It is currently 23 Sep 2017, 09:52

Happening Now:

Alleviate MBA app anxiety! Come to Chat Room #2


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M14-16

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124614 [0], given: 12079

M14-16 [#permalink]

Show Tags

New post 16 Sep 2014, 00:53
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (01:00) correct 44% (00:49) wrong based on 108 sessions

HideShow timer Statistics

A stationery store sells pens and pencils. If the price of each item in cents has a positive integer value, how much do 5 pencils cost?


(1) 5 pencils and 3 pens cost 30 cents.

(2) 4 pencils and 4 pens cost 32 cents.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124614 [0], given: 12079

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124614 [3], given: 12079

Re M14-16 [#permalink]

Show Tags

New post 16 Sep 2014, 00:53
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Official Solution:


(1) 5 pencils and 3 pens cost 30 cents. Given: \(5x+3y=30\). This equation has only one positive integer solution:\(x=3\) and \(y=5\), so the price of 5 pencils is \(5*3=15\) cents. Sufficient.

(2) 4 pencils and 4 pens cost 32 cents. Given: \(4x+4y=32\), so \(x+y=8\). This equation has more than one positive integer solution, for example: \(x=1\) and \(y=7\) or \(x=3\) and \(y=5\). Not sufficient.


Answer: A
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124614 [3], given: 12079

2 KUDOS received
Manager
Manager
User avatar
Joined: 10 May 2014
Posts: 142

Kudos [?]: 101 [2], given: 28

Premium Member
Re: M14-16 [#permalink]

Show Tags

New post 30 Oct 2014, 15:40
2
This post received
KUDOS
Hi Bunuel,

I think this is a great question. I falled for the trap and picked C here. At a very first glance I read this question as:

- Question stem: 5x = ?
- Statement 1: 5x + 3y = 30. I thought that since I had 1 equation and 2 variables I couldn´t solve for this.
- Statement 2: x + y = 8. Again, 1 equation and 2 variables.

So I thought the answer was C.

I understand that what makes Statement 1 sufficient is that the question stem gives us an "Integer Constraint" (“…if the price of each item in cents has a positive integer value…”)

But my question is: how will I realize about this in the next similar problem I have and prevent from falling for this trap again? Should I pay close attention to whether the question stem mentions this "Integer Constraint" (such as in the portion of the question mentioned above)?
_________________

Consider giving me Kudos if I helped, but don´t take them away if I didn´t! :)

What would you do if you weren´t afraid?

Kudos [?]: 101 [2], given: 28

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124614 [1], given: 12079

Re: M14-16 [#permalink]

Show Tags

New post 31 Oct 2014, 05:24
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
minwoswoh wrote:
Hi Bunuel,

I think this is a great question. I falled for the trap and picked C here. At a very first glance I read this question as:

- Question stem: 5x = ?
- Statement 1: 5x + 3y = 30. I thought that since I had 1 equation and 2 variables I couldn´t solve for this.
- Statement 2: x + y = 8. Again, 1 equation and 2 variables.

So I thought the answer was C.

I understand that what makes Statement 1 sufficient is that the question stem gives us an "Integer Constraint" (“…if the price of each item in cents has a positive integer value…”)

But my question is: how will I realize about this in the next similar problem I have and prevent from falling for this trap again? Should I pay close attention to whether the question stem mentions this "Integer Constraint" (such as in the portion of the question mentioned above)?


This is a C-Trap question. "C trap" question is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

Check for more here: c-trap-questions-177044.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124614 [1], given: 12079

Manager
Manager
avatar
Joined: 28 Oct 2015
Posts: 57

Kudos [?]: 6 [0], given: 127

Re: M14-16 [#permalink]

Show Tags

New post 13 Jun 2016, 02:16
Very tricky one indeed. One more thing which needs to be highlighted is the fact that there could be another solution to the equation 5x+3y=30 which is x=0 and y=10 but since we are given in the question that the number of pens and pencils are positive integer values, this solution is not possible.

Kudos [?]: 6 [0], given: 127

Manager
Manager
avatar
B
Joined: 08 Jan 2015
Posts: 86

Kudos [?]: 9 [0], given: 53

GMAT ToolKit User
Re: M14-16 [#permalink]

Show Tags

New post 10 Aug 2016, 23:03
minwoswoh wrote:
Hi Bunuel,

I think this is a great question. I falled for the trap and picked C here. At a very first glance I read this question as:

- Question stem: 5x = ?
- Statement 1: 5x + 3y = 30. I thought that since I had 1 equation and 2 variables I couldn´t solve for this.
- Statement 2: x + y = 8. Again, 1 equation and 2 variables.

