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Driver's license -- Overlapping sets

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by Stockmoose16 » Thu Oct 23, 2008 2:41 pm
To receive a driver license, sixteen year-olds at Culliver High School have to pass both a written and a practical driving test. Everyone has to take the tests, and no one failed both tests. If 30% of the 16 year-olds who passed the written test did not pass the practical, how many sixteen year-olds at Culliver High School received their driver license?

(1) There are 188 sixteen year-olds at Culliver High School.

(2) 20% of the sixteen year-olds who passed the practical test failed the written test.

Can someone show me how correctly solve this problem using a double-set matrix? I got the following numbers:

Pass Practical Fail Practical Total
Pass written .7x=.8Y .3x X

Fail written .2Y 0 .2y

Total Y .3x 188

From this info, we know:

X= .8Y/.7

But is it accurate to say Y+.3X=188? (the bottom total from left to right)? I think it should be X+Y=188, but I'm not sure why, since this is a double set matrix, and each line should add up.

Any insight is appreciated.
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by cramya » Thu Oct 23, 2008 4:01 pm
Whats the oa?

I am getting E)

I am getting the same equation both ways.

Please see attached.
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by rohangupta83 » Thu Oct 23, 2008 4:02 pm
--------Written----------------------Practical------------------------Total

Pass----X (eq1) -------------Y(eq3)------------------------X+Y

Fail-----0.2Y(eq4)---------0.3X(eq2)-------------------0.3X+0.2Y

Total----X+0.2Y---------------------0.3X+Y------------------------188

From statement 1
Total number of 16 year olds = 188

Let the number of students who passed the written exam = X (eq1)

30% of students who passed the written exam failed the practical exam, therefore number of students who failed the practical exam = 0.3X (eq2)

This is all we have from statement 1 and question.

Moving onto statement 2

Let number of students who passed the practical exam = Y (eq3)

Now 20% of students who passed the practical, failed the written. Therefore, students who failed the written test are = 0.2Y(eq4)


X+Y+0.3X+0.2Y = 188
or
1.3X+1.2Y=188

This is what I got = answer E (insufficient-was not able to solve any further)
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by Stockmoose16 » Thu Oct 23, 2008 4:05 pm
rohangupta83 wrote:--------Written----------------------Practical------------------------Total

Pass----X (eq1) -------------Y(eq3)------------------------X+Y

Fail-----0.2Y(eq4)---------0.3X(eq2)-------------------0.3X+0.2Y

Total----X+0.2Y---------------------0.3X+Y------------------------188

From statement 1
Total number of 16 year olds = 188

Let the number of students who passed the written exam = X (eq1)

30% of students who passed the written exam failed the practical exam, therefore number of students who failed the practical exam = 0.3X (eq2)

This is all we have from statement 1 and question.

Moving onto statement 2

Let number of students who passed the practical exam = Y (eq3)

Now 20% of students who passed the practical, failed the written. Therefore, students who failed the written test are = 0.2Y(eq4)


X+Y+0.3X+0.2Y = 188
or
1.3X+1.2Y=188

This is what I got = answer E (insufficient-was not able to solve any further)
OA is C
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by cramya » Thu Oct 23, 2008 4:08 pm
It has to be C or E. If its C then I may be missing something in setting up the equation like u
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by Stockmoose16 » Thu Oct 23, 2008 4:09 pm
cramya wrote:It has to be C or E. If its C then I may be missing something in setting up the equation like u
It is definitely C. It's from the MGMAT CATs.
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by rohangupta83 » Thu Oct 23, 2008 4:17 pm
ok here is the reason why the answer is C

there are 188 students and all of them took both the written exam and the practical exam

So

X+0.2Y = 188 (is 1 equation)
Y+0.3X = 188 (is the second equation)

or

0.7X = 0.8Y
0.7X - 0.8Y = 0 (equation 3)

From the matrix (change the total from 188 to 2*188 = 376) as total students who took the written exam = 188 and total students who took the practical exam = 188)

1.3X + 1.2Y = 376 (equation 4)

solve these 2 equations
you'll get X and Y

Hope that helps!
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by cramya » Thu Oct 23, 2008 4:22 pm
Like I said I I missed another equation which is

.70x = .80y

hence C)
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by rohangupta83 » Thu Oct 23, 2008 4:24 pm
would never have figured this one out in the real exam..
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by Stockmoose16 » Thu Oct 23, 2008 4:24 pm
rohangupta83 wrote:ok here is the reason why the answer is C

there are 188 students and all of them took both the written exam and the practical exam

So

X+0.2Y = 188 (is 1 equation)
Y+0.3X = 188 (is the second equation)

or

0.7X = 0.8Y
0.7X - 0.8Y = 0 (equation 3)

From the matrix (change the total from 188 to 2*188 = 376) as total students who took the written exam = 188 and total students who took the practical exam = 188)

1.3X + 1.2Y = 376 (equation 4)

solve these 2 equations
you'll get X and Y

Hope that helps!
If you were to calculate the answer out, what number would you get?
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by cramya » Thu Oct 23, 2008 4:26 pm
Typo of .80



.70x= .20y (given in B)

Still C)

Its a good one.

Hi StockMoose.
For future posts (like Eric said) if you could include the OA with the SPOILER function that would be awesome!
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by earth@work » Thu Oct 23, 2008 4:27 pm
oh no...i was completly wrong...sorry..trying again
Last edited by earth@work on Thu Oct 23, 2008 4:41 pm, edited 2 times in total.
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by cramya » Thu Oct 23, 2008 4:31 pm
Ok guys I am going crazy here

.70x = .80y

Rohan, I am so confused even after seeing the OA and figuring this out(said =.20y in my previous post). I am sure I would have gone for E) just like u.

Its all in the game; win some loose some just pray we dont loosse too many on G day(none at all would be a dream but great)!


StockMoose,
Whats the source? Manhattan again?
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by rohangupta83 » Thu Oct 23, 2008 4:35 pm
damnit! i'm getting 2 different answers

either the answer is 200 or 105

Y = 200
X = 229 or 105

but 200 can't be the answer as the max could be 188 which is also not possible in this case so I'd go for 105!

I am not at all confident though..
Last edited by rohangupta83 on Thu Oct 23, 2008 4:40 pm, edited 2 times in total.
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by rohangupta83 » Thu Oct 23, 2008 4:39 pm
yep Cramya, this one would become one of my freebies for sure. More than 30 mins and still can't figure it out accurately.
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