XavierAlexander wrote:
Julie wants to be sure that she has enough pies for each of her 30 guests to have at least one slice. One pie can be divided into eight slices. If \(⌈x⌉\)represents the least integer greater than \(x\), and \(x\) is greater than \(0\), will \(⌈x⌉\) pies be enough for each guest to have at least one slice?
(1) \(5 < 2x < 12\)
(2) \(x\) is a multiple of \(3\)
Guys, the official answer is: BHere is the explanation from Manhattan:Each pie produces 8 slices and Julie needs to feed 30 guests. ⌈x⌉
is defined as an integer, so the question is asking about an integer value of pies. 3 pies would only produce 24 slices, which is not enough. 4 pies will produce 32 slices. Julie will need at least 4 pies to feed all her guests
(1) INSUFFICIENT: Simplify the inequality.
5 < 2x < 12
2.5 < x < 6
x can be anything between 2.5 and 6, giving multiple possible values for ⌈x⌉
. Test Cases to determine whether all values of ⌈x⌉
are at least 4. Keep in mind that x does not have to be an integer, even though ⌈x⌉
does.
Case 1: x = 5.99, ⌈x⌉
= 6. Yes, there are enough pies.
Case 2: x = 2.51, ⌈x⌉
= 3. No, there are not enough pies.
Since there is at least one Yes case and at least one No case, this statement is not sufficient. Eliminate choices (A) and (D).
(2) SUFFICIENT: The question specifies that x is greater than 0. Therefore, x can be any positive multiple of 3. All of these produce enough pies for Julie.
Case 1: x = 3, ⌈x⌉
= 4. Yes, there are enough pies.
Case 2: x = 6, ⌈x⌉
= 7. Yes, there are enough pies.
Eliminate choices (C) and (E).
The correct answer is (B).