Find all School-related info fast with the new School-Specific MBA Forum

It is currently 25 Oct 2014, 05:46

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Joanna bought only $0.15 stamps and $0.29 stamps. How many

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Manager
Manager
User avatar
Joined: 06 Apr 2010
Posts: 144
Followers: 3

Kudos [?]: 113 [2] , given: 15

Reviews Badge
Joanna bought only $0.15 stamps and $0.29 stamps. How many [#permalink] New post 26 Sep 2010, 10:48
2
This post received
KUDOS
14
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

49% (02:05) correct 51% (01:06) wrong based on 581 sessions
Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?

(1) She bought $4.40 worth of stamps.
(2) She bought an equal number of $0.15 stamps and $0.29 stamps.
[Reveal] Spoiler: OA
15 KUDOS received
GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 978
Location: Toronto
Followers: 261

Kudos [?]: 710 [15] , given: 3

Re: Stamps [#permalink] New post 27 Feb 2011, 21:42
15
This post received
KUDOS
1
This post was
BOOKMARKED
gmat1220 wrote:
Ian,
Please correct me. In GMAT neither statements contradict. So its good idea to take the hint from 2) statement.
Solve for the value of stamps using 1) and 2)
x=y and 15x + 29y = 440.
Hence x=y=10


Yes, since the Statements never contradict each other, you can be sure from Statement 2 that there must be one solution where x=y, even when you only use Statement 1 alone. The only question then is whether there might be a second solution.

gmat1220 wrote:
Now suspect if 1) ALONE is the "credited" answer. To prove that no other solution exists just put in random integer < 10 and random integer > 10 for x, y in the equation 15x + 29y = 440. In choosing x and y, I know for sure if x > 10 then y < 10 and vice versa.
If I get more than one pair of solution, the answer is C otherwise it is A.


No, I would not just haphazardly plug in all conceivable values of y here to see which work; that would take a long time. We have an equation involving positive integers:

15x + 29y = 440

Now, two of the numbers (15 and 440) are multiples of 5. That guarantees that the third number, 29y, is also a multiple of 5, and so y must be a multiple of 5 (if it is not immediately clear that 29y needs to be a multiple of 5 here, you can rewrite the equation as 29y = 440 - 15x = 5(88 - 3x), from which we can see that 29y is equal to a multiple of 5). Doing this you greatly cut down on the number of values you need to test; you now only need to check y= 5, 10 and 15 (since if y = 20, the sum is too large).
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

Expert Post
6 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23421
Followers: 3614

Kudos [?]: 28948 [6] , given: 2874

Re: Stamps [#permalink] New post 26 Sep 2010, 10:56
6
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
udaymathapati wrote:
Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?
(1) She bought $4.40 worth of stamps.
(2) She bought an equal number of $0.15 stamps and $0.29 stamps.


Let x be the # of $0.15 stamps and y the # of $0.29 stamps. Note that x and y must be an integers. Q: x=?

(1) She bought $4.40 worth of stamps --> 15x+29y=440. Only one integer combination of x and y is possible to satisfy 15x+29y=440: x=10 and y=10. Sufficient.

(2) She bought an equal number of $0.15 stamps and $0.29 stamps --> x=y. Not sufficient.

Answer: A.

So when we have equation of a type ax+by=c and we know that x and y are non-negative integers, there can be multiple solutions possible for x and y (eg 5x+6y=60) OR just one combination (eg 15x+29y=440). Hence in some cases ax+by=c is NOT sufficient and in some cases it is sufficient.

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

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

2 KUDOS received
Manager
Manager
avatar
Joined: 06 Apr 2010
Posts: 83
Followers: 2

Kudos [?]: 13 [2] , given: 2

GMAT ToolKit User
Re: Stamps [#permalink] New post 18 Oct 2010, 01:02
2
This post received
KUDOS
I hate C traps!!The good news is that both statements do no contradict each other. So, I know that the 2nd statement provides a clue, even if it is not sufficient on its own. And, from the numbers given( 0.15, 0.29 and 4.40), I look for some sort of relationship among them. In this case, the number should be a multiple of 5 in order to give a 0 in 4.40. And, 0.15 + 0.29 =0.44. Sometimes the solution is so obvious that I cant see it even if it is staring straight at me....sigh..
2 KUDOS received
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1541
Followers: 5

Kudos [?]: 84 [2] , given: 39

Re: Joanna bought only $0.15 stamps and $0.29 stamps. How many [#permalink] New post 08 Feb 2013, 11:21
2
This post received
KUDOS
udaymathapati wrote:
Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?

