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3 Cards in this Set
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The quotient of a division operation is the integer x, the divisor is the integer y, and the dividend is the integer z. If the remainder of this operation is 4, what is x in terms of y and z? * (z−4)/y* (z)/(y−4) * (z+4)/y * yz/4 * z/(y+4) |
Solution: A Terminology, anyone? By definition, Dividend ÷ Divisor = Quotient, with a Remainder (if any). Match the given variables up with these roles to get z ÷ y = x with a remainder of 4. That remainder of 4 came about in effect because we started with 4 “extra” in z; if z had been 4 less than it is, we would have come out with a clean answer of just x. In other words, (z – 4) ÷ y = x. And that’s what we have in answer choice (A). Alternative route: remember that to “rephrase” a remainder, you can employ a fraction, and instead of a remainder of r, think of continuing to divide that remainder by the divisor, which by definition gives you the fraction rdivisor . So in our problem, since we know y is the divisor, we can write z The quotient of a division operation is the integer x, the divisor is the integer y, and the dividend is the integer z. If the remainder of this operation is 4, express x in terms of y and z ÷ y = x+ 4y . Isolate x by subtracting 4y from both side of the equation (easy to to do if you write the z ÷ y as zy) . You wind up again with (z−4)y = x.
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(62) In the sports center, the capacity of swimming pool A is 60 percent of the capacity of swimming pool B. How many more gallons of water are in pool A than in pool B? 1. Pool A is 80 percent full; pool B is 40 percent full.2. When full, pool B contains 40,000 gallons of water.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient to answer the question asked
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed… |
Solution: C When we read that Acap= .6(Bcap), we have a relationship between the two pools. However, we lack two important pieces of information: the actual size of the pools and how full they are. Even though we can determine the relative amounts of water with the information in sentence (1), we have no idea how many gallons that would represent unless we assign an actual size to one of the pools! Conversely, when we look ONLY at sentence (2), we will not know how full each pool is. It is only with all information from both sentences that we reach sufficiency, so we answer C. |
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The number of bananas harvested in 2000 was the integer x. In 2001, the number of bananas harvested grew by 150% from the year 2000. In 2002, the number of bananas harvested grew by 400% from the year 2000. What was the percentage growth in the number of bananas harvested from the year 2001 to the year 2002?
100%
167%
200%
250%
500% |
Solution: A This question tests several items within the heading of percent change. First you need to determine the amount of bananas in 2001 and 2002. If we use 100 as our starting point, we will get that Bananas ′01 = 250 (the original 100 PLUS the 150% increase) and that Bananas ′02 = 500 (the original 100 PLUS the 400% increase). To determine the percent change from ’01 to ’02, we’ll plug these into (New value‐ Initial Value)/(Initial Value), for (500‐250)/(250). This will yield 250/250, or 1, for a 100% increase, answer A. |
