12 Days of Christmas GMAT Competition - Day 10: A bakery produces an : Two-part Analysis (TPA)

Last visit was: 01 May 2026, 12:05

It is currently 01 May 2026, 12:05

hr1212

GMAT Forum Director

Joined: 18 Apr 2019

Last visit: 01 May 2026

Posts: 938

Own Kudos:

1,363

[1]

Given Kudos: 2,218

GMAT Focus 1: 775 Q90 V85 DI90 Verified score

Products:

Expert

Expert reply

GMAT Focus 1: 775 Q90 V85 DI90 Verified score

Posts: 938

Kudos: 1,363

[1]

27 Dec 2024, 09:31

Kudos

Bookmarks

Bunuel

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

A bakery produces an average of 170 cupcakes per day for 5 days and x cupcakes per day for the next y days. The bakery’s overall average production is 200 cupcakes per day for the entire 5 + y day period.

Select for x the value of x and for y the value of y that would be jointly consistent with the given information. Make only two selections, one in each column.

Total cupcakes produced = 170*5 + x*y = 200*(5 + y)

850 + xy = 1000 + 200y
(x - 200)y = 150

Checking options for x>200

x	y
215	10	Correct
250	3	Not possible

Hence, the correct value for (x, y) = (215, 10)

miniB21

Joined: 06 Sep 2024

Last visit: 01 May 2026

Posts: 88

Own Kudos:

[1]

Given Kudos: 64

Products:

Posts: 88

Kudos: 27

[1]

27 Dec 2024, 09:32

Kudos

Bookmarks

170 cupcakes per day for 5 days and x cupcakes per day for the next y days.
Total prodn = 170x5+xy

The bakery’s overall average production is 200 cupcakes per day for the entire 5 + y day period.
average production = 170x5+xy/5+y = 200
This gives us y(x-200)=150

Factorise 150 and look at the option that fit into this equation.
The only one that works is 10(215-200)=150

Hence the answer is *x=215 and y=10*

aviraj1703

Joined: 27 May 2024

Last visit: 10 Mar 2025

Posts: 98

Own Kudos:

123

[1]

Given Kudos: 6

Posts: 98

Kudos: 123

[1]

27 Dec 2024, 09:50

Kudos

Bookmarks

Average = 200

=> 170*5 + x*y = 200 * (y + 5)
=> 850 + xy = 200y + 1000
=> y(x-200) = 150

This means x > 200 for sure now from the options putting x = 215 we get y = 10
For x = 250 we get y = 3

Answer: (215, 10)

RahulPMT

Joined: 20 Dec 2024

Last visit: 05 Jul 2025

Posts: 34

Own Kudos:

[1]

Given Kudos: 3

Posts: 34

Kudos: 42

[1]

27 Dec 2024, 10:00

Kudos

Bookmarks

Writing equation for average:

(170*5+x*y)/(y+5) = 200

on simplification: (x-200)*y=150
Also, note that x should be > 200, only then the avg of 170 and x would be 200.

Testing 215, immediately we get y=10 ans

AbhiS101

Joined: 03 Jul 2024

Last visit: 25 Jan 2026

Posts: 80

Own Kudos:

[1]

Given Kudos: 19

Location: India

Schools: IIMA '26 IIMB '26 IIM Calcutta '26 NUS '27

GPA: 68%

Schools: IIMA '26 IIMB '26 IIM Calcutta '26 NUS '27

Posts: 80

Kudos: 86

[1]

27 Dec 2024, 10:02

Kudos

Bookmarks

Bunuel

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

Total cupcakes in the first 5 days: 170 cupcakes/day * 5 days = 850 cupcakes
Total cupcakes in the next y days: x cupcakes/day * y days = xy cupcakes
Total cupcakes over the entire period: 850 + xy
Total number of days: 5 + y
Overall average: (850 + xy) / (5 + y) = 200
Now we test the given options:
If y = 10: (850 + 10x) / (5 + 10) = 200 => 850 + 10x = 3000 => 10x = 2150 => x = 215. This works.
Let's check the other options for y to see if any others work just to be sure.
If y = 50: (850 + 50x) / (5 + 50) = 200 => 850 + 50x = 11000 => 50x = 10150 => x = 203. This is not an option.
Since we found a valid solution with y=10 and x=215, we don't need to test any further.
Answer: x = 215, y = 10

Kinshook

Major Poster

Joined: 03 Jun 2019

Last visit: 01 May 2026

Posts: 5,991

Own Kudos:

5,865

[1]

Given Kudos: 163

Location: India

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,991

Kudos: 5,865

[1]

27 Dec 2024, 10:04

Kudos

Bookmarks

A bakery produces an average of 170 cupcakes per day for 5 days and x cupcakes per day for the next y days. The bakery’s overall average production is 200 cupcakes per day for the entire 5 + y day period.

