Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: Sam has x flavors of candies with which to make goody bags for Frank's birthday party. Sam tosses out y flavors, because he doesn't like them. How many different 10-flavor bags can Sam make from the remaining flavors? (It doesn't matter how many candies are in the bag, only how many flavors). (1) If Sam had thrown away two more flavors of candy, he could have made exactly 3,003 different 10-flavor bags. (2) x = y + 17

  1. Statement (1) alone is sufficient but statement (2) alone is not

  2. Statement (2) alone is sufficient but statement (1) alone is not

  3. Both statements (1) and (2) together are sufficient but none of them alone is sufficient

  4. Both statements independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement 1: (x-y-2)C10 = 3003. Since 15C10 = 3003, x-y-2 = 15, so x-y = 17. Statement 2: x-y = 17. Both statements provide the same information independently.

AI explanation

This problem uses the combinations formula, where the number of 10-flavor bags equals nCr with n equal to x minus y and r equal to 10. Statement 1 gives the combination result for n minus 2 as 3003, and since nCr increases uniquely with n for a fixed r, this yields exactly one valid value for n. Statement 2 provides the equation x minus y equals 17, which directly sets n to 17. Therefore, both statements independently provide sufficient information to find the number of bags.

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