To receive a driver license, sixteen year-olds at Culliver High School

Answer C (I think)

(1) insufficient
(2) insufficient because it doesn't give details as to the total number of students

Combined,
w - % of 188 who passed the written test
p - % of 188 who passed the practical tests
0.3w -failed practical test
0.2p - failed written test
license holders = 0.7w=0.8w

first equation 0.3w +0.7w+0.2p =188 --> w+0.2p =188
second equation p+0.3w=188

2 variables with 2 equations, which means you can find the answer

I am going to say E on this..cause while i know the number of 16-year olds..i dont know how many actually applied for the drivers license..this question as is written would be E..

anyone else have the same view as I?

The question stem says that all students must take the tests.

Man this is hard..

p=% passed practical
w=% passed written..

(1-p)=.3W from the stem

1) 188 students insuff, (2) (1-w)=0.2p

P+(1-p)+w+(1-w)=188

p+.3W+w+0.2p=188

1.2p+1.3W=188

I dont get..how this can be C? i have 2 variables 1 equation..

can someone explain?

I used a different approach and got C as the answer, but I'm not sure if my value answer holds true. Basically I got that 50% of the students involved in the tests got their driver's license.

This means that 188/2 = 94 students got their license instead of 112.

A+B+C=188

.3(a+b)=a

.2(b+c)=c

solve for B, which equals 112

There are four outcomes. You can:
A) Pass Written and Pass Practical (which implies you get a license)
B) Pass Written and Fail Practical
C) Fail Written and Pass Practical
D) Fail Written and Fail Practical.

We are given that no one (0%) has failed both (outcome D) and that 30% Pass written, Fail practical (outcome B).
We need to find the number corresponding to outcome A (not the percentage!)


(1) There are 188 sixteen year-olds at Culliver High School.
Great, this tells you that 0 kids fall into outcome D and 57 kids fall into outcome B. But this doesn't tell you how many fall into outcome A. It tells you that the total number of kids in outcome A and outcome C is 188-57=131.


(2) 20% of the sixteen year-olds who passed the practical test failed the written test.
We now know that 20% are in outcome C. Since we know the % of kids in outcomes B, C, and D, we can figure out the % of kids in outcome A. There are 50% of kids in outcome A, since outcomes B+C+D = 50%. But, this still doesn't tell how many students are in outcome A, just the percentage.

Given both (1) and (2), we now know that 50% of 188 students (or 94 students) passed both the written and practical exam.

So the answer is C.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

This is a "2by2" question, one of the most common type of question in GMAT math
we get a table as below:


There are 3 variables (a,b,c) and one equation (c=0.3(a+c)) in the original condition, and 2 equations are given by the conditions, so there is high chance (C) will be the answer
Looking at the conditions together,
a+b+c=188, b=0.2(a+b), and this is sufficient to achieve an answer,
so the answer becomes (C).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

It's C. There were 112 having the driving licence. 140 passed the practical test including 28 (20% of 140) did not pass the writing (hence 112 passed both), 160 passed the writing test including 48 (30% of 160) did not pass the practical test. 112 + 28 + 48 = 188, which left us 0 person who failed both test as indicated.
PiyushK solution can help determine these values.
Hope this help!

Hello Bunuel, is this correct approach? Even the most helpful reply on this question uses similar approach.

Thanks in advance!

When considering the statements together, 0.7x = 0.8y and y +0.3x= 188, give x = 160 and y = 140. Hence, the number of students who received their driver license is 0.7x = 0.8y = 112.

Answer: C.

Hope it helps.