(1) She bought $4.40 worth of stamps.
(2) She bought an equal number of $0.15 stamps and $0.29 stamps.



Key is to realise that 0.15+0.29 = 0.44 and thus from statement one u can buy 10 combinations of the 0.44 stamps
1 KUDOS received
Manager
Manager
avatar
Joined: 30 May 2010
Posts: 191
Followers: 3

Kudos [?]: 47 [1] , given: 32

Re: Stamps [#permalink] New post 26 Sep 2010, 11:05
1
This post received
KUDOS
C is a trap. I hate these questions, because you have to work out the possibilities. Is there a simpler way to determine if (A) only has one solution? I usually just draw a little chart and start filling it in.
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Status: Upset about the verbal score - SC, CR and RC are going to be my friend
Joined: 30 Jun 2010
Posts: 318
Followers: 6

Kudos [?]: 16 [1] , given: 6

Re: Stamps [#permalink] New post 29 Sep 2010, 21:23
1
This post received
KUDOS
where 440 mentioned??

Only in statement 1. You should not use the information from statement 1 unless you are considering to combine both statement 1 and statement 2 to arrive at answer C.
_________________

My gmat story
MGMAT1 - 630 Q44V32
MGMAT2 - 650 Q41V38
MGMAT3 - 680 Q44V37
GMATPrep1 - 660 Q49V31
Knewton1 - 550 Q40V27

1 KUDOS received
GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 978
Location: Toronto
Followers: 261

Kudos [?]: 710 [1] , given: 3

Re: Stamps [#permalink] New post 27 Feb 2011, 09:41
1
This post received
KUDOS
bugSniper wrote:
Additionally if I have an equation ax+by = c; if the coefficients a,b are co-prime, can I be certain that there could possibly be only one combination(other than probably a or b being 0) of a,b that would solve the equation?


No, that's not generally the case. You can find very simple equations with coprime coefficients and multiple integer solutions. If you take, picking an example almost at random,

2x + 3y = 17

this will have integer solutions whenever 17-3y is even, so has positive integer solutions whenever y is odd (and small enough to make the equation work) -- that is, it has positive integer solutions when y = 1, 3 and 5.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

1 KUDOS received
Intern
Intern
avatar
Joined: 17 Dec 2012
Posts: 10
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: Joanna bought only $0.15 stamps and $0.29 stamps. How many [#permalink] New post 07 Feb 2013, 11:56
1
This post received
KUDOS
Hi,

just saw this very useful information in a MGMAT explanation.

In order to prove that no other pair exists, you could figure out what number of stamps are required to do a TRADE between the $0.15 and $0.29 stamps.
You would need to trade 29 of the $0.15 stamps against 15 of the $0.29 stamps.
Hence you need at least either 30 of the $0.15 stamps or 16 of the $0.29 stamps to be able to do a trade, because according to the statment Joanna buys at least one of each stamp.

To further illustrate this, let's assume Joanna bought $8.80 worth of stamps.
Then she could have bought 20 of each of the stamps. (20 * $0.15) + (20 * $0.29) = $8.80
Furthermore you could trade 15 of the $0.29 stamps against 29 of the $0.15 stamps. [(20 + 29) * $0.15] + [(20 - 15) * $0.29] = $8.80

Since the amount of $4.40 limits the number of stamps to 10 each, there is no trade possible and therefore you don't need to do further tests.

