Last visit was: 19 Nov 2025, 16:53 It is currently 19 Nov 2025, 16:53
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
pmal04
User avatar
Joined: 05 Jan 2009
Last visit: 30 Apr 2017
Posts: 48
Own Kudos:
1,059
 [63]
Given Kudos: 2
Posts: 48
Kudos: 1,059
 [63]
At the bakery, Lew spent a total of $6.00 for one kind of Updated on: 27 Jul 2015, 14:51
Originally posted by pmal04 on 07 Apr 2009, 10:57.
Last edited by Bunuel on 27 Jul 2015, 14:51, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
5
Kudos
Add Kudos
58
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

59% (02:38) correct 41% (02:21) wrong based on 1148 sessions

History

Date
Time
Result
Not Attempted Yet
At the bakery, Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut. How many doughnuts did he buy?

(1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes.
(2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35.
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
pike
User avatar
Current Student
Joined: 08 Jan 2009
Last visit: 27 Dec 2020
Posts: 245
Own Kudos:
494
 [12]
Given Kudos: 7
GMAT 1: 770 Q50 V46
GMAT 1: 770 Q50 V46
Posts: 245
Kudos: 494
 [12]
At the bakery, Lew spent a total of $6.00 for one kind of 19 Nov 2011, 05:18
9
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
D = price of one donut
C = price of one cupcake
x = number of donuts bought
y = number of cupcakes bought

xD + yC = $6.00

1) 2D = 3C - 0.10
We do not know x or y, NS

2) (D + C) / 2 = 0.35
Same problem, NS

1+2) We can solve for D and C, but we can't solve for the quantity of each that has been bought.

E.
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
77,001
 [8]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,001
 [8]
At the bakery, Lew spent a total of $6.00 for one kind of Updated on: 17 Oct 2022, 00:29
Originally posted by KarishmaB on 05 Feb 2014, 22:54.
Last edited by KarishmaB on 17 Oct 2022, 00:29, edited 1 time in total.
3
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
Smita04
At the bakery Lew spent a total of 6$ for one kind of cupcake and one kind of doughnut. How many donuts did he buy?

(1) Price of 2 doughty was $.10 less than 3 cupcakes
(2) Average price of 1 doughnut and 1 cupcake was $.035
Show more

There is an error in this question.
"Average price of 1 doughnut and 1 cupcake was $0.35"
It doesn't make sense if the average price is 3.5 cents. The numbers don't work. It must be 35 cents. Convert everything to cents.

Using both statements together, you get
3C - 2D = 10 (C is the price of cupcakes and D is the price of doughnuts)
C + D = 35*2

Solving them simultaneously, you get C = 30, D = 40.

If Nc is number of cupcakes and Nd is number of doughnuts,
30*Nc + 40*Nd = 600
3*Nc + 4*Nd = 60
The first solution I get is Nd = 3, Nc = 16
We will get many more solutions such as Nd = 6, Nc = 12. Also, Nd = 9, Nc = 8 etc
Hence both statements together are not sufficient.
Answer (E)

Note that in this equation: 3*Nc + 4*Nd = 60, if instead of 60, the total price were say 18, there would have been only one solution.
3*Nc + 4*Nd = 18
Nc = 2, Nd = 3
Other possible solutions will be Nc = 6, Nd = 0; Or Nc = -2, Nd = 6 etc
Since we cannot buy negative or 0 number of items (she spends money on doughnuts AND cupcakes so she must have bought at least one of each), no other solution works.
General Discussion
User avatar
kraizada84
User avatar
Joined: 13 Mar 2012
Last visit: 19 Nov 2018
Posts: 149
Own Kudos:
524
 [4]
Given Kudos: 48
Concentration: Operations, Strategy
Posts: 149
Kudos: 524
 [4]
At the bakery, Lew spent a total of $6.00 for one kind of 15 Apr 2012, 22:56
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Smita04
At the bakery lew spent a total of 6$ for one kind of cupcake and one kind of doughnut. How many donuts did he buy?
1) price of 2 doughty was $.10 less than 3 cupcakes
2) average price of 1 doughnut and 1 cupcake was $.035
Show more

let
cupcakes purchased= x
doughnut purchased= y

price of one cupcake and doughnut be c and d respectively,
then

cx+dy = 6

we need to find y.

statement 1) 2d= 3c - 0.1
INsufficient

statement 2) (c+d)/2 = 0.035
c+d = 0.035*2

Insufficient

1) and 2)

we can have c and d but we have no info about x and y.

Insufficient.

hence E

Hope this helps..!!
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,739
Own Kudos:
35,355
 [3]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,739
Kudos: 35,355
 [3]
At the bakery, Lew spent a total of $6.00 for one kind of 11 Dec 2019, 08:19
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
pmal04
At the bakery, Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut. How many doughnuts did he buy?

(1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes.
(2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35.
Show more

Target question: How many doughnuts did Lew buy?

Let D = the NUMBER of donuts purchased.
Let C = the NUMBER of cupcakes purchased.
Let X = the PRICE per donut (in CENTS)
Let Y = the PRICE per cupcake (in CENTS)

ASIDE: Given that we have 4 different variables, we will likely need 4 equations to answer the target question.

