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probability of the product of numbers

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by LevelOne » Fri Jul 03, 2009 2:53 am
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
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by rah_pandey » Fri Jul 03, 2009 3:26 am
Please read this

https://www.beatthegmat.com/re-check-bef ... 17162.html
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by LevelOne » Fri Jul 03, 2009 3:38 am
Have these questions been posted before?
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by rahulg83 » Fri Jul 03, 2009 3:50 am
1) 1/6, only once when you choose x-y and x+y, you will get this kind of expression..

Ans 1/(4C2) = 6
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by LevelOne » Fri Jul 03, 2009 3:53 am
rahulg83, the first one is correct :wink: any thoughts on the second one? I can send an attachment.
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by rahulg83 » Fri Jul 03, 2009 4:07 am
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
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by LevelOne » Fri Jul 03, 2009 4:36 am
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!
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by rahulg83 » Fri Jul 03, 2009 5:04 am
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?
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by LevelOne » Fri Jul 03, 2009 5:07 am
9 minutes is the exact answer, thanks. I was missing (x-7) to solve it properly.
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