Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 20 Jul 2019, 05:03

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.

Close

Request Expert Reply

Confirm Cancel

Joe bought only twenty cent stamps and thirty cent stamps. How many

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 02 Sep 2010
Posts: 40
WE 1: Business Development Manger
WE 2: Assistant Manager-Carbon Trading
WE 3: Manager-Carbon Trading
Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 13 Dec 2010, 06:53
25
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (01:49) correct 37% (01:17) wrong based on 677 sessions

HideShow timer Statistics


Joe bought only twenty cent stamps and thirty cent stamps. How many twenty cent stamps did he buy?

(1) Joe bought more than 8 twenty cent stamps.
(2) Joe bought a total of $2.50 worth of stamps.

The OA says C but I am getting B ..guys can you please explain

I applied my reasoning that .2x+.3y=2.50
so .2*5=1.0
.3*5=1.5
Hence we add and we can get 2.50 ..so B should be sufficient..I tried but there are no other integer choices for this combination.

Please help .... :(
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56303
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 13 Dec 2010, 07:26
4
12
rite2deepti wrote:
Joe bought only twenty cent stamps and thirty cent stamps. How many twenty cent stamps did he buy?

(1) Joe bought more than 8 twenty cent stamps.
(2) Joe bought a total of $2.50 worth of stamps.

The OA says C but I am getting B ..guys can you please explain

I applied my reasoning that .2x+.3y=2.50
so .2*5=1.0
.3*5=1.5
Hence we add and we can get 2.50 ..so B should be sufficient..I tried but there are no other integer choices for this combination.

Please help .... :(


Actually there are more integer solutions possible to satisfy statement (2):

Joe bought only twenty cent stamps and thirty cent stamps. How many twenty cent stamps did he buy?

(1) Joe bought more than 8 twenty cent stamps --> clearly insufficient.

(2) Joe bought a total of $2.50 worth of stamps --> \(2x+3y=25\): as \(x\) and \(y\) must be an integers we must check whether this equation has unique solution (for more on this check below links) --> \(2x=25-3y\), so 25 minus multiple of 3 must be multiple of 2, following pairs of (x,y) are possible: (2, 7), (5, 5), (8, 3), (11, 1). Not sufficient.

(1)+(2) As from (1) \(x>8\) then from (2) only one pair is left: \(x=11\) and \(y=1\). Sufficient.

Answer: C.

For more on this type of questions check:
eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html
martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html
a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html
joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html
a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html
joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html
at-an-amusement-park-tom-bought-a-number-of-red-tokens-and-126814.html
collections-confused-need-a-help-81062.html

P.S. Also you should have spotted that x=5 and y=5 for (2) is not correct solution as (1) says that x>8. So if x=5 were correct solution then statements would clearly contradict each other, but on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Hope it's clear.
_________________
General Discussion
Senior Manager
Senior Manager
User avatar
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 345
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross) - Class of 2014
GMAT 1: 730 Q49 V39
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 13 Dec 2010, 08:20
Agreed--the x>8 is the key.

C for me.
_________________
Senior Manager
Senior Manager
avatar
Joined: 18 Sep 2009
Posts: 256
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 13 Dec 2010, 10:36
Let no.of 0. 20 cent stamps "x", and 0.30 cent stamps "y"
stmnt (1) is not sufficient because:
x(0.20)+(x+8)(0.30)=?. we do not know x and total amount. Eliminate it.

stmnt (2) is not sufficient because:
x(0.20) +y(0.30)= 2.50. two unknowns in one equation. eliminate it.

(1)+(2)
x(0.20)+(x+8)(0.30)= 2.50.
we can easily solve "x" and"y" values. so answer is C
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56303
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 13 Dec 2010, 10:48
4
TomB wrote:
Let no.of 0. 20 cent stamps "x", and 0.30 cent stamps "y"
stmnt (1) is not sufficient because:
x(0.20)+(x+8)(0.30)=?. we do not know x and total amount. Eliminate it.

stmnt (2) is not sufficient because:
x(0.20) +y(0.30)= 2.50. two unknowns in one equation. eliminate it.

(1)+(2)
x(0.20)+(x+8)(0.30)= 2.50.
we can easily solve "x" and"y" values. so answer is C


About the red part: generally such kind of linear equations (ax+by=c) have infinitely many solutions for x and y, and we cannot get single numerical values for the variables. But since x and y represent # of stamps then they must be non-negative integers and in this case 2x+3y=25 is no longer a simple linear equation it's Diophantine equation (equations whose solutions must be integers only) and for such kind on equations there might be only one combination of x and y possible to satisfy it. When you encounter such kind of problems you must always check by trial and error whether it's the case.