Given: Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut.
In other words, Lew spent 600 CENTS
We can write: DX + CY = 600

Okay that's 1 equation. When I SCAN the two statements, I can see that I will be able to create one equation for each statement.
This means we will have a total of 3 equations, which likely means the combined statements are insufficient.
Given this let's jump to ......

Statements 1 and 2 combined
From statement 1, we can write: 2X = 3Y - 10
From statement 2, we can write: 1X + 1Y = 70 (CENTS)

We can solve this system to get, X = 40 and Y = 30
When we can plug these values into our first equation, DX + CY = 600, we get: D(40) + C(30) = 600
Rewrite as: 40D + 30C = 600
Divide both sides by 10 to get: 4D + 3C = 60

There are several solutions to this equation. Here are two:
Case a: D = 3 and C = 16. In this case, the answer to the target question is Lew bought 3 donuts
Case b: D = 6 and C = 12. In this case, the answer to the target question is Lew bought 6 donuts

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
avatar
Aditya110
avatar
Joined: 02 Nov 2019
Last visit: 06 May 2024
Posts: 3
Given Kudos: 35
Posts: 3
Kudos: 0
At the bakery, Lew spent a total of $6.00 for one kind of 20 Apr 2021, 07:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi. Is there any quick method to know if there are only one or several solutions in a linear equation with two variables? In this case, there are several solutions, but does one have to use only trial and error method?

BrentGMATPrepNow VeritasKarishma
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
77,001
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,001
At the bakery, Lew spent a total of $6.00 for one kind of 21 Apr 2021, 03:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Aditya110
Hi. Is there any quick method to know if there are only one or several solutions in a linear equation with two variables? In this case, there are several solutions, but does one have to use only trial and error method?

BrentGMATPrepNow VeritasKarishma
Show more

Check this post:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -of-thumb/

It discusses integer solution in detail.
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 19 Nov 2025
Posts: 547
Own Kudos:
1,115
 [1]
Given Kudos: 13
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 750 Q51 V39
Expert
Expert reply
GMAT 1: 750 Q51 V39
Posts: 547
Kudos: 1,115
 [1]
At the bakery, Lew spent a total of $6.00 for one kind of 21 Apr 2021, 06:07
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
pmal04
At the bakery, Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut. How many doughnuts did he buy?

(1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes.
(2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35.
Show more


Say, you have 2 linear equations of the form:
Ax + By = C, and Px + Qy = R, where A,B,P,Q are the (numerical) coefficients
Case 1: If A/P = B/Q = C/R => Infinite solutions
Case 2: If A/P = B/Q but not equal to C/R => No solution
Case 3: A/P not equal to B/Q => Unique solution
This actually also follows from the standard form of a straight line: y = mx + c

For this question:
Let the price of a cupcake be $c and that of a doughnut be $d
Let the number of cupcakes be x and the number of doughnuts be y
xc + yd = 6 ... (i)
Statement 1: 2d = 3c - 0.1 ... (ii)
Here, (i) and (ii) would NOT result in a unique solution since there are too many variables - Not sufficient
Statement 2: d + c = 0.7 ... (iii)
(ii) and (iii) can be solved to calculate the price of each: c = $0.50 and d = $0.20
But we cannot determine x or y - Not Sufficient
Combining both:
Using the values of c and d, from (i): 5x + 2y = 60
Here, there are 2 unknowns, ideally there should be infinite solutions. However, we know that x and y are positive integers (additional constraint). Hence, there may NOT be infinite solutions - we should check the values:
Starting solution: x = 12 and y = 0
Decrease x by 2 (coefficient of y) and increase y by 5 (coefficient of x) to get the next solutions:
x = 10, y = 5
x = 8, y = 10
x = 6, y = 15
x = 4, y = 20
x = 2. y = 25
x = 0, y = 30 (you don't need to solve all. I was just showing the method)
So, we do NOT have a unique value - Not Sufficient
Answer E
avatar
sanjeevsinha082
avatar
Joined: 20 Apr 2020
Last visit: 22 Sep 2021
Posts: 44
Own Kudos:
11
 [1]
Given Kudos: 2
Location: India
Posts: 44
Kudos: 11
 [1]
At the bakery, Lew spent a total of $6.00 for one kind of 29 Jun 2021, 05:31
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Combine 1 and 2, we can solve out price for C and D, C=$0.3, D=$0.4
To fulfill the total cost $6.00, number of C and D have more than one combination, for
example: 4C and 12D, 8C and 9D…
Answer is E
User avatar
deep1624
User avatar
Joined: 22 Oct 2022
Last visit: 27 Jun 2024
Posts: 9
Own Kudos:
2
Given Kudos: 88
Location: India
Posts: 9
Kudos: 2
At the bakery, Lew spent a total of $6.00 for one kind of 20 Feb 2023, 17:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sujoykrdatta
pmal04
At the bakery, Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut. How many doughnuts did he buy?

(1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes.
(2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35.


