Last visit was: 09 Oct 2024, 21:17 It is currently 09 Oct 2024, 21:17
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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

Pam owns an inventory of unopened packages of corn and rice

SORT BY:
Date
Kudos
 1   2   
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
Vinayprajapati
Joined: 24 May 2013
Posts: 56
Own Kudos [?]: 165 [78]
Given Kudos: 99
Send PM
GMAT ToolKit User
Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   15 Apr 2016, 21:55
8
Kudos
70
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

58% (02:23) correct 42% (02:03) wrong based on 1078 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
Pam owns an inventory of unopened packages of corn and rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have ?

1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
adiagr
Joined: 18 Jan 2010
Posts: 209
Own Kudos [?]: 1030 [26]
Given Kudos: 9
Send PM
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   08 Jun 2016, 22:28
17
Kudos
9
Bookmarks
Vinayprajapati
Pam owns an inventory of unopened packages of corn and rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have ?

1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice

This is an obvious C trap question. If we combine both statements, we will get an answer.
So this problem is likely to be solved by one statement only. (With experience you can say that this statement would be A)

If we take factors of 282 we get: 2*3*47.

Statement 1
17c+13r = 282 = 6 * 47. [ where c = corn packages and r = rice packages]

Note that 17 and 13 are co-prime.

Our aim is to find such values of c and r such that 17c+13r = 47.

47 = 34+13.
c=2; r=1

We can get a unique answer.

Corn Package = 2*6 = 12 (We dont need to calculate this).

Statement 2

We know that c= 2r. But we dont know exact numbers so not sufficient.

A is the answer.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 15354
Own Kudos [?]: 68664 [24]
Given Kudos: 444
Location: Pune, India
Send PM
Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   17 Apr 2016, 20:12
8
Kudos
16
Bookmarks
Expert Reply
Konstantin1983
I hate such questions because, as in statement 1, you must be sure that such equation doesn't have unique solution. And with such numbers..How come should i guess about 12 and 6? Picking numbers is time-consuming

This question is based on the concept of "integral solutions". Since in such real world examples, x and y cannot be negative or fractional, usually these equations have a finite number of solutions.
After you get one solution, you will quickly know how many solutions the equation has. But getting the first set of values which satisfy the equation requires a little bit of brute force.
But the good thing here is that this is a DS question. You don't need to find the actual solution. The only thing you "need" is to establish that there is a single solution only. (Obviously, there has to be a solution since she does own $282 worth of packages.)

That can be done relatively easily.
First, check out this post for a conceptual discussion on this question type (case 2):
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/06 ... -of-thumb/

Once you understand this, the following will make sense to you.

17x + 13y = 282
If x = 0, y is 21.something (not an integer)
If x = 1, y = 20.something
If x = 2, y = 19.something
If x = 3, y = 17.something

Now you know that there will be only one set of values satisfying this equation. Why? Because y will be less than 17 in the first set of values which satisfy this equation. So if you want to get the next set that satisfies, you will need to subtract it by 17 which will make y negative. So in any case, there will be a unique solution to this equation.
Hence statement 1 is sufficient.

Answer (A)
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11498
Own Kudos [?]: 36699 [7]
Given Kudos: 333
Send PM
Reviews Badge
Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   17 Apr 2016, 00:49
4
Kudos
3
Bookmarks
Expert Reply
stonecold
chetan2u
Vinayprajapati
Pam owns an inventory of unopened packages of corn and rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have ?

1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice

hi,
The Q puts to you a C trap..
the first statement gives you SUM of two variables..
AND the II gives you the ratio of two variables..

and there it is C, BUT more than often the SUM gives you enough INFO to be sufficient..

let the number of packages of corn be C and that of rice be R..

I. 17C + 13R = 282..
check for values of C and see if any integer value of R is possible ..
C can take values from 1 to 282/17 = 16..

Only C as 12 and R as 6 is possible..
SUff

II. She has twice as many packages of corn as of rice
C = 2R..
various answers possible..

A


Hey Chetan I have a doubt in this Question..
I marked the correct answer as i thought in my head that 13 and 17 are prime so the common factor would repeat after 13*17 hence only one value satisfy.
Now my question is the process of putting the integers as 1,2,3,4...takes a loooooong time..
Is there any other shorter way to tackle this question .
regards
S.C.S.A

Hi MeghaP and stonecold,

Is there a shortcut-- it will depend from Q to Q, depending on the properties of the number involved..
Should you depend on a short cut-- MAY BE but do not miss out on other combinations which may as well satisfy the equation...

let me explain through this example-


NOTE- I had initially done the Q by taking values one by one, and you too when you get hang of the tables, would be able to do faster. So when now you have written about a shortcut, I can give you one in this Q..

