Probability Question. Cant solve :-(

[miteshsholay]

http://postimage.org/image/lvzfb8xbl/

In the rectangle shown above, AD=6, AB=8. What is the
probability that PD<45^1/2?
a) 1/8
b) 2/8
c) 3/8
d) 1/4
e) 3/7

[jnelson0612]

Please provide the original source of this question.

[miteshsholay]

Jamie,
I got this question from the following pdf
http://www.scribd.com/doc/105674344/125-Awesome-Quant-Questions
The que. no. 10 in this pdf is the one.
I know its not from any renowned GMAT prep material, but a good question nevertheless.

[RonPurewal]

that document doesn't have answer choices. where did you get the answer choices?
in any case, this is a pretty cool problem (although it's badly written -- see below). it would be nice if there were some sort of attribution.

anyway...
in any case, the problem is sloppily written. for this problem to mean anything at all, it MUST specify that the point P is chosen at random from anywhere on side AB.
this is essential, and they didn't state it -- so, as written, this problem could have any probability at all as the answer.

if we know that P is chosen at random, then you just have to find where it would need to be for PD to be √45.
for that, you can solve the Pythagorean theorem:
6^2 + (AP)^2 = (√45)^2
36 + (AP)^2 = 45
AP = 3
so, for PD to be less than √45, we need to pick P anywhere from 0 to 3 units away from A.
since AB is 8 units long -- again, assuming that P is chosen at random from that side -- this gives us a probability of 3/8.

[miteshsholay]

I agree that the problem is not clearly written. But could not help wondering about it.
Anyway thanks a lot for the reply.
I have a doubt.

According to your suggested solution, we got a range 0 to 3. So I guess we are assuming that AP can only be integers 1,2 or 3 and not 1.5, 2.4, 2.7 and so on.
Should this thing be also specified in the problem or we just have to assume that all lengths are integers?

Again, I know we should not trust and worry too much about problems from ambiguous sources, still I would appreciate if this gets cleared.

[RonPurewal]

I agree that the problem is not clearly written. But could not help wondering about it.
Anyway thanks a lot for the reply.
I have a doubt.

According to your suggested solution, we got a range 0 to 3. So I guess we are assuming that AP can only be integers 1,2 or 3 and not 1.5, 2.4, 2.7 and so on.
Should this thing be also specified in the problem or we just have to assume that all lengths are integers?

Again, I know we should not trust and worry too much about problems from ambiguous sources, still I would appreciate if this gets cleared.

no. in fact, if you assume integers (which you shouldn't), then the probability is 2/7.
if you assume an integer length, then there are only seven possibilities, 1 through 7. (can't be 0 or 8, because the diagram clearly indicates that point P does not coincide with A or B.)
of those seven possibilities, only 1 and 2 work. (3 doesn't work, because √45 is not less than √45.)

the probability in this instance is 3/8, because you have to pick a point from anywhere between 0 and 3. that continuous region accounts for exactly 3/8 of AB, hence the probability.

[miteshsholay]

got it.
thanks a lot Ron.

[tim]

:)

[peterr89]

sorry but that the problem is not clearly written
http://www.centplay.com/affiliate/id_139/

[miteshsholay]

i took this from a random source online. Posted this coz it was bothering me for long. :-)
the gmat problems are not this unclear.

[jnelson0612]

Agreed.