Total cupcakes produced = 170*5 + xy = 850 + xy = 200(5+y) = 1000 + 200y
xy = 150 + 200y
y = 150/(x-200)
x>200
x & y are positive integers

x	215	250
y	10	3

Since y=3 is not possible
x = 215; y = 10

Select for x the value of x and for y the value of y that would be jointly consistent with the given information. Make only two selections, one in each column.

x	y
215	10

VJ0695

Joined: 24 May 2024

Last visit: 02 Sep 2025

Posts: 16

Own Kudos:

[1]

Given Kudos: 4

Posts: 16

Kudos: 16

[1]

27 Dec 2024, 10:08

Kudos

Bookmarks

170*5+xy= 200(5+y)
Y(x-200)=150
X=215, y=10

AVMachine

Joined: 03 May 2024

Last visit: 26 Mar 2026

Posts: 190

Own Kudos:

154

[1]

Given Kudos: 40

Posts: 190

Kudos: 154

[1]

27 Dec 2024, 10:13

Kudos

Bookmarks

A bakery produces an average of 170 cupcakes per day for 5 days and x cupcakes per day for the next y days. The bakery’s overall average production is 200 cupcakes per day for the entire 5 + y day period.

Analyze: (170 * 5 + xy) / (5+y) = 200

850 + xy = 1000 + 200y

xy - 200y = 150

y(x-200) = 150; from here we can say that x>200

Now check the options;
x = 250, then y would be 3, which is not an option.

x = 215, then y would be 10. bingo.

GraCoder

Joined: 15 Dec 2024

Last visit: 18 Jan 2026

Posts: 65

Own Kudos:

[1]

Given Kudos: 19

Posts: 65

Kudos: 70

[1]

27 Dec 2024, 10:24

Kudos

Bookmarks

Bunuel

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

Total cupcakes for first 5 days = 170 * 5 = 850
Total cupcakes for next y days = x*y
Average for 5+y days = (850 + xy)/(5 + y) = 200
=> 850 + xy = 1000 + 200y
xy = 150 + 200y
(x - 200)y = 150

Clearly x >= 200 from the above eq hence if x = 215 => y = 10
if x = 250 => y = 3

Therefore x = 215 and y = 10

Heix

Joined: 21 Feb 2024

Last visit: 30 Apr 2026

Posts: 468

Own Kudos:

167

[1]

Given Kudos: 63

Location: India

Concentration: Finance, Entrepreneurship

Schools: Ross MM "26 NUS Columbia '27

GMAT Focus 1: 485 Q76 V74 DI77 Verified score

GPA: 3.4

WE:Accounting (Finance)

Products:

Schools: Ross MM "26 NUS Columbia '27

GMAT Focus 1: 485 Q76 V74 DI77 Verified score

Posts: 468

Kudos: 167

[1]

27 Dec 2024, 10:26

Kudos

Bookmarks

Show Spoiler

Attachment:

GMAT-Club-Forum-r9mtovav.jpeg [ 274.06 KiB | Viewed 1427 times ]

Elite097

Joined: 20 Apr 2022

Last visit: 04 Feb 2026

Posts: 737

Own Kudos:

568

[1]

Given Kudos: 346

Location: India

Schools: Sloan '25 Columbia '27 Haas '27

GPA: 3.64

Schools: Sloan '25 Columbia '27 Haas '27

Posts: 737

Kudos: 568

[1]

27 Dec 2024, 10:30

Kudos

Bookmarks

MKeerthu

Joined: 12 Mar 2024

Last visit: 02 Apr 2025

Posts: 53

Own Kudos:

[1]

Given Kudos: 22

Posts: 53

Kudos: 59

[1]

27 Dec 2024, 10:30

Kudos

Bookmarks

The answer is 215 and 10.

Given 170 *5 +xy / 5+y = 200

solving this we get 850+xy = 1000+200y

x-200 = 150/y

Substituting value of y=10 we get x=215. Thus the answer.

