Data Sufficiency

Hi Gurus,
One question I came across in MGMAT free CAT test (I was not able to complete the test as it timed out in between , just wanted to know if I did this question in the right way)

A set of students in a school appeared for driving test which consists of a written test and a practical test. A student gets license only if he passes both written and practical. 30% of those students who passed the written exam failed in the practical. Find out the total number of students who got the license?
1. Total number of students = 188
2. 20% of those who passed the practical exam failed the written exam.

My Solution:

Let those who passed written be W and those who passed the practical be P. Our aim is to find the fraction of students who will passed both Written and Practical

From the question
70% of those who passed written exam got the license (Given: 30% of those students who passed the written exam failed in the practical). So our aim is to find 0.7W

I drew a tabular form with the Written/Practical as columns and Passed/Failed as rows.
So Written-Passed = W, Practical Passed = P, Written Failed = Unknown, Practical Failed = 0.3W

1. Total students = 188
No chance of finding W or P with this alone.

2. Means 80% of those who passed practical got license.
So 0.8P = 0.7W or W = (8/7)*P

So Written Failed = 0.2P (fill in the table)

But cannot find W or P here.

Combining 1 & 2:

Written Passed + Written Failed + Practical Passed + Practical Failed = Total

W + 0.2P + P + 0.3W = 188

Also we have from 2 --> W = (8/7)*P

So we can solve for W and P.

Hence C is the answer.

PS:- There could be small variations in the question as I am recollecting it as the test has timed out

This looks wrong to me, what about the people that failed both? They are not accounted for. Since the percentages are taken from 188 have to meet one of three conditions?
1. passed written, passed practical
2. passed written, failed practical
3. failed written AND failed practical = x?

the 30% meets condition 2, 70% meets condition 1, but those percentages should be taken from (188-x)

(2) gives us 80% of those who pass Practical Pass written. But does not give a way to determine x

I dunno though I will keep working

I am still getting that 1 and 2 combined are not sufficient.

I definitely feel that #2 in your solution step is wrong. the 80% definitely does not mean people that got their license. Of the group that took the Practical exam and passed the practical, 80% went on to pass the written portion as well, 20% did not pass the written and did not receive their license, in addition to those who took the Practical and failed. If there is a way to get the unknown from bothsides somehow I am at a loss. If not then Im just banging my head 2 insufficients. I guess I will wait for a better math person to step in but I am going with (e)

can anyone else chime in?

IMO it's (E)

W -> Passed Written exam
NW -> Didn't pass Written exam
P -> Passed the Practical exam
NP -> Didn't pass the Practical exam

Couldn't find two different equations to solve for x or y.

IMO E

There are three conditions in the above questions. To calculate the number of students who get the licence we need to know

1.) passed practical+ passed theory
2.) passed practical+ didn't pass theory
3.) didn't pass practical+ passed thoery
4.) didn't pass practical+ didn't pass theory

Now consider Statement 1:

a.) Total number of students do not give us all the information above.---insufficient

Statement 2:

b.) It gives no information abt how many students passed the practical.

No. of students who passed the practical =P, Failed the practical= P'
No. of students who passed the written =W, Failed the written W'

20P/100=W'; 30W/100=P'

We dont know the values of P' and W' from the question.---insufficient.

Combining statement 1 and statement 2:

total students=188
20P/100=W'; 30W/100=P'
4 unknows, 2 equations..not possible to calculate....Insufficient.

E.