Thanks to Tim from MGMAT :-)
1 KUDOS received
Intern
Intern
avatar
Joined: 09 Apr 2013
Posts: 2
Followers: 0

Kudos [?]: 1 [1] , given: 2

Diophantine Equations related Data Sufficiency. [#permalink] New post 16 Jun 2013, 16:32
1
This post received
KUDOS
Here is the method to never fail to answer correctly Diophantine-equations-related Data Sufficiency problems.

1. First, be sure that the 2 variables must be non-negative integers or positive integers and that each statement provides a linear equation relating the 2 variables. Furthermore, be sure that the 2 equations are not equivalent (2x+3y=20 and 6x+9y=60 are equivalent) and are reduced to the form: ax + by = c whith integral coefficients and constant term such that GCF (a,b)=1.

2. Find an initial Solution: "Take advantage" of the fact that statements never contradict each other and thus system of equations constructed with both statements have always at least one solution. So resolve the system of equations.

3. Unicity: Once you arrive to a solution, say (x0, y0), go back to the first statement alone, for example, and check the unicity of the solution using only that statement by applying the test below. In case the solution is unique, statement 2 is superfluous and statement 1 is sufficient. The answer is A or D. In case the solution is not unique the answer is B, C or E.

Apply the test on statement (2). And update your answer.

If there is more than one solution using each statement alone then the answer is C.

-------------------------------------------------------------------------------------------------------------------------------------------------
Now here is the rule that indicates whether or not a non-negative integer solution is unique to an equation:
Suppose the equation be: ax+by=c (reduced with a, b, c positive integers. i.e. GCF(a,b)=1)
If (x0-b)<0 AND (y0-a)<0 then there is no other non-negative integer solution than (x0, y0) and the corresponding statement is sufficent.
If (x0-b)>=0 OR (y0-a)>=0 then other non-negative integers solutions exist and the statement is not sufficient.

If the variables must be positive the test is:
If (x0 - b)<=0 AND (y0 - a)<=0 then there is no other positive integer solution than (x0, y0) and the corresponding statement is sufficent.
If (x0 - b)>0 OR (y0 - a)>0 then other positive integers solutions exist and the statement is not sufficient.

Note: The test is to subtract each coefficient from the solution found for the opposite variable.
--------------------------------------------------------------------------------------------------------------------------------------------------
Let's apply this to a real GMAT problem:
A man buys some juice boxes. The boxes are from two different brands, A and B. How many boxes of brand A did the man buy if he bought $5.29 worth of boxes?
(1) The price of brand A box is $0.81 and the price of brand B box is $0.31
(2) The total amount of boxes is 9

Variables here must be positive integers -number of juice boxes- since it is suggested that some juice boxes are from brand A and the rest from brand B.
1. The equations provided are:
(1) 0.81A + 0.31B = 5.29.
(2) A + B = 9
Which are reduced to:
(1) 81A + 31B = 529
(2) A + B = 9,
which is a system of reduced, linear, non-equivalent equations.

2. Find an initial Solution:
(1) 81A + 31B = 529. GCF(31, 81)=1.
(2) A + B = 9

Mutliplying (2) by 31 and subtracting it from (1) we get:
50A=250 so A=5 and B=4.
An initial solution is (5, 4)

3. Unicity:
Unicity for statement (1):
81(5) + 31(4) = 529
Since
(5 - 31) <=0 AND (4 - 81)<=0 then there no other positive solution than (5, 4) so statement (1) is sufficient.

Unicity for statement (2):
It is obvious that statement (2) alone is not sufficient but the test is still applicable.
1(5) + 1(4) = 9
Since
(5 - 1) >0 OR (4 - 1) > 0 then there are other positive solutions than (5, 4) so statement (2) is not sufficient.
Answer A.

