ON A CERTAIN ROAD, 10% OF THE MOTORISTS EXEED THE POSTED SPEED LIMIT AND RECEIVE SPEEDING TICKETS’ BUT 20%OF THE MOTORISTS WHO EXEED THE POSTED SPEED LIMIT DONT RECEIVE SPEEDING TICKETS. WHAT PERCENT OF THE MOTORISTS ON THAT ROAD EXEED THE POSTED SPEED LIMIT?
12.5%. Motorists exceed the Speed limit and get tickets= a Total motorists on the road= (a/10%). Total mostorists on the road exceed the speed limit=a/(1-20%)=(a/80%). The answer= (a/80%)/(a/10%)= 12.5%.
In this question, which is more of a reasoning question, let us keep these things in view. On a certain road, there are some motorists , whom we shall call the whole group . Then some of them exceed the limit and receive tickets.i.e 10% of the whole group Then there are who also exceed but do not get caught. They are the 20% group . This 20% group is in essence part of the whole group but in addition to the 10%. This is made clear from the use of the co-ordinate conjunction “but”, in order to contrast them from the 10% the Let us not assume that this 20% is 20% the 10% which will make 2% of the whole group and if so the total then must be 12% There is no such answer.
Now Look at this sentence – “but 20 percent of the motorists who exceed the posted speed limit don’t receive speeding tickets” Here the 20 percent, which is the subject of the sentence, has the main verb as “don’t receive” and hence refers to a clear 20% of the total motorists. Supposing we remove the portion”who exceed the posted speed limit’, even then the original sentence maintains the meaning. Therefore it is inessential to the sentence and can not be decider of the quantum
Let me also state this. Normally, when there is a law, those who escape punishment are more than those who get punished. Aren’t they? Hence the 20%, in absolute terms and as per norms of the world, is likely to be more than the 10%. hence it can not be just 2 or 2.5%.
A true GMAT question that draws on Critical Reasoning, Sentence Correction and Problem Solving. Wah!This is my personal view.
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