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1/r of a circular pizza has been eaten. If the rest of the pizza is di

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1/r of a circular pizza has been eaten. If the rest of the pizza is di  [#permalink]

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New post 30 Oct 2018, 02:52
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A
B
C
D
E

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Question Stats:

79% (01:18) correct 21% (01:56) wrong based on 38 sessions

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\(\frac{1}{r}\) of a circular pizza has been eaten. If the rest of the pizza is divided into m equal slices, then each of these slices is what fraction of the whole pizza?


A) \(\frac{r}{rm}\)

B) \(\frac{(r-1)}{rm}\)

C) \(\frac{1}{m}\)

D) \(\frac{(m-1)}{rm}\)

E) \(\frac{(m-r)}{rm}\)

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Re: 1/r of a circular pizza has been eaten. If the rest of the pizza is di  [#permalink]

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New post 30 Oct 2018, 03:39
1/r of a circular pizza has been eaten. If the rest of the pizza is divided into m equal slices, then each of these slices is what fraction of the whole pizza?


A. r/m

B. (r−1)/(mr)

C. 1/m

D. (m−1)/m

E. (m−r)/m

Let size of pizza be 8
r= 4 so pizza eaten would be 2 , and left is 6
m=3 and each equal size would be 2

fraction of each size to whole pizza would be 2/8=1/4

only option B suffices the relation...
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Re: 1/r of a circular pizza has been eaten. If the rest of the pizza is di  [#permalink]

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New post 30 Oct 2018, 04:09
1/r of a circular pizza has been eaten. If the rest of the pizza is divided into m equal slices, then each of these slices is what fraction of the whole pizza?
Sol-
total area = πr^2
Eaten= 1/r (πr^2) = πr

left= total- eaten = πr(r-1)

m equal slices= (πr(r-1))/m

fraction of the whole pizza= (πr(r-1))/m*(πr^2) = r-1/mr (B)
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Re: 1/r of a circular pizza has been eaten. If the rest of the pizza is di  [#permalink]

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New post 31 Jan 2019, 23:49
Let r = 10 and m = 3.

\(\frac{1}{10}\) of the pizza is eaten then remaining part is \(\frac{9}{10}\). Now this part is divided into 3 parts, so each part is \(\frac{3}{10}\).

A) \(\frac{r}{rm}\) = \(\frac{1}{3}\).................INCORRECT

B) \(\frac{(r-1)}{rm}\) = \(\frac{3}{10}\)..........CORRECT

C) \(\frac{1}{m}\) = \(\frac{1}{3}\)...........INCORRECT

D) \(\frac{(m-1)}{rm}\) = \(\frac{1}{15}\)............INCORRECT

E) \(\frac{(m-r)}{rm}\) = \(\frac{-7}{30}\)..............INCORRECT

OPTION: B
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Re: 1/r of a circular pizza has been eaten. If the rest of the pizza is di  [#permalink]

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New post 01 Feb 2019, 00:03
Bunuel wrote:
\(\frac{1}{r}\) of a circular pizza has been eaten. If the rest of the pizza is divided into m equal slices, then each of these slices is what fraction of the whole pizza?


A) \(\frac{r}{rm}\)

B) \(\frac{(r-1)}{rm}\)

C) \(\frac{1}{m}\)

D) \(\frac{(m-1)}{rm}\)

E) \(\frac{(m-r)}{rm}\)


After 1/r pizza is eaten, remaining = 1-(1/r) = (r-1)/r

This remaining pizza is to be divided into m equal slices

i.e. each slice = (r-1)/r / m = (r-1)/mr

Slice as fraction of pizza = (r-1)/mr / 1 = (r-1)/mr

Answer: Option B
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Re: 1/r of a circular pizza has been eaten. If the rest of the pizza is di  [#permalink]

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New post 01 Feb 2019, 11:31
Bunuel wrote:
\(\frac{1}{r}\) of a circular pizza has been eaten. If the rest of the pizza is divided into m equal slices, then each of these slices is what fraction of the whole pizza?


A) \(\frac{r}{rm}\)

B) \(\frac{(r-1)}{rm}\)

C) \(\frac{1}{m}\)

D) \(\frac{(m-1)}{rm}\)

E) \(\frac{(m-r)}{rm}\)


let r = 3 and m = 2
so pizza eaten = 1/3
left 2/3
m slices '2/3 * 1/2 ' ; ; left 1/3
plug in r & m in options
we get
B as 1/3
IMO B
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Re: 1/r of a circular pizza has been eaten. If the rest of the pizza is di   [#permalink] 01 Feb 2019, 11:31
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