Say, you have 2 linear equations of the form:
Ax + By = C, and Px + Qy = R, where A,B,P,Q are the (numerical) coefficients
Case 1: If A/P = B/Q = C/R => Infinite solutions
Case 2: If A/P = B/Q but not equal to C/R => No solution
Case 3: A/P not equal to B/Q => Unique solution
This actually also follows from the standard form of a straight line: y = mx + c

For this question:
Let the price of a cupcake be $c and that of a doughnut be $d
Let the number of cupcakes be x and the number of doughnuts be y
xc + yd = 6 ... (i)
Statement 1: 2d = 3c - 0.1 ... (ii)
Here, (i) and (ii) would NOT result in a unique solution since there are too many variables - Not sufficient
Statement 2: d + c = 0.7 ... (iii)
(ii) and (iii) can be solved to calculate the price of each: c = $0.50 and d = $0.20
But we cannot determine x or y - Not Sufficient
Combining both:
Using the values of c and d, from (i): 5x + 2y = 60
Here, there are 2 unknowns, ideally there should be infinite solutions. However, we know that x and y are positive integers (additional constraint). Hence, there may NOT be infinite solutions - we should check the values:
Starting solution: x = 12 and y = 0
Decrease x by 2 (coefficient of y) and increase y by 5 (coefficient of x) to get the next solutions:
x = 10, y = 5
x = 8, y = 10
x = 6, y = 15
x = 4, y = 20
x = 2. y = 25
x = 0, y = 30 (you don't need to solve all. I was just showing the method)
So, we do NOT have a unique value - Not Sufficient
Answer E
Show more


how did you get c=0.5 and d = 20?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,368
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,368
At the bakery, Lew spent a total of $6.00 for one kind of 21 Feb 2023, 01:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
deep1624
sujoykrdatta
pmal04
At the bakery, Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut. How many doughnuts did he buy?

(1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes.
(2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35.


Say, you have 2 linear equations of the form:
Ax + By = C, and Px + Qy = R, where A,B,P,Q are the (numerical) coefficients
Case 1: If A/P = B/Q = C/R => Infinite solutions
Case 2: If A/P = B/Q but not equal to C/R => No solution
Case 3: A/P not equal to B/Q => Unique solution
This actually also follows from the standard form of a straight line: y = mx + c

For this question:
Let the price of a cupcake be $c and that of a doughnut be $d
Let the number of cupcakes be x and the number of doughnuts be y
xc + yd = 6 ... (i)
Statement 1: 2d = 3c - 0.1 ... (ii)
Here, (i) and (ii) would NOT result in a unique solution since there are too many variables - Not sufficient
Statement 2: d + c = 0.7 ... (iii)
(ii) and (iii) can be solved to calculate the price of each: c = $0.50 and d = $0.20
But we cannot determine x or y - Not Sufficient
Combining both:
Using the values of c and d, from (i): 5x + 2y = 60
Here, there are 2 unknowns, ideally there should be infinite solutions. However, we know that x and y are positive integers (additional constraint). Hence, there may NOT be infinite solutions - we should check the values:
Starting solution: x = 12 and y = 0
Decrease x by 2 (coefficient of y) and increase y by 5 (coefficient of x) to get the next solutions:
x = 10, y = 5
x = 8, y = 10
x = 6, y = 15
x = 4, y = 20
x = 2. y = 25
x = 0, y = 30 (you don't need to solve all. I was just showing the method)
So, we do NOT have a unique value - Not Sufficient
Answer E


how did you get c=0.5 and d = 20?
Show more

In the solution you quote, c and d denote prices of cupcakes and doughnuts in dollars.

(1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes:
2d = 3c - 0.1

(2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35:
d + c = 0.7

So, we have a system of two linear equation: 2d = 3c - 0.1 and d + c = 0.7. Multiply the second equation by 2 and subtract the result from the first equqation:

2d - 2(d + c) = (3c - 0.1) - 2*0.7
-2c = 3c - 1.5
c = 0.3.

Substitute c = 0.3 into d + c = 0.7 to get d = 0.4.

Hope it's clear.
User avatar
samarpan.g28
User avatar
Joined: 08 Dec 2023
Last visit: 19 Nov 2025
Posts: 324
Own Kudos:
125
Given Kudos: 1,236
Location: India
Concentration: General Management, Human Resources
Schools: IIMA '26 Schulich Sept '26 Montreal '26 HEC Sept '26
GPA: 8.88
WE:Engineering (Technology)
Schools: IIMA '26 Schulich Sept '26 Montreal '26 HEC Sept '26
Posts: 324
Kudos: 125
At the bakery, Lew spent a total of $6.00 for one kind of 28 Apr 2024, 14:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pmal04
At the bakery, Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut. How many doughnuts did he buy?

(1) The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes.
(2) The average (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35.
Show more
­You will find 2 equations from statements 1 and 2 where the variables will be individual prices of cupcakes and doughnuts. However, by solving the equations, you will find the prices only, not their quantities. Choose (E).
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,589
Own Kudos:
1,079
Posts: 38,589
Kudos: 1,079
At the bakery, Lew spent a total of $6.00 for one kind of 24 May 2025, 21:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105390 posts
kingbucky
496 posts