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# Set word problems

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Manager
Joined: 06 Jun 2003
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18 Sep 2003, 11:27
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Guys .. thanks for all the great work .. need help in a problem which I just can't seem to figure out (from GMAT+) :

All trainees in a certain aviator training program must take both a written test and a flight test. If 70 percent of the trainees passed the written test, and 90 percent of the trainees passed the flight test, what percent of the trainees passed both the tests?

(1) 10 percent of the trainees did not pass either test
(2) 20 percent of the trainees passed only the flight test

The answer is D (either choice) .. but how?
Manager
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18 Sep 2003, 13:05
here's what i get....i attempted choice B first b/c it was easier

i used a venn diagram but i'll try to convey my point as best as possible

we know: 70 passed Written (W)
and :90 passed Flight (F)
total of 160 --> obviously there is an overlap

statement B:
set up this table :

passed W only:
passed F only :
passed both F&W:
total = 100%

passed F only is given: 20, so passed both F&W would be (90-20) b/c we know that 90 in total passed F...but 20 passed ONLY F, which so 70 is the overlap (passed both F&W)...and thus 100%-20%-70%=10% but no more than 70 passed the W, so the 10% must be the people that did not pass any......

so B is sufficient....

however, now looking at A...keep in mind that having done B first will make A look like a snap...

but A basically says what we "figured" out from B (if we had decided to solve it...which we probably shouldn't have b/c it's a DS question...but never the less)

A says that 10% passed neither, meaning that 90% passed Wonly, Fonly, and W&F...and if you try out some numbers there is only 1 way that you can maintain all the given parameters...which is F only: 20, F&W (90-20) and W only 0

you can set up this equation: you know that Wonly + Fonly + W&F= 90
but W&F is basically 90-Fonly OR 70-Wonly

solve for whatever you want Wonly+Fonly + (90-Fonly) = 90 => Wonly=0
OR Wonly+Fonly + (70-Wonly)= 90 => Fonly=20

so both are sufficient b/c they basically tell us the same thing....

i hope this clarifies it a bit...it is easier to see with a venn diagram, try it...
Manager
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18 Sep 2003, 14:06
Thanks for the quick reply, guy123.

I think I have almost got it. Please see if my reasoning is correct:

total(pass) + total(fail) = 100

total_pass(f only + w only + both) + total_fail(f only + w only + both) = 100

(90 + 70 - overlap) + total_fail(f only + w only) = 100

(160 - overlap) + total_fail(f only + w only) = 100

Is this correct so far?
Manager
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18 Sep 2003, 15:01
yes, technically what you're doing is correct, but you don't need to do all that though...i made my explanation long b/c i wanted you to be able to answer any venn diagram type problem:

some basic points to remember:

1) DRAW a venn diagram (designate one side as the Wonly, one side as the Fonly and the middle overlap as both F&W).
2) then draw a square around both circles (anything that doesn't fall into the circles (in this case % that failed both--passed neither--goes into the square but outside the circles)
3) remember though that one circle MUST equal the total # (or in this case %) for that particular event, scenario or whatever you want to call it.

so in this case (Wonly + the number in the overlap must equal TOTAL % for W)...this is the beauty of the relationship b/c since the overlap has to be the same # (or % in this case) there is only one way you can get the numbers to match up..b/c (Fonly + the number in the overlap must equal TOTAL for F)...and we were given the totals for F & W so we will always be able to find the particular numbers to complete the venn diagram....you don't really need to stress to much about the "equation"...i just threw that in there b/c i wanted to explain that we could get an answer if we wanted to ...but you can easily "see" the answer when using venn diagrams...

if you still can't visualize it then i can upload a representation on MS Word....from my experience these types of questions are pretty common...i took the gmat last week and i got a similar one and nailed it...easy points in my opinion...
Manager
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18 Sep 2003, 19:37
Here's a venn diagram, as close as I could get in ASCII:

F 90 F&W W 70
--------------------------
| 20 |70 | 0 |
--------------------------
fail 10

Does this look ok?
BTW what was your score in the GMAT? Any pointers?

Thanks.
Manager
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18 Sep 2003, 21:04
yes...it looks like you got it....are you starting to visualize it easier now?

i used to suck at these questions, but then i learned how to use venn diagrams and now i can answer ANY similar questions...

if you have the offical guide then try problems #133, 153, 186, 225, 336

some are easier using venn diagrams and some are easier using tables (but they're all similar)...i can post teh questions if you don't have the OG

but anyways, i got a 640...i was pretty dissappointed with it...i'm retaking it on the 1st of October....

pointers: get teh OG if you haven't already....make sure you know how to do all the problem types in there and you'll be fine....some that tend to show up more often are D=R*T problems....and work problems (ie. it takes Jan 6 hours to do the job by herself and Tim 4 hours to do the job by himself...how long does it take them together)...

all i can offer is, stay FOCUSED and READ THE QUESTION COMPLETELY BEFORE YOU ANSWER AND DOUBLE CHECK BEFORE YOU CLICK...i f*ed up on a couple b/c i was to quick in solving and clicking.....
Manager
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19 Sep 2003, 17:02
I got it .. thanks for all the help .. and good luck for your next attempt!!
cool!   [#permalink] 19 Sep 2003, 17:02
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