Hope this helps.
Manager
Manager
avatar
Joined: 30 May 2010
Posts: 191
Followers: 3

Kudos [?]: 47 [0], given: 32

Re: Stamps [#permalink] New post 26 Sep 2010, 11:08
I guess if there is not a quicker way, at least look for which of the numbers will be easier to work with. It is a lot easier to determine if something is divisible by 15 than 29. So start with zero 29 cent stamps and subtract it from 4.40, and see if the result is divisible by 15. If you find more than one solution, stop working and look at the next statement.
Manager
Manager
avatar
Joined: 21 Oct 2007
Posts: 204
GRE 1: 1250 Q780 V540
Followers: 5

Kudos [?]: 49 [0], given: 15

GMAT ToolKit User
Re: Stamps [#permalink] New post 29 Sep 2010, 08:24
jpr200012 wrote:
start with zero 29 cent stamps and subtract it from 4.40

in this particular case, I belieeve, we can't start with zero 29 cent stamps, we should start with 1, because stimulus says Jonna bought both kind of stamps.
_________________

If you like my post, please press Kudos+1

Senior Manager
Senior Manager
avatar
Joined: 13 Aug 2010
Posts: 315
Followers: 1

Kudos [?]: 10 [0], given: 1

Re: Stamps [#permalink] New post 29 Sep 2010, 20:57
Bunuel,im not getting why is B insufficient. we have 15x + 29y = 440 and since x=y, we have 15x + 29x = 440 then x = 10. so y= 10. Can you please explain. Thanx in advance
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23421
Followers: 3614

Kudos [?]: 28948 [0], given: 2874

Re: Stamps [#permalink] New post 29 Sep 2010, 21:54
Expert's post
prab wrote:
Bunuel,im not getting why is B insufficient. we have 15x + 29y = 440 and since x=y, we have 15x + 29x = 440 then x = 10. so y= 10. Can you please explain. Thanx in advance


As noted above by Dreamy you can not use info from statement (1) to solve statement (2), so for (2) we don't know that total $4.40 were spent.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 23 Jan 2011
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: Stamps [#permalink] New post 26 Feb 2011, 11:53
Quote:
So when we have equation of a type ax+by=c and we know that x and y are non-negative integers, there can be multiple solutions possible for x and y (eg 5x+6y=60) OR just one combination (eg 15x+29y=440). Hence in some cases ax+by=c is NOT sufficient and in some cases it is sufficient.


Is 5x+6y=60 a good example for this case?
The only solutions to the above equation(considering only integers are acceptable; you cannot have 1.5 stamps) are x=0;y=10 (or) x=6;y=5. Unless I'm missing another solution. Don't you think 5x+10y=60 would be a better example to show multiple solutions. Just curious.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23421
Followers: 3614

Kudos [?]: 28948 [0], given: 2874

Re: Stamps [#permalink] New post 26 Feb 2011, 12:02
Expert's post
bugSniper wrote:
Quote:
So when we have equation of a type ax+by=c and we know that x and y are non-negative integers, there can be multiple solutions possible for x and y (eg 5x+6y=60) OR just one combination (eg 15x+29y=440). Hence in some cases ax+by=c is NOT sufficient and in some cases it is sufficient.


Is 5x+6y=60 a good example for this case?
The only solutions to the above equation(considering only integers are acceptable; you cannot have 1.5 stamps) are x=0;y=10 (or) x=6;y=5. Unless I'm missing another solution. Don't you think 5x+10y=60 would be a better example to show multiple solutions. Just curious.


First of all the example is not about stamps problem, it's a general example about Diophantine equations and yes, I think it's a good example as it has more than one integer solution.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 23 Jan 2011
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: Stamps [#permalink] New post 26 Feb 2011, 12:14
Additionally if I have an equation ax+by = c; if the coefficients a,b are co-prime, can I be certain that there could possibly be only one combination(other than probably a or b being 0) of a,b that would solve the equation?
Intern
Intern
avatar
Joined: 23 Jan 2011
Posts: 8
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: Stamps [#permalink] New post 26 Feb 2011, 12:17
Bunuel wrote:
bugSniper wrote:
Quote:
So when we have equation of a type ax+by=c and we know that x and y are non-negative integers, there can be multiple solutions possible for x and y (eg 5x+6y=60) OR just one combination (eg 15x+29y=440). Hence in some cases ax+by=c is NOT sufficient and in some cases it is sufficient.