\(17x+13y=282\)
=> \(4x+13x+13y=282\)..
\(4x+13(x+y) = 282\)...
now some info you should gather from here
1) 13(x+y) should form most of 282 as 13>4 and x+y>x...
2) (x+y) should be a multiple of 2 but not of 4---
3) if entire 282 was formed from 13(x+y), x+y <22 as 13*22>282..

so values of x+y can be 2, 6, 10, 14, 18 only..
Since we are looking for the largest value from 13(x+y), lets try with x+y =18.
\(4x+13(x+y)=4x+13*18=4x+234 = 282\)...
so \(4x= 282-234=48.. x=12\)..
satisfies all conditions written above.. OK x=12, y= 18-12=6

lets try the next possible
\(x+y = 14\)..
\(4x+13(x+y)=4x+13*14=4x+182 = 282\)...
so \(4x= 282-182=100... x=25\)..
is it possible that x= 25 and x+y=14, when both x and y are non negative.... NO
any number below this 10,8,2 can be ruled out straight way as they would make x much larger than x+y..

so our answer is that ONLY one set of number are possible..
General Discussion
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11498
Own Kudos [?]: 36699 [2]
Given Kudos: 333
Send PM
Reviews Badge
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   15 Apr 2016, 22:53
2
Bookmarks
Expert Reply
Vinayprajapati
Pam owns an inventory of unopened packages of corn and rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have ?

1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice

hi,
The Q puts to you a C trap..
the first statement gives you SUM of two variables..
AND the II gives you the ratio of two variables..

and there it is C, BUT more than often the SUM gives you enough INFO to be sufficient..

let the number of packages of corn be C and that of rice be R..

I. 17C + 13R = 282..
check for values of C and see if any integer value of R is possible ..
C can take values from 1 to 282/17 = 16..

Only C as 12 and R as 6 is possible..
SUff

II. She has twice as many packages of corn as of rice
C = 2R..
various answers possible..

A
User avatar
D
stonecold
Alum
Joined: 12 Aug 2015
Posts: 2265
Own Kudos [?]: 3253 [1]
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Send PM
GMAT ToolKit User
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   17 Apr 2016, 00:17
1
Kudos
chetan2u
Vinayprajapati
Pam owns an inventory of unopened packages of corn and rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have ?

1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice

hi,
The Q puts to you a C trap..
the first statement gives you SUM of two variables..
AND the II gives you the ratio of two variables..

and there it is C, BUT more than often the SUM gives you enough INFO to be sufficient..

let the number of packages of corn be C and that of rice be R..

I. 17C + 13R = 282..
check for values of C and see if any integer value of R is possible ..
C can take values from 1 to 282/17 = 16..

Only C as 12 and R as 6 is possible..
SUff

II. She has twice as many packages of corn as of rice
C = 2R..
various answers possible..

A


Hey Chetan I have a doubt in this Question..
I marked the correct answer as i thought in my head that 13 and 17 are prime so the common factor would repeat after 13*17 hence only one value satisfy.
Now my question is the process of putting the integers as 1,2,3,4...takes a loooooong time..
Is there any other shorter way to tackle this question .
regards
S.C.S.A
avatar
bethebest
Joined: 01 Mar 2014
Posts: 97
Own Kudos [?]: 33 [0]
Given Kudos: 616
Schools: Tepper '18
Send PM
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   17 Apr 2016, 00:29
chetan2u
Vinayprajapati
Pam owns an inventory of unopened packages of corn and rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have ?

1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice

hi,
The Q puts to you a C trap..
the first statement gives you SUM of two variables..
AND the II gives you the ratio of two variables..

and there it is C, BUT more than often the SUM gives you enough INFO to be sufficient..

let the number of packages of corn be C and that of rice be R..

I. 17C + 13R = 282..
check for values of C and see if any integer value of R is possible ..
C can take values from 1 to 282/17 = 16..

Only C as 12 and R as 6 is possible..
SUff

II. She has twice as many packages of corn as of rice
C = 2R..
various answers possible..

A

I have come across a lot of such questions to recognize the trap. But I do not know the mathematical way to conclude that only one combination will fit in. For example, in this case C has to be 12 and R has to be 6. How can we rule out other possibilities? Please suggest. Thank you!
User avatar
S
Konstantin1983
Joined: 02 Dec 2014
Posts: 304
Own Kudos [?]: 307 [1]
Given Kudos: 353
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE:Sales (Telecommunications)
Send PM
Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   17 Apr 2016, 13:35
1
Kudos
I hate such questions because, as in statement 1, you must be sure that such equation doesn't have unique solution. And with such numbers..How come should i guess about 12 and 6? Picking numbers is time-consuming
avatar
B
knuckleduster
Current Student
Joined: 26 May 2013
Posts: 33
Own Kudos [?]: 27 [9]
Given Kudos: 28
GMAT 1: 730 Q50 V39
GPA: 3.6
Send PM
GMAT ToolKit User Reviews Badge
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   18 Apr 2016, 20:13
9
Kudos
One thing I find convenient in these kind of questions is to get help from the other statement that is given as a trap. For example, for this one '(2) She has twice as many packages of corn as of rice' statement should help you pick out the numbers efficiently since you would be choosing twice as as many corn packages as of rice. C = 12 R =6 becomes easy to find
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11498
Own Kudos [?]: 36699 [1]
Given Kudos: 333
Send PM
Reviews Badge
Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   18 Apr 2016, 20:22
1
Kudos
Expert Reply
knuckleduster
One thing I find convenient in these kind of questions is to get help from the other statement that is given as a trap. For example, for this one '(2) She has twice as many packages of corn as of rice' statement should help you pick out the numbers efficiently since you would be choosing twice as as many corn packages as of rice. C = 12 R =6 becomes easy to find

