GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jan 2019, 19:45

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52231
Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

17 Jun 2018, 18:44
16
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:19) correct 27% (01:26) wrong based on 482 sessions

### HideShow timer Statistics

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

_________________
Manager
Joined: 10 Jun 2018
Posts: 55
Location: Australia
Concentration: Technology, General Management
GPA: 2.88
WE: Science (Pharmaceuticals and Biotech)
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

17 Jun 2018, 19:55
1
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.

_________________

Not a professional entity or a quant/verbal expert or anything. So take my answers with a grain of salt.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2447
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

17 Jun 2018, 22:00
2
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.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Senior SC Moderator
Joined: 22 May 2016
Posts: 2343
Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

18 Jun 2018, 09:45
2
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

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.
_________________

Never look down on anybody unless you're helping them up.
--Jesse Jackson

Manager
Joined: 07 Feb 2017
Posts: 188
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

18 Jun 2018, 11:06
1 - 1/8 - 2/12 = 17/24
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4548
Location: United States (CA)
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

20 Jun 2018, 16:23
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.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Joined: 14 Dec 2017
Posts: 524
Location: India
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

20 Jun 2018, 21:11
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

Thanks,
GyM
_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2447
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

20 Jun 2018, 21:48

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.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Joined: 20 Jul 2018
Posts: 89
GPA: 2.87
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

25 Aug 2018, 07:53
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

Posted from my mobile device
_________________

Hasnain Afzal

"When you wanna succeed as bad as you wanna breathe, then you will be successful." -Eric Thomas

Senior Manager
Joined: 07 Oct 2017
Posts: 260
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

25 Aug 2018, 10:22
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.
Attachment:

1535221450182.jpg [ 65.29 KiB | Viewed 2693 times ]

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
_________________

Thank you =Kudos
The best thing in life lies on the other side of the pain.

Director
Joined: 19 Oct 2013
Posts: 509
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

22 Oct 2018, 10:29
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
Joined: 30 Apr 2017
Posts: 28
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

08 Jan 2019, 11:15
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
Joined: 03 Dec 2017
Posts: 18
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other  [#permalink]

### Show Tags

14 Jan 2019, 22:24
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
Re: Half of a large pizza is cut into 4 equal-sized pieces, and the other &nbs [#permalink] 14 Jan 2019, 22:24
Display posts from previous: Sort by