nipunjain14 wrote:
MathRevolution wrote:
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
If q and r are both odd numbers, which of the following must also be odd?
A. q – r
B. (q + r)^2
C. q(q + r)
D. (qr)^2
E. q/r
Since q and r are odd numbers we can put q and r as q=2*Q+1 and r=2*R+1, for some integers Q, R.
A. q-r=(2*Q+1)-(2*R+1)=2*(Q-R) ---> must be an even number.
B. (q + r)^2 =(2Q+2R+2)^2= 4*(Q+R+1)^2 ---> must be an even number.
C. q(q+r) = (2Q+1)(2Q+2R+2)= 2*(2Q+1)(Q+R+1) ---> must be an even number.
D. (qr)^2 = ((2Q+1)(2R+1))^2 = (4QR +2Q +2R +1)^2
by putting 2QR+Q+R = T we have (2T+1)^2= 4T^2 + 4T +1=2(2T^2 +2T)+1 ---> must be an odd number.
E. q/r cannot be an integer
The answer is, therefore, (D).
Y cant q/r be odd?
let us assume q = 27 and r = 3
then q/r = 9 which is odd
Any specific relation between q and r is not specified.
Please explain why E is wrong option
Hi,
why E is wrong?
It is because the question asks you "
which of the following must also be odd?"...
"must" word makes the choice wrong..
you can find ways of\(\frac{q}{r}\)being odd and ways of\(\frac{q}{r}\)being non integer, so it does not fall into must category..
E also would have been an answer, had the Q asked "
which of the following CAN also be odd?"..
I Hope the Reasoning is clear
Thanks I understand now. We need to keepin mind all aspects when facing "Must be" type questions