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Math Expert V
Joined: 02 Sep 2009
Posts: 62542
Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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Question Stats: 76% (01:51) correct 24% (02:02) wrong based on 812 sessions

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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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Senior SC Moderator V
Joined: 22 May 2016
Posts: 3673
Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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5
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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:
$$(\frac{24}{24}-\frac{7}{24})=\frac{17}{24}$$

*$$\frac{1}{2}$$ 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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Manager  B
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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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2
1
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.

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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3348
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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3
1

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 = $$\frac{24x – 7x}{24x}$$ = $$\frac{17}{24}$$ Hence, the correct answer is option 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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1 - 1/8 - 2/12 = 17/24
Target Test Prep Representative V
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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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1
1
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.

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Director  P
Joined: 14 Dec 2017
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Location: India
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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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

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

Thanks,
GyM
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Joined: 04 Jan 2015
Posts: 3348
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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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.

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Manager  S
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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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1
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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Senior Manager  S
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Posts: 250
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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2
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

Consider kudos if that helped.
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Posts: 506
Location: Kuwait
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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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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

$$\frac{1}{2}$$ is cut into 4 slices

Another $$\frac{1}{2}$$ is cut into 6 slices

He ate $$\frac{1}{4}$$ of the $$\frac{1}{2}$$ so it is $$\frac{1}{2} * \frac{1}{4} = \frac{1}{8}$$

Similarly for the other half he ate $$\frac{2}{6}$$, so it is $$\frac{2}{6} * \frac{1}{2}$$ = $$\frac{1}{6}$$.

Total eaten = $$\frac{1}{8} + \frac{1}{6} = \frac{3}{24} + \frac{4}{24} = \frac{7}{24}$$

Uneaten = 1 - Eaten = $$1 - \frac{7}{24} = \frac{24}{24} - \frac{7}{24} = \frac{17}{24}$$

Intern  B
Joined: 30 Apr 2017
Posts: 34
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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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∗12∗14=3x24x∗12∗14=3x
For each part divided into 6 smaller parts,
• The area = 24x∗12∗16=2x24x∗12∗16=2x
Therefore, the person ate = 3x + 2x + 2x = 7x
• So, fraction of the pizza that is uneaten = 24x–7x24x24x–7x24x = 1724
Intern  B
Joined: 03 Dec 2017
Posts: 30
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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1/2 part into 4 equals --> 1.5x each
1/2 part into 6 equals --> 1x each

total --> 12 parts -->12x

eaten --> 1.5x + 2x
not eaten --> 4.5x + 4x

fraction not eaten = 8.5 /12 ==> 85/120 ==> 17/24
Director  G
Joined: 04 Aug 2010
Posts: 554
Schools: Dartmouth College
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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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

Let the pizza = 24 ounces.

Half of a large pizza is cut into 4 equal-sized pieces.
Here, 12 ounces of the pizza are divided into 4 larger pieces, with the result that the weight of each larger piece = $$\frac{12}{4} = 3$$ ounces.

The other half is cut into 6 equal-sized pieces.
Here, the remaining 12 ounces are divided into 6 smaller pieces, with the result that the weight of each smaller piece = $$\frac{12}{6} = 2$$ ounces.

If a person were to eat 1 of the larger pieces and two of the smaller pieces, what fraction of the pizza would remain uneaten?
1 larger piece + 2 smaller pieces = 3 + (2*2) = 7 ounces.
Weight uneaten = (total weight) - (weight eaten) = 24-7 = 17 ounces.
$$\frac{weight-uneaten}{total-weight} = \frac{17}{24}$$

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Intern  B
Joined: 27 May 2018
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Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

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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

I think Percentage is the easiest and 30 sec solution.
one half 4 pieces of each 12.5%
One half 6 pieces of each 8.33%
total nearly equal to 21% eaten, remaining 79%
ans scan
A-5/12=40%
B-13/24= 50%
C-7/12=60%
D-2/3=67%

only answer choice E as others are too far away.
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