Hi,
it may not be advisable here, unless you are very careful...
say 12 and 6 you have found same way..
BUT there is another solution for the EQUATION, then statement I will not be sufficient whereas you will mark it as sufficient..
so you have to ensure that there are no further solutions apart from 12 and 6..
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 15354
Own Kudos [?]: 68664 [3]
Given Kudos: 444
Location: Pune, India
Send PM
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   18 Apr 2016, 21:45
3
Kudos
Expert Reply
knuckleduster
One thing I find convenient in these kind of questions is to get help from the other statement that is given as a trap. For example, for this one '(2) She has twice as many packages of corn as of rice' statement should help you pick out the numbers efficiently since you would be choosing twice as as many corn packages as of rice. C = 12 R =6 becomes easy to find

That is certainly a good idea, provided it is used carefully. I wrote a post on this concept sometime back:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/07 ... t-part-ii/
User avatar
S
thangvietname
Joined: 09 Jun 2010
Posts: 525
Own Kudos [?]: 529 [0]
Given Kudos: 916
Send PM
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   08 Jun 2016, 07:49
there is one similar question in og 2015 but it is more easy because we can prove that there is only one set of solution in case of A.

is this problem from gmatprep? i doubt that gmat force us to make too complex accounting
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 15354
Own Kudos [?]: 68664 [0]
Given Kudos: 444
Location: Pune, India
Send PM
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   08 Jun 2016, 20:41
Expert Reply
thangvietnam
there is one similar question in og 2015 but it is more easy because we can prove that there is only one set of solution in case of A.

is this problem from gmatprep? i doubt that gmat force us to make too complex accounting

Note that this is a 700+ level question. This concept can be tested in GMAT. If you use some tricks, you can solve the question very easily with few calculations.
Check out my discussion on this question above. Also, knuckleduster talks about a strategy that can be used here to solve it very quickly. I have also given a link above where that strategy has been discussed in detail.
User avatar
P
jkolachi
Joined: 12 Oct 2015
Posts: 238
Own Kudos [?]: 379 [4]
Given Kudos: 144
Location: Canada
Concentration: Leadership, Accounting
Schools: Ivey '19 (A) Queen's 19 (A) Schulich Jan 18 Intake (A)
GMAT 1: 700 Q47 V39
GPA: 3
WE:Accounting (Accounting)
Send PM
Reviews Badge
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   24 May 2017, 13:48
3
Kudos
1
Bookmarks
Here's my simple solution. Since 17 & 13 are both primes (always look out for prime numbers), we can use prime factorization.

282 - divide by 2 -> 141 divide by 3--> 47 (which breaks into 17 *2 + 13(1))

So (17(2)+13(1) * 6) = $282.... there's only one way to get to $282. 17*12 + 13*6. other methods won't work so sufficient.

Should be out of this question in 60 seconds if you're quick.
avatar
B
McWill
Current Student
Joined: 26 Feb 2019
Posts: 9
Own Kudos [?]: 7 [0]
Given Kudos: 68
Location: United States (CA)
Schools: Wharton '23 (D) CBS '23 (A) Tuck '23 (WL)
GMAT 1: 720 Q49 V40
GPA: 3.4
Send PM
Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   20 Jul 2019, 10:15
VeritasKarishma, Bunuel

To clarify, is the quick, "lightbulb" method to solve this question recognizing that the LCM of 13 and 17 is found only once between 0 and 282? Or is it that because we can rule out any solution of Rice being greater than 17 and can therefore deduce that the solution must exist with Rice<17 ---> and therefore, if we subtract 17 from this number (to find the next solution) it will give us a negative and thus no additional solution?

I understand that both ways that I have outlined are based on the same concept, so my question is can we just go straight to the "LCM occurring only once test" or do we have to rule out a few potential values first?

