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At 9:00 AM, a certain ice cream cart has twice as many

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At 9:00 AM, a certain ice cream cart has twice as many

by Gmat_mission » Sun May 13, 2018 10:33 am

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At 9:00 AM, a certain ice cream cart has twice as many chipwiches as it does mud pies. During the day, only chipwiches are sold, and at 5:00 PM, the cart has the exact same number of mud pies as it did at 9:00 AM, but now the number of mud pies is twice the number of chipwiches. Assuming no items were otherwise lost or gained, how many of the following must be true?

I. The number of chipwiches sold must be a multiple of 3

II. The number of mud pies must be even

III. The number of chipwiches the cart has at 5:00 PM must be even

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

[spoiler]OA=C[/spoiler].

I am really confused here. <i class="em em-sob"></i> I'd really appreciate any help. Please. Thanks in advance.
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by [email protected] » Sun May 13, 2018 11:34 am
Hi Gmat_mission,

We're told that at 9:00 AM, a certain ice cream cart has TWICE as many chipwiches as it does mud pies. During the day, only chipwiches are sold, and at 5:00 PM, the cart has the exact SAME number of mud pies as it did at 9:00 AM, but now the number of mud pies is TWICE the number of chipwiches. We're asked - assuming no items were otherwise lost or gained, how many of the following MUST be true. This question has a number of patterns 'hidden' within it - and you can define those patterns by TESTing VALUES.

First, ONLY the number of chipwiches changes; the 'before' number is TWICE the number of mud pies and the 'after' number is HALF the number of mud pies. Thus, the number of mud pies must be a number that can be doubled and halved and end in an integer both times. Since you can't have a "fraction" of a mud pie, the number of mud pies MUST be EVEN.

Next, let's TEST VALUES to see what types of patterns emerge when the number of mud pies changes....
IF there are....
2 mud pies, there are 4 chipwiches to start and 1 chipwich at the end, so 3 chipwiches were sold.
4 mud pies, there are 8 chipwiches to start and 2 chipwiches at the end, so 6 chipwiches were sold.
6 mud pies, there are 12 chipwiches to start and 3 chipwiches at the end, so 9 chipwiches were sold.
Etc.

I. The number of chipwiches sold must be a MULTIPLE of 3
Roman Numeral 1 IS true; there will always be some multiple of 3 chipwiches sold (that pattern can be seen in the examples).

II. The number of mud pies must be EVEN
Roman Numeral 2 IS true; we determined that at the beginning (since you can't have a 'fraction' of a chipwich; that would occur if the number of mud pies was Odd).

III. The number of chipwiches the cart has at 5:00 PM must be EVEN
Roman Numeral 3 is NOT true; we have two examples that prove it.

Final Answer: C

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by Jeff@TargetTestPrep » Wed May 16, 2018 10:10 am
Gmat_mission wrote:At 9:00 AM, a certain ice cream cart has twice as many chipwiches as it does mud pies. During the day, only chipwiches are sold, and at 5:00 PM, the cart has the exact same number of mud pies as it did at 9:00 AM, but now the number of mud pies is twice the number of chipwiches. Assuming no items were otherwise lost or gained, how many of the following must be true?

I. The number of chipwiches sold must be a multiple of 3

II. The number of mud pies must be even

III. The number of chipwiches the cart has at 5:00 PM must be even

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
We can let the number of mud pies be 10 at 9 AM. Thus, the number of mud pies at 5 PM is still 10. The number of chipwiches at 9 AM is 10 x 2 = 20; however, the number of chipwiches at 5 PM is 10/2 = 5. We see that Roman numeral I could be true since 20 - 5 = 15 is a multiple of 3. We also see that II could be true since we assume there are 10 mudpies. However, III is definitely not true since we only have 5 chipwiches at 5 PM.

To prove I and II must be true, we can let x = the number of mud pies at 9 AM or 5 PM. Thus there are 2x chipwiches at 9 AM and x/2 chipwiches at 5 PM. We see that x must be even; otherwise, x/2 wouldn't be a whole number. So II must be true. Finally, the number of chipwiches sold during the day is 2x - x/2 = 4x/2 - x/2 = 3x/2 = 3(x/2). Since x/2 is a whole number, 3(x/2) must be a multiple of 3. So I must be true also.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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