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THE QUANTITATIVE SECTION
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Those Barrels of Oil
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So what was the answer to the question about the barrels of oil A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil The first barrel is poured into a second barrel, also a right circular cylinder, which is empty The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel A There is no empty capacity B 100 gallons C 300 gallons D 700 gallons E 800 gallons The answer is D We don t know what the actual dimensions of the first barrel are, but we know that the volume of a cylinder = r2h (r = radius and h = height), and in the case of the first barrel, r 2h = 100 gallons We don t know the exact dimensions of the second barrel either, but we know that its height is twice that of the first barrel, so 2h, and its diameter is twice that of the first barrel, and since the diameter of a circle is double the radius, it follows that the radius of the second barrel must be twice that of the first barrel as well, so 2r The volume of the second barrel, therefore, is = (2r)2(2h) = 8 r2h = 8 ( r2h) Therefore, the second barrel has a volume eight times that of the first barrel, so 8 100 gallons = 800 gallons If the 100 gallons in the first barrel are poured into the second barrel, then the remaining empty capacity of the second barrel is 800 gallons minus the 100 gallons, which equals 700 gallons
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THE ANSWERS: NOT NECESSARILY YOUR FRIENDS
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The answers can be your friends under certain circumstances If, for example, the answers to a certain question were as follows: A 2 B C 2 D 4 E 8 then you would know that the number has to be part of your answer, so you could be sure to include it in your calculations Noticing this fact ahead of time could also keep you from attempting to make any calculations with an approximation of , such as 314159 It always pays to look at the answers ahead of time to see what form the answer might take But, and this is a big old but, you should never trust the answers They are treacherous and deceitful, and don t let anyone tell you otherwise The GMAT test writers work through all of the
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THE TECHNIQUES OF GMAT PROBLEM SOLVING
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wrong answers you could come up with a misplaced decimal here, a misplaced negative sign there and slip them into the answer choices to lead you astray Consider the answer choices for our hypothetical barrels of oil: A There is no empty capacity: this is for the skeptics out there who assume that this must be a trick question B 100 gallons: this is a number that is already in the question, and it is the answer choice someone would make if he figured that the second barrel is twice the size of the first barrel, or if he misread the question as asking how many gallons are now in the second barrel C 300 gallons: this would be the correct answer if a person figured that the second barrel was twice as high and twice as wide, so therefore it is 2 2 = 4 times larger than the first barrel D 700 gallons: this is the correct answer E 800 gallons: this is the capacity of the second barrel; a person could easily reach this second-to-last step, see this answer, and mark it down without actually finishing the question The GMAT test writers think up misleading answers for every question, and they test out different wrong answers on actual test takers to see which ones they are most likely to fall for Yes, this is sneaky And yes, it makes the test more difficult The only ways to combat this sneakiness are to 1 Know your stuff, ie, work lots of practice problems 2 Read the questions very carefully and know what is being asked 3 Check your work as you go
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