So I thought the answer was C.

I understand that what makes Statement 1 sufficient is that the question stem gives us an "Integer Constraint" (“…if the price of each item in cents has a positive integer value…”)

But my question is: how will I realize about this in the next similar problem I have and prevent from falling for this trap again? Should I pay close attention to whether the question stem mentions this "Integer Constraint" (such as in the portion of the question mentioned above)?


IMO you should be always cautious on similar tasks (number of cakes/pencils/animals). They actually follow a similar pattern, so just solve as much of them as possible. And alway pay attention to INTEGER CONSTRAINT.

Kudos [?]: 9 [0], given: 53

Intern
Intern
avatar
Joined: 28 Nov 2016
Posts: 1

Kudos [?]: [0], given: 2

Re: M14-16 [#permalink]

Show Tags

New post 28 Nov 2016, 17:31
I was not the only one who thought like you..

minwoswoh wrote:
Hi Bunuel,

I think this is a great question. I falled for the trap and picked C here. At a very first glance I read this question as:

- Question stem: 5x = ?
- Statement 1: 5x + 3y = 30. I thought that since I had 1 equation and 2 variables I couldn´t solve for this.
- Statement 2: x + y = 8. Again, 1 equation and 2 variables.

So I thought the answer was C.

I understand that what makes Statement 1 sufficient is that the question stem gives us an "Integer Constraint" (“…if the price of each item in cents has a positive integer value…”)

But my question is: how will I realize about this in the next similar problem I have and prevent from falling for this trap again? Should I pay close attention to whether the question stem mentions this "Integer Constraint" (such as in the portion of the question mentioned above)?

Kudos [?]: [0], given: 2

Manager
Manager
avatar
B
Joined: 02 Nov 2013
Posts: 97

Kudos [?]: 9 [0], given: 10

Location: India
Re: M14-16 [#permalink]

Show Tags

New post 01 Dec 2016, 10:28
56 seconds that it.

I found it simple as by looking at statement I, There is only one solution i.e. x=3 and y=5. Only one answer.
Statement II: 4x+4y=32 will have multiple answers for x and y from which fixing one value is not possible.
x=2 then y= 6
x=4 and y=4
x=6 and y=2
Not sufficient.
Hence answer is A.

Kudos [?]: 9 [0], given: 10

Intern
Intern
avatar
B
Joined: 05 Sep 2016
Posts: 11

Kudos [?]: [0], given: 28

GMAT ToolKit User Premium Member CAT Tests
Re: M14-16 [#permalink]

Show Tags

New post 25 May 2017, 07:29
How can I get fast to X=3 and Y=5? should I just plug in numbers? is this the best way to do it?

Kudos [?]: [0], given: 28

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124614 [1], given: 12079

Re: M14-16 [#permalink]

Show Tags

New post 25 May 2017, 07:46
1
This post received
KUDOS
Expert's post

Kudos [?]: 124614 [1], given: 12079

Senior Manager
Senior Manager
avatar
S
Joined: 22 Aug 2013
Posts: 421

Kudos [?]: 122 [0], given: 259

Location: India
M14-16 [#permalink]

Show Tags

New post 25 May 2017, 11:35
cocojiz wrote:
How can I get fast to X=3 and Y=5? should I just plug in numbers? is this the best way to do it?


Hi

Let me see if I can help a bit.

we have 5x + 3y = 30 and we know both x and y have to be positive integers.
5x is obviously a multiple of 5, and on the right side 30 is also a multiple of 5. So, by simple logic, '3y' also must be a multiple of 5.
For '3y' to be a multiple of 5, 'y' must be a multiple of 5.

so we put y=5, and get 5x + 3*5 = 30. This gives us x=3
If we put y=10, we get x =0 which is not possible.

There is another way. 5x + 3y = 30 and we know both x and y have to be positive integers.
3y is obviously a multiple of 3, and on the right side 30 is also a multiple of 3. So, by simple logic, '5x' also must be a multiple of 3.
For '5x' to be a multiple of 3, 'x' must be a multiple of 3.

so we put x=3, and get 5*3 + 3y = 30. This gives us y=5
If we put x=6, we get y =0 which is not possible

This method sometimes helps.

Kudos [?]: 122 [0], given: 259

Intern
Intern
avatar
Joined: 27 Jun 2017
Posts: 1

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

CAT Tests
Re M14-16 [#permalink]

Show Tags

New post 05 Aug 2017, 06:21
I think this is a high-quality question and I agree with explanation.

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

Re M14-16   [#permalink] 05 Aug 2017, 06:21
Display posts from previous: Sort by

M14-16

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

Moderators: Bunuel, Vyshak



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

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

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®.