kiran120680 wrote:
Set P consists of the first n positive multiples of 3 and set Q consists of the first m positive multiples of 5. The sum of all the numbers in set P is equal to R and the sum of all the numbers in set Q is equal to S. If 'm 'and 'n' are positive integers, is the difference between R and S odd?
I. m is odd and n is even
II. m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integer
Here is how I solved. This is a Yes/No question and you need to find all the areas to see if you are getting consistent answers.
By looking at the statements, I got an idea that while testing conditions, n has to be odd and m has to be even! So I took two examples so it'll be easy to test/solve:
Example 1: P={3,6,9} => n=3 and ΣP=18=R & Q= {5,10} =>m=2 and ΣQ=15=S
Nowhere in the questions it is mentioned that the multiples should be consecutive. So I'm gonna take different numbers now.
Example 2: P={3,9,15} => n=3 and ΣP=27=R & Q= {10,15} =>m=2 and ΣQ=25=S
Another hint: We gotta find if R-S=odd. As per number property rules, odd-even=odd or even-odd=odd(keep this in kind while taking examples. It'll help!)
Moving onto the statements
Statement (1): m is odd and n is even
Now the role of examples come in. From example 1, R-S= 18-15=3 ODD......YES
example 2, R-S= 27-25=2 EVEN...........NO
Different answers.....INSUFFICIENT
Statement (2): m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x
m=4x+3=odd (odd+even=odd) and n=2x= even
Now this statement is as same as statement 1
Different answers.....INSUFFICIENT
Combining statement (1) + (2) would be same as above. Different answers. INSUFFICIENT
Hence, answer is
option E