Problem Solving

1) If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability that their product will be of the form of x^2 - (by)^2, where b is an integer?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/6

2) A circular medallion made of a circular piece of colored glass is surrounded by a metal frame. If the radius of the medallion is r centimeters and the width of the metal frame is s centimeters, then in terms of s and r, what is the area of the metal frame, in square centimeters?

A. pi(r-s)^2
B. pi(r^2 - s^2)
C. 2pi(r-s)
D. pi*r(2r-s)
E. pi*s(2r-s)

All OAs will be posted. Thanks

Please read this

https://www.beatthegmat.com/re-check-bef ... 17162.html

Have these questions been posted before?

1) 1/6, only once when you choose x-y and x+y, you will get this kind of expression..

Ans 1/(4C2) = 6

rahulg83, the first one is correct any thoughts on the second one? I can send an attachment.

See from the center till the edge (complete medallion), the distance is 'r' and thickness(the shaded part, metal frame) is 's'

Area of frame = pi [r^2-(r-s)^2] (why?)
= pi (r^2-r^2-s^2+2*r*s)
= pi(-s^2+2*r*s)
= pi * s (2r-s), Answer E

that's a good answer. it seems like, initially, I didn't deal properly with pi*(r-s)^2.

This problem might seem really simple but I'm getting the equation mixed up.

Q: A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 7 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?

please help!

If you had posted the options, it would have been much easier...
Anyways, my answer is 9 minutes...
First, we need to assume that call is gonna be for more than 7 minutes..(we are not sure of per minute rate for plan A, if the call is for less than 7 minutes)
now suppose total call length is x minutes
Under plan A, call charges will be 0.60 + (x-7) *0.06
Under plan B, call charges will be x*0.08

For same call charges, we need to equate above equations

0.60+(x-7)*0.06=x*0.08

or 0.18=x(0.08-0.06)
or x=9 minutes...
Is this the answer?

9 minutes is the exact answer, thanks. I was missing (x-7) to solve it properly.