Thanks in advance!
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 15354
Own Kudos [?]: 68664 [2]
Given Kudos: 444
Location: Pune, India
Send PM
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   21 Jul 2019, 00:44
2
Kudos
Expert Reply
McWill
VeritasKarishma, Bunuel

To clarify, is the quick, "lightbulb" method to solve this question recognizing that the LCM of 13 and 17 is found only once between 0 and 282? Or is it that because we can rule out any solution of Rice being greater than 17 and can therefore deduce that the solution must exist with Rice<17 ---> and therefore, if we subtract 17 from this number (to find the next solution) it will give us a negative and thus no additional solution?

I understand that both ways that I have outlined are based on the same concept, so my question is can we just go straight to the "LCM occurring only once test" or do we have to rule out a few potential values first?

Thanks in advance!

LCM of 13 and 17 doesn't have much to do with it since you are not multiplying 13 with 17 but instead 13 with some number and 17 with another.

e.g. 17x + 13y = 277
x = 1, y = 20 satisfies this.
Next solution will be x = 14, y = 3
Both valid solutions though LCM of 13 and 17 occurs only once in 277 too.
User avatar
G
Karthik740
Joined: 20 Oct 2020
Posts: 37
Own Kudos [?]: 70 [0]
Given Kudos: 20
Location: India
Concentration: Strategy, Finance
GMAT 1: 720 Q50 V38
GPA: 4
Send PM
Reviews Badge
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   28 May 2021, 06:31
Why do we need to assume it's an integral solution?
We can very well assume that the package quantities are not integers.

Generally, on the GMAT questions, "INTEGERS" are mentioned specifically in the question stem.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 96014
Own Kudos [?]: 666799 [1]
Given Kudos: 87567
Send PM
CAT Tests Forum Quiz Mode
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   28 May 2021, 08:21
1
Kudos
Expert Reply
Karthik740
Why do we need to assume it's an integral solution?
We can very well assume that the package quantities are not integers.

Generally, on the GMAT questions, "INTEGERS" are mentioned specifically in the question stem.

We are told that "Pam owns an inventory of [i]unopened packages of corn and rice...[/i]" so we can deduce that the number of packages must be integers.
avatar
B
yahya729
Joined: 30 Apr 2021
Posts: 36
Own Kudos [?]: 7 [0]
Given Kudos: 39
GMAT 1: 710 Q50 V37
Send PM
Reviews Badge
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   02 Jun 2021, 06:51
this co-prime won't always work. for example 3x+5y=42>> 3x+5y=6x7. it'll work with 6(x=2), but not with 7, given that we are only looking for integers >=0. but then if x=2 is a solution, you could multiple by 7 and have x=14,y=0 as a starting point, and then go down by the LCM approach which mean 3x-15 and 5y+15. so x=14,9,4 and y=0,3,6. however it's a bit easier to solve for a smaller number like 42 and not so easy for something larger where lots of iterations will just take time
User avatar
S
Aishyk97
Joined: 13 Sep 2021
Posts: 87
Own Kudos [?]: 27 [0]
Given Kudos: 77
Send PM
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink] Pam owns an inventory of unopened packages of corn and rice   09 Aug 2023, 00:32
KarishmaB
Konstantin1983
I hate such questions because, as in statement 1, you must be sure that such equation doesn't have unique solution. And with such numbers..How come should i guess about 12 and 6? Picking numbers is time-consuming

This question is based on the concept of "integral solutions". Since in such real world examples, x and y cannot be negative or fractional, usually these equations have a finite number of solutions.
After you get one solution, you will quickly know how many solutions the equation has. But getting the first set of values which satisfy the equation requires a little bit of brute force.
But the good thing here is that this is a DS question. You don't need to find the actual solution. The only thing you "need" is to establish that there is a single solution only. (Obviously, there has to be a solution since she does own $282 worth of packages.)

That can be done relatively easily.
First, check out this post for a conceptual discussion on this question type (case 2):
https://www.gmatclub.com/forum/veritas- ... -of-thumb/

Once you understand this, the following will make sense to you.

17x + 13y = 282
If x = 0, y is 21.something (not an integer)
If x = 1, y = 20.something
If x = 2, y = 19.something
If x = 3, y = 17.something

Now you know that there will be only one set of values satisfying this equation. Why? Because y will be less than 17 in the first set of values which satisfy this equation. So if you want to get the next set that satisfies, you will need to subtract it by 17 which will make y negative. So in any case, there will be a unique solution to this equation.
Hence statement 1 is sufficient.

Answer (A)

Hi KarishmaB Bunuel

Can you please explain the highlighted portion to me?
I know many people have provided explanations but I am finding it difficult to reach certainty that there will be only one set of solutions available. How can I be sure without doing tedious calculations?
GMAT Club Bot
gmatclubot
Re: Pam owns an inventory of unopened packages of corn and rice [#permalink]
09 Aug 2023, 00:32
 1   2   
Moderator:
Bunuel
Math Expert
96014 posts