ManifestDreamMBA

Joined: 17 Sep 2024

Last visit: 21 Feb 2026

Posts: 1,387

Own Kudos:

899

[1]

Given Kudos: 243

Posts: 1,387

Kudos: 899

[1]

27 Dec 2024, 10:34

Kudos

Bookmarks

Number	Average	Sum
5	170	850
y	x	xy

Overall avg = 200

850+xy = 200(5+y)
y= 150 /(x- 200)
both x and y have to be positive

x>200, checking with x= 215, y = 10

Bunuel

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

nishantswaft

ISB School Moderator

Joined: 17 Oct 2024

Last visit: 16 Mar 2026

Posts: 158

Own Kudos:

120

[1]

Given Kudos: 18

Posts: 158

Kudos: 120

[1]

27 Dec 2024, 10:57

Kudos

Bookmarks

To solve the problem, let's set up the equation for the bakery's total cupcake production:

The total number of cupcakes produced over 5+y days is:

170*5 + x*y

The average production per day is given as 200 cupcakes, so:

Total cupcakes/total days = 200

Or, 170*5 + x*y / 5+y = 200

Or, 170⋅5+x⋅y=200⋅(5+y)

Or, 850+x⋅y=1000+200y

Or, x⋅y=200y+1000−850

Or, x⋅y=200y+150

Divide through by y (assuming y≠0):

x=200+150/y

Now, test values of y that result in an integer value for x.

Option that fits is

Y= 10 and X=215

A_Nishith

Joined: 29 Aug 2023

Last visit: 12 Nov 2025

Posts: 452

Own Kudos:

203

[1]

Given Kudos: 16

Posts: 452

Kudos: 203

[1]

27 Dec 2024, 10:58

Kudos

Bookmarks

Step 1: Key information
For the first 5 days: Average = 170 cupcakes/day
Total cupcakes produced:
1170×5 = 850

For the next y days:
Average = x cupcakes/day
Total cupcakes produced: x*y

Overall period:
5+y days with an average of 200 cupcakes/day
Total cupcakes produced over all days:
200×(5+y)=1000+200y

Step 2: Equation for total production
The total cupcakes produced over all days is the sum of cupcakes produced in the two periods:
850+x*y=1000+200y

Rearranging for x and y:
x*y=150+200y
x=200+ 150/y

Step 3: Test options
We need to select
x and y that satisfy this equation.

Option 1:
x=250,
y=10
Substitute y=10:
x=200+ 150/10 = 200+15 = 215 (NOT consistent with x=250).

Option 2: x=215, y=10
Substitute y=10:
x=200+ 150/10 = 200+15 = 215(CONSISTENT).

Option 3:
x=250, y=50
Substitute y=50:
(NOT consistent with x=250)
x= 200+ 150/50 =200+3=203(NOT consistent with x=250).

Final Answer:
x: 215
y: 10

Prakhar9802

Joined: 07 Aug 2023

Last visit: 15 Apr 2026

Posts: 63

Own Kudos:

[1]

Given Kudos: 1

Posts: 63

Kudos: 68

[1]

27 Dec 2024, 11:01

Kudos

Bookmarks

Total number of cupcakes would be equal -

170*5 + x*y = 200 (5+y)
850 + xy = 1000 + 200y
y(x-200) = 150

Put in values,

x has to be greater than 200. so put in x = 215, we get,

15y = 150
y= 10.

Therefore,

x = 215, y = 10

Bunuel

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

HansikaSachdeva

Joined: 17 May 2024

Last visit: 22 Dec 2025

Posts: 60

Own Kudos:

[1]

Given Kudos: 143

Location: India

Concentration: Social Entrepreneurship, Sustainability

Posts: 60

Kudos: 65

[1]

27 Dec 2024, 11:02

Kudos

Bookmarks

For the first 5 days,
Average cupcakes = 170
Total cupcakes = 5 * 170 = 850

For the next y days,
Average cupcakes = x
Total cupcakes = x * y = xy

Overall average = 200 for 5 + y days

Overall average = Total cupcakes / Total days = 200
(850 + xy) / (5 + y) = 200

Solving,
y(x - 200) = 150

We know that x > y

Substituting from the given options,
x = 215
y(215 - 200) = 150
y = 10

Therefore, x = 215 and y = 10