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Half of a large pizza is cut into 4 equal-sized pieces, and the other

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Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 17 Jun 2018, 19:44
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Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?


A. 5/12

B. 13/24

C. 7/12

D. 2/3

E. 17/24

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Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 17 Jun 2018, 20:55
Drawing out a pizza (well, a circle) would probably be the best way to visualize this question. You can then see what is being eaten and what is not.

But anyways, the way to solve it 'correctly' I suppose is to make each half of the pizza a fraction that can be worked with easily. So the first half is divided into four pieces. Imagine that if the pizza was divided evenly, then you have 4/8 of the pizza this way. The other half would therefore be 6/12.

Now, since a large slice was eaten, the 4/8 is reduced to 3/8. Two of the smaller slices were eaten, and hence 6/12 is reduced to 4/12. Now, we just need to add 3/8 and 4/12 together to get the answer. Notice that in the answers, you have 3, 12, and 24 as denominators. I just take the largest one - because in this case, you can always simplify an answer with a denominator of 24 to one with a denominator of 3 or 12 if need be/possible, but it's harder to work with the other denominators if either is not the answer.

So we have 3/8 + 4/12
<=> 9/24 + 8/24
<=> 17/24.

Hence the answer is E.
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Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 17 Jun 2018, 23:00
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Solution



Given:
    • Half of a large pizza is cut into 4 equal-sized pieces
    • The other half is cut into 6 equal-sized pieces
    • A person ate 1 of the larger pieces, and 2 of the smaller pieces

To find:
    • What fraction of the pizza would remain uneaten

Approach and Working:
We are dividing the whole pizza into two halves, each of which is divided into 4 parts and 6 parts.
    • Therefore, we can assume the total area of the pizza to be 24x sq. units [LCM of 4 and 6]

For each part divided into 4 smaller parts,
    • The area = \(24x * \frac{1}{2} * \frac{1}{4} = 3x\)

For each part divided into 6 smaller parts,
    • The area = \(24x * \frac{1}{2} * \frac{1}{6} = 2x\)

Therefore, the person ate = 3x + 2x + 2x = 7x
    • So, fraction of the pizza that is uneaten = \(\frac{24x – 7x}{24x}\) = \(\frac{17}{24}\)

Image

Hence, the correct answer is option E.

Answer: E
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Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 18 Jun 2018, 10:45
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Bunuel wrote:
Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?


A. 5/12

B. 13/24

C. 7/12

D. 2/3

E. 17/24

Another way - just fractions. The pizza = 1. Leave that aside until the end.

1) \(\frac{1}{2}\) of a pizza is cut into 4 equal pieces*

Each newly cut piece becomes: \(\frac{(\frac{1}{2})}{4}=\frac{1}{8}\)

2) The other 1/2 of the pizza is cut into 6 equal pieces
Each newly cut piece: \(\frac{(\frac{1}{2})}{6}=\frac{1}{12}\)

3) 1 larger piece and 2 smaller pieces are eaten.

Total eaten: \((\frac{1}{8}+\frac{2}{12})=(\frac{3}{24}+\frac{4}{24})=\frac{7}{24}\)

Take the denominator as the basis for a "whole" of 1. The pizza (\(=1=\frac{24}{24}\))

4) Total not eaten:
\((\frac{24}{24}-\frac{7}{24})=\frac{17}{24}\)

Answer E

*\(\frac{1}{2}\) cut equally into = "divided by" 4: \(\frac{(\frac{1}{2})}{4}\). The divisor, 4, has an implied denominator of 1 in the expression: \(\frac{(\frac{1}{2})}{(\frac{4}{1})}\) . . . invert and multiply.
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Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 18 Jun 2018, 12:06
1 - 1/8 - 2/12 = 17/24
Answer E
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Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 20 Jun 2018, 17:23
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Bunuel wrote:
Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?


A. 5/12

B. 13/24

C. 7/12

D. 2/3

E. 17/24


Each larger piece is (1/2)/4 = 1/8 of the pizza and each smaller piece is (1/2)/6 = 1/12 of the pizza. Thus, 1 larger piece and 2 smaller pieces are 1/8 + 2(1/12) = 3/24 + 4/24 = 7/24 of the pizza, and the portion of the pizza that remains after these 3 pieces are eaten is 1 - 7/24 = 17/24.

Answer: E
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Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 20 Jun 2018, 22:11
Bunuel wrote:
Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?


A. 5/12

B. 13/24

C. 7/12

D. 2/3

E. 17/24


Given that half a pizza is cut into 4 pieces, we get 4 pieces of each 1/8 th of the full pizza

the other half is cut into 6 pieces, we get 6 pieces of each 1/12 th of the full pizza

The person ate 1 large piece & 2 smaller pieces = 1/8 + (2*1/12) = 7/24 of the pizza is eaten

We are asked fraction of pizza that is uneaten = 1 - 7/24 = 17/24

Answer E.


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Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 20 Jun 2018, 22:48

Solution



Given:

    • A pizza is cut into two equal halves.
    • One half is further cut into 4 equal size pieces.
    • Another half is cut into 6 equal size pieces.
    • A person eats 1 slices from 4 equal size pieces and 2 slices from 5 equal size pieces.

To find:

    • We need to find what fraction of the pizza will remain uneaten.

Approach and Working:

Let’s assume that complete pizza is of size x.
    • Now, when pizza is cut into two equal halves, each half will be of x/2 size.

One half is cut in 4 slices:
    • When x/2 pizza is further cut into 4 equal slices then each slice will be of x/8 size.

Another half is cut in 6 slices:
    • When x/2 pizza is further cut into 6 equal slices then each slice will be of x/12 size.

Now, if A person eat 1 slices from 4 equal size pieces and 2 slices from 5 equal size pieces.
    • He will eat x/8+2* (x/12)= x/8+x/6= 7x/24 size of the pizza.

Hence, the uneaten pizza will be 17x/24 or 17/24 fraction of the pizza will remain uneaten.


Hence, the correct answer is option E.

Answer: E
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Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 25 Aug 2018, 08:53
Assume pizza is a circle so half pizza is a semi circle with angle 180
For 4 pieces=180/4=45
For 6 pieces=180/6=30
So large pizza piece is of 45 angle
Niw if a person were to eat 1 large and two small pieces so total eaten part would be= 45+2(30)=105
Total uneaten part is=360-105=255
So fraction is = 255/360 = 17/24

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Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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New post 25 Aug 2018, 11:22
Bunuel wrote:
Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?


A. 5/12

B. 13/24

C. 7/12

D. 2/3

E. 17/24
Answer is E

Consider kudos if that helped.
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Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other &nbs [#permalink] 25 Aug 2018, 11:22
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