Correct answer is C
What I don't understand why is it x is (2+4+6+8....100) and not (2+4+6+8....50) or y is (1+3+5...+99) and not (1+3+5...+49)
Even if i use GMAT solution and use (2+4+6+8....50) similarly calculate y I get answer B
