SKH121 wrote:
SKH121 wrote:
Quantity A |
Quantity B |
The sum of all the even integers from 18 to 36 inclusive |
The sum of all the even integers from 22 to 38 inclusive |
A)Quantity A is greater.
B)Quantity B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Thank you for your reply.
The posted answer is exactly the same as the book explanation, and i still couldn't get it.
Maybe someone has another explanation.
So we have two quantitites..
1) A=Sum of all even numbers from 18 to 36 = 18+20+22+24+26+...34+36.
2) B=Sum of all even numbers from 22 to 38 = 22+24+26+...34+36+38.
Let 22+24+...36 be a, so A=18+20+a=38+a and B=a+38..
Thus A=B
another way..
1) A=Sum of all even numbers from 18 to 36 = 18+20+22+24+26+...34+36
Sum of consecutive numbers, or consecutive even integers is average * number of terms
Average = \(\frac{first+last}{2}=\frac{18+36}{2}=27\)
Number of terms = \(\frac{36-18}{2}+1=9+1=10\)
Sum = 27*10=270
2) B=Sum of all even numbers from 22 to 38 = 22+24+26+...34+36+38.
Average = \(\frac{first+last}{2}=\frac{22+38}{2}=30\)
Number of terms = \(\frac{38-22}{2}+1=8+1=9\)
Sum = 30*9=270
so A=B
C
_________________
Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html