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Re: QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink]
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jen6 wrote:
Can we also just look at the fractions of 5/6 and 3/5 alone and then determine which answer choices aren't multiples of both 5 & 6?


Yes we can. After Maria remove the cookies the remaining number of cookies is \(1-\frac{5}{6}=\frac{1}{6}\) .
Then Andrea removes \(\frac{3}{5}\)remaining cookies. So cookies left is \(1-\frac{3}{5}=\frac{2}{5}\).


Original Number of cookies ---------> After Maria removed ---------------------> After Andrea removed cookies

x ---------------------------------------------> \(\frac{1}{6}x\) ----------------------------------------> \(\frac{1}{6}\times\frac{2}{5}x=\frac{2}{30}x\).

Now \(\frac{2}{30}x\) and \(\frac{1}{6}x\) must be whole numbers. Hence number of cookies must be a multiple of 30.

You can identify this from the denominator of fractions \(\frac{5}{6}\) and \(\frac{2}{5}\).
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Re: QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink]
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Why didn't u simplify 2/30 into 1/15? Because at 1/15, then we say the number of cookies must be a multiple of 15 and therefore, our answers would be different.
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Re: QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink]
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jen6 wrote:
Why didn't u simplify 2/30 into 1/15? Because at 1/15, then we say the number of cookies must be a multiple of 15 and therefore, our answers would be different.



Thanks for pointing out. You are correct!

Both \(\frac{2}{30}x\) and \(\frac{1}{6}x\) must be whole numbers. At an intermediate steo the number of cookies cannot be a fraction.
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Re: QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink]
sandy wrote:
Maria removed \(\frac{5}{6}\) of the cookies from a jar, and then Andrea removed \(\frac{3}{5}\) of the remaining cookies from the same jar. Which of the following could NOT be the number of cookies originally in the jar?

Indicate all possible values.

A. 6
B. 15
C. 30
D. 60
E. 200
F. 210
G. 340

Drill 3
Question: 7

Page: 319


Show: :: OA
A, B, E, G


Note:

First of all someone removed 6/5 of the cookies. It means that total number is cookie must be the multiple of 6. So, eliminate the options that are not the multiple of 6.

15 ....200.......340. Cancelled.

Second point is that remaining cookies must be the multiple of 5.

Option A)

6 * (5/6) = 1..............out

Option C)

30 * (5/6) = 25 that is a multiple of 5.

Option D)

60 *(5/6) = 50 , multiple of 5.

Option F)

210 * (5/6) = 35, a multiple of 5.



So, A, B E, G are the options.
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Re: QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink]
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Re: QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink]
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