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QOTD#18 Maria removed of the cookies from a jar, and then An

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QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink] New post 03 Apr 2017, 03:34
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Question Stats:

52% (00:55) correct 47% (01:50) wrong based on 17 sessions
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


[Reveal] Spoiler: OA
A, B, E, G
[Reveal] Spoiler: OA

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Re: QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink] New post 06 Apr 2017, 10:11
Expert's post
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


Let x = original # of cookies

So, AFTER (5/6)x cookies are removed, there are x/6 cookies REMAINING.
This tells us that x must be divisible by 6.

Andrea removed 3/5 of the REMAINING cookies.
So, she removed 3/5 of the x/6 remaining cookies.
(3/5)(x/6) = x/10
So, x must be divisible by 10

So, x must be divisible by 6 AND by 10

Examine the answer choices:
A. 6 NOT divisible by 10. KEEP
B. 15 NOT divisible by 10. KEEP
C. 30 is divisible by 6 AND 10. ELIMINATE
D. 60 is divisible by 6 AND 10. ELIMINATE
E. 200 NOT divisible by 6. KEEP
F. 210 is divisible by 6 AND 10. ELIMINATE
G. 340 NOT divisible by 6. KEEP

Answer:
[Reveal] Spoiler:
A, B, E, G


Cheers,
Brent
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Re: QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink] New post 25 May 2018, 23:17
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?
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Re: QOTD#18 Maria removed of the cookies from a jar, and then An [#permalink] New post 26 May 2018, 00:14
Expert's post
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] New post 26 May 2018, 03:42
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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] New post 26 May 2018, 13:32
Expert's post
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] New post 24 Jul 2018, 20:34
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


[Reveal] Spoiler: 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.
Re: QOTD#18 Maria removed of the cookies from a jar, and then An   [#permalink] 24 Jul 2018, 20:34
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QOTD#18 Maria removed of the cookies from a jar, and then An

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