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

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.

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.

Answer: E

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

2/3 of one part of the pizza is uneaten. 3/4 of the other part is uneaten. So somewhere between 2/3 and 3/4 of the whole pizza is uneaten, and only answer E is greater than 2/3, so it must be right.

Answer is E

Consider kudos if that helped.

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

Oh, you definitely can -- we just don't need to with these answer choices. But if you get a common denominator, we're not eating 16/24 of one half, and 18/24 of the other. The two halves are equal in size, so as in any weighted average situation where we combine two groups of the same size, the uneaten fraction will be halfway between 16/24 and 18/24, so it will be 17/24.

I suppose it depends how you think about weighted averages, but if you had a group of men and women working for a company, and 2/3 of the men and 3/4 of the women had MBA degrees, then at the company, somewhere between 2/3 and 3/4 of the employees would have MBA degrees. If we have a lot more men than women, the fraction will be close to 2/3, and if we have a lot more women than men, the fraction will be close to 3/4. If we have the same number of men and women, the overall fraction of employees with MBA degrees will be the average of, or midpoint of, 2/3 and 3/4, which is 17/24, as you can easily see if you get a common denominator. That's the exact situation we have in this question, except we have two halves of a pizza instead of two groups of employees.

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

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.
\(\frac{weight-uneaten}{total-weight} = \frac{17}{24}\)

How to solve if we consider the pizza as 2x and the two equal pieces as x

Then it will be x/4
And for other it will be x/6

x/4 + 2(x/6) = x/4 + x/3 = 7x/12

Now since the total pizza is 2x;
2x - 7x/12 = 24x-7x/12 = 17x/12

What am I doing wrong here?

Posted from my mobile device

IanStewart I would just like to know what thoughts come to your mind when you look at this question. What method would you apply and how would you visualise the logic in this question

wow That's a really cool way of looking at this question

could you explain the logic why one cannot simply compare 2/3 and 3/4. I know it is because of the fact that we are first dividing the pizza into half and then making the respective divisions. But would like to understand how and why the numbers work in this question

The key of asking the above question is to understand the concept of ratios better

I am not sure if I quite understood the above.

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