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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
Joined: 16 Aug 2015
Posts: 5048
GMAT 1: 800 Q59 V59
GPA: 3.82
At a certain university, 75% of students have driver’s licences and 6 [#permalink]

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29 Nov 2017, 00:25
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Difficulty:

45% (medium)

Question Stats:

56% (01:01) correct 44% (01:03) wrong based on 57 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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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Status: Quant Expert Q51 Joined: 02 Aug 2014 Posts: 65 Re: At a certain university, 75% of students have driver’s licences and 6 [#permalink] ### Show Tags 29 Nov 2017, 03:02 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 Answer B _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5048 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: At a certain university, 75% of students have driver’s licences and 6 [#permalink] ### Show Tags 01 Dec 2017, 01:08 => 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 306 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. Therefore, the answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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Re: At a certain university, 75% of students have driver’s licences and 6   [#permalink] 01 Dec 2017, 01:08
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