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# At a certain university, 75% of students have driver’s licences and 6

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Math Revolution GMAT Instructor
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At a certain university, 75% of students have driver’s licences and 6 [#permalink]

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28 Nov 2017, 23:25
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Difficulty:

55% (hard)

Question Stats:

50% (00:54) correct 50% (01:03) wrong based on 42 sessions

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[GMAT math practice question]

At a certain university, 75% of students have driver’s licences and 60% of the students with driver’s licences are foreign students. What percentage of the total students are foreign students without a driver’s licence?

1) There are 5,000 students at the university.
2) 55% of students at the university are foreigners.
[Reveal] Spoiler: OA

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Re: At a certain university, 75% of students have driver’s licences and 6 [#permalink]

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29 Nov 2017, 02:02
1) There are 5,000 students at the university.

Using this information we can know the number of students that have driver lisence and foreigners but we know nothing about people who don't have drivers lisence, they could be all foreigners and half of them could be foreigners, so no enough information.

2) 55% of students at the university are foreigners.

75% of students have driver’s licences and 60% of the students with driver’s licences are foreign students. So 0.75*0.6= 0.45 so 45% of students in the university are foreigners with a driver's lisence. 55% of students at the university are foreigners. so 10% is the percentage of foreigners without a driver’s licence. Sufficient

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Kudos [?]: 56 [0], given: 15

Math Revolution GMAT Instructor
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Kudos [?]: 3154 [0], given: 0

GPA: 3.82
Re: At a certain university, 75% of students have driver’s licences and 6 [#permalink]

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01 Dec 2017, 00:08
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Attachment:

A.png [ 2.57 KiB | Viewed 151 times ]

$$45s + 30s + b + d = 100s.$$
$$b + d = 25s.$$

The question asks for the value of $$\frac{b}{100s}$$.

To solve problems involving 2x2 matrices and percentages, we need 3 percentages. Since we have 2 percentages, 75% and 60%, one more percentage is required.

Condition 1) does not provide a percentage, while condition 2) gives us a percentage. So, the answer is most likely to be B.

Condition 1)
$$100s = 5,000.$$
$$s = 50.$$
This is not sufficient.

Condition 2)
$$45s + b = 55s$$
$$b = 10s$$
Thus $$(\frac{b}{100s})*100$$ = $$(\frac{10s}{100s})*100$$ = $$10 %.$$
This is sufficient.

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Re: At a certain university, 75% of students have driver’s licences and 6   [#permalink] 01 Dec 2017, 00:08
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