So statement (2) is not sufficient not because there is one equation and two variables but because there exist more than one pair of integers x and y for which this equation holds true: (2, 7), (5, 5), (8, 3), (11, 1).

For more on such questions check:
equations-100204.html
gmat-prep2-92785.html
car-dealer-data-sufficiency-105682.html
_________________
Senior Manager
Senior Manager
avatar
Joined: 18 Sep 2009
Posts: 256
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 13 Dec 2010, 12:44
Bunnel, thanks for the explanation.
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9443
Location: Pune, India
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 13 Dec 2010, 22:23
For detailed explanation on how to solve for integral solutions, check out the following post:

http://gmatquant.blogspot.com/2010/11/integral-solutions-of-ax-by-c.html
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
avatar
Joined: 07 Apr 2014
Posts: 104
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 05 Sep 2014, 23:59
rite2deepti wrote:
Joe bought only twenty cent stamps and thirty cent stamps. How many twenty cent stamps did he buy?

(1) Joe bought more than 8 twenty cent stamps.
(2) Joe bought a total of $2.50 worth of stamps.

The OA says C but I am getting B ..guys can you please explain

I applied my reasoning that .2x+.3y=2.50
so .2*5=1.0
.3*5=1.5
Hence we add and we can get 2.50 ..so B should be sufficient..I tried but there are no other integer choices for this combination.

Please help .... :(



1--> no suff.
2--> .20x+ .30y= 2.5 muliple by 5 to remove clumsy.

1x +1.5y= 12.5 ---> now if x= 11 then y=1 or if x= 6 then y= 5 and similar way you could get different count for 20 cent stamps.

now 1+2 --> from one we got more than 8 hence it must be suff cuz, if x= 9 or 10 , you wont get proper value for y as y should be an integer.

Hence 11 - 20 cents stamps
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 22 Jan 2018, 22:46
rite2deepti wrote:
Joe bought only twenty cent stamps and thirty cent stamps. How many twenty cent stamps did he buy?

(1) Joe bought more than 8 twenty cent stamps.
(2) Joe bought a total of $2.50 worth of stamps.

The OA says C but I am getting B ..guys can you please explain

I applied my reasoning that .2x+.3y=2.50
so .2*5=1.0
.3*5=1.5
Hence we add and we can get 2.50 ..so B should be sufficient.I tried but there are no other integer choices for this combination.

Please help .... :(


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Assume a and b are number of stamps with twenty cents and thirty cents, respectively.

Since we have 2 variables (a and b) and 0 equations, C is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2):

a > 8
0.2a + 0.3b = 2.5
2a + 3b = 25

Case 1: a = 9
We have 18 + 3b = 25 or 3b = 7. It doesn't have an integer solution.

Case 2: a = 10
We have 20 + 3b = 25 or 3b = 7. It doesn't have an integer solution.

Case 3: a = 11
We have 22 + 3b = 25 or 3b = 3. Thus the pair of a = 11, b = 1 is a solution.

Case 4: a = 12
We have 24 + 3b = 25 or 3b = 1. It doesn't have an integer solution.

Thus we have a unique solution.

Both conditions together are sufficient.

Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT(Common Mistake Type) 4(A).

Condition 1) a > 8.
We can't specify the value of a from the condition 1).
The condition 1) is not sufficient.

Condition 2) 2a + 3b = 25
We have solutions a = 2, b = 7 and a = 5, b = 5.
Since it doesn't have a unique solution, the condition 2) is not sufficient.

Therefore, the answer is C.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
avatar
B
Joined: 31 Dec 2017
Posts: 51
GMAT ToolKit User
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many  [#permalink]

Show Tags

New post 12 Jul 2019, 05:27
B-trap answer for this type of question.
I figure out that:
+The answer could be B or C depends on which info you have from the 1st statement
If:
+It's a condition as this question, the answer is C
+It gives extra info such as the total number of objects, the answer is B
Correct me if I'm wrong, in case of not having enough time to list all possible pairs, guessing would be great to save time and move on.
GMAT Club Bot
Re: Joe bought only twenty cent stamps and thirty cent stamps. How many   [#permalink] 12 Jul 2019, 05:27
Display posts from previous: Sort by

Joe bought only twenty cent stamps and thirty cent stamps. How many

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne