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GMAT/Data Sufficiency - Candy Man Combinations
Candy Man Combinations
Sammy has x flavors of candies with which to make goody bags for Frank's birthday party. Sammy tosses out y flavors, because he doesn't like them. How many different 10-flavor bags can Sammy make from the remaining flavors? (It doesn't matter how many candies are in a bag, only how many flavors).
(1) If Sammy had thrown away 2 additional flavors of candy, he could have made exactly 3,003 different 10-flavor bags.
(2) x = y + 17
(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
| ОТВЕТЫ И КОММЕНТАРИИ |
| Решение |
In order to determine how many 10-flavor combinations Sammy can create, we simply need to know how many different flavors Sammy now has. If Sammy had x flavors to start with and then threw out y flavors, he now has x – y flavors.
Therefore, we can rephrase this questions as: What is x – y ?
According to statement (1), if Sammy had x – y – 2 flavors, he could have made exactly 3,003 different 10-flavor bags.
We could use the combination formula below to determine the value of x – y – 2, which is equal to n in the equation below:
Solving this equation would require some time and more familiarity with factorials than is really necessary for the GMAT. However, keep in mind that you do not need to solve this equation; you merely need to be certain that the equation is solvable. (Note, if you begin testing values for n, you will soon find that n = 15.)
Once we know the value of n, we can easily determine the value of x – y, which is simply 2 more than n. Thus, we know how many different flavors Sammy has, and could determine how many different 10-flavor combinations he could make.
Statement (2) is tells us that x = y + 17.
Subtracting y from both sides of the equation yields the equation x – y = 17.
Thus, Sammy has 17 different flavors. This information is sufficient to determine the number of different 10-flavor combinations he could make.
The correct answer is D: Each statement ALONE is sufficient.
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A motorist travels 120 miles to his destination at an average speed of 60 miles
per hour and returns to his starting point at an average speed of 40 miles per
hour. His average speed for the entire trip is
А) 53 miles per hour
В) 50 miles per hour
С) 48 miles per hour
D) 45 miles per hour
Е) 52 miles per hour
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