Bunuel wrote:
In how many ways can 4 students out of n students be selected to represent the school in a competition?
(1) If there were 3 more students, number of ways of selecting 4 students would be 840.
(2) If there were 3 less students, number of ways of selecting 4 students would be 360.
Rephrase the question:What is the value of n?
Statement 1 Alone:This gives us \(_{n + 3}C_{4} = 840\) or \(\frac{(n + 3)(n + 2)(n + 1)n}{4!} = 840\). The left side is increasing, so there is one unique positive solution for this; thus statement 1 is sufficient.
Statement 1 Alone:Thus gives us \(_{n - 3}C_{4} = 360\) or \(\frac{(n - 3)(n - 4)(n - 5)(n - 6)}{4!} = 360\). The left side is increasing, so there is one unique positive solution for this; thus statement 2 is sufficient.
Answer: DNote that numbers for this question are all over the place ... 360 refers to 6P4 and 840 is 7P4; that doesn't affect our ability to say whether it's sufficient or not.
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