Is 5x+6y=60 a good example for this case?
The only solutions to the above equation(considering only integers are acceptable; you cannot have 1.5 stamps) are x=0;y=10 (or) x=6;y=5. Unless I'm missing another solution. Don't you think 5x+10y=60 would be a better example to show multiple solutions. Just curious.


First of all the example is not about stamps problem, it's a general example about Diophantine equations and yes, I think it's a good example as it has more than one integer solution.



Fair enough. Thank you.
Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 929
Followers: 11

Kudos [?]: 200 [0], given: 123

Reviews Badge
Re: Stamps [#permalink] New post 27 Feb 2011, 10:27
Ian,
Please correct me. In GMAT neither statements contradict. So its good idea to take the hint from 2) statement.
Solve for the value of stamps using 1) and 2)
x=y and 15x + 29y = 440.
Hence x=y=10

Now suspect if 1) ALONE is the "credited" answer. To prove that no other solution exists just put in random integer < 10 and random integer > 10 for x, y in the equation 15x + 29y = 440. In choosing x and y, I know for sure if x > 10 then y < 10 and vice versa.
If I get more than one pair of solution, the answer is C otherwise it is A.

IanStewart wrote:

No, that's not generally the case. You can find very simple equations with coprime coefficients and multiple integer solutions. If you take, picking an example almost at random,

2x + 3y = 17

this will have integer solutions whenever 17-3y is even, so has positive integer solutions whenever y is odd (and small enough to make the equation work) -- that is, it has positive integer solutions when y = 1, 3 and 5.
Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 929
Followers: 11

Kudos [?]: 200 [0], given: 123

Reviews Badge
Re: Stamps [#permalink] New post 27 Feb 2011, 23:15
Ian
Your explanation almost blows me away :-) Such a profound explanation about factors. I am lovin it ! Please have my kudos !

IanStewart wrote:
gmat1220 wrote:
Ian,
Please correct me. In GMAT neither statements contradict. So its good idea to take the hint from 2) statement.
Solve for the value of stamps using 1) and 2)
x=y and 15x + 29y = 440.
Hence x=y=10


Yes, since the Statements never contradict each other, you can be sure from Statement 2 that there must be one solution where x=y, even when you only use Statement 1 alone. The only question then is whether there might be a second solution.

gmat1220 wrote:
Now suspect if 1) ALONE is the "credited" answer. To prove that no other solution exists just put in random integer < 10 and random integer > 10 for x, y in the equation 15x + 29y = 440. In choosing x and y, I know for sure if x > 10 then y < 10 and vice versa.
If I get more than one pair of solution, the answer is C otherwise it is A.


No, I would not just haphazardly plug in all conceivable values of y here to see which work; that would take a long time. We have an equation involving positive integers:

15x + 29y = 440

Now, two of the numbers (15 and 440) are multiples of 5. That guarantees that the third number, 29y, is also a multiple of 5, and so y must be a multiple of 5 (if it is not immediately clear that 29y needs to be a multiple of 5 here, you can rewrite the equation as 29y = 440 - 15x = 5(88 - 3x), from which we can see that 29y is equal to a multiple of 5). Doing this you greatly cut down on the number of values you need to test; you now only need to check y= 5, 10 and 15 (since if y = 20, the sum is too large).
Re: Stamps   [#permalink] 27 Feb 2011, 23:15
    Similar topics Author Replies Last post
Similar
Topics:
Joanna bought only $0.15 stamps and $0.29 stamps. How many kirankp 2 05 Jan 2010, 06:59
1 Joanna bought only $0.15 stamps and $0.29 stamps. How many Economist 3 22 Mar 2009, 20:51
Joanna bought only $0.15 stamps and $0.29 stamps. How many nikhilpoddar 4 23 Sep 2008, 13:04
Joanna bought only $0.15 stamps and $0.29 stamps. How many sam76 2 24 Feb 2008, 17:15
Joanna bought only $0.15 stamps and $0.29 stamps. How many gluon 9 15 Sep 2007, 14:45
Display posts from previous: Sort by

Joanna bought only $0.15 stamps and $0.29 stamps. How many

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 28 posts ] 



cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.