GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 Sep 2018, 04:38

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

Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40

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

Hide Tags

Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 860
WE: Supply Chain Management (Energy and Utilities)
Premium Member CAT Tests
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

Show Tags

New post 14 Jul 2018, 03:04
4
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

51% (02:52) correct 49% (03:14) wrong based on 35 sessions

HideShow timer Statistics

Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6803
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

Show Tags

New post 14 Jul 2018, 05:00
1
PKN wrote:
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.


30a+35b+40c=420

(1) b=c
So 30a+75b=420
If b=2, 30a=420-150=270.....a=9 so >5
If b=4, 30a=420-300=120....a=4 and b=c=2 so none is greater than 5
Insufficient


(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.

So a=c and \(b\leq{c}\)
So 30a+35b+40c=420......70a+35b=420.....you can divide entire equation by 35
2a+b=12.....
Max value of a is 5 and therefore max value of c is 5 and b cannot be greater than c
No combination of a,b,c greater than 5 is possible..
So sufficient

B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

RC Moderator
User avatar
D
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 640
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
Re: Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

Show Tags

New post 14 Jul 2018, 05:10
To find if Alice bought more than 5 stamps of any of the three values

Let x be the number of 30 stamps and x > 0
Let y be the number of 35 stamps and y > 0
Let z be the number of 40 stamps and z > 0

Alice spent a total of $4.20 in buying these stamps

=> 30x + 35y + 40z = $4.20 = 420 cents ------- (1)

Statement 1

The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.

=> y = z

=> From equation 1, 30x + y(35 + 40) = 420

=> 30x + 75y = 420

Case 1)

x = 9, y = 2 satisfies the equation. So might have bought more than 5 30 cent stamps.

case 2)

x = 4, y = 4 satisfies the equation. So might have bought less than 5 30 cent stamps.

Since we don't get an unique answer, statement 1 is not sufficient.

Statement 2

The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.

=> x = z and y \(\leq\) z = x

From equation 1, we get 30x + 40x + 35y = 420

=> 70x + 35y = 420 ---------- (2)

Since y \(\geq\) 0 and y \(\leq\) x lets start figuring out the minimum possible value for y

If y \(\geq\)0 and y is an integer lets start at y=1

=> 70x + 35 = 420

=> 70x = 385

=> x is not an integer which is false => y > 1

Lets see if y = 2

From equation 2, => 70x + 70 = 420

=> 70x = 350

=> x = 5

Since the minimum possible value for y is 2 and if y=2 => x = z = 5

=> x, z \(\leq\) 5

Statement 2 is sufficient

Hence option B
_________________

If you like my post press kudos +1

New - RC Butler - 2 RC's everyday

Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag.

Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 860
WE: Supply Chain Management (Energy and Utilities)
Premium Member CAT Tests
Re: Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

Show Tags

New post 14 Jul 2018, 05:12
chetan2u wrote:
PKN wrote:
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.


30a+35b+40c=420

(1) b=c
So 30a+75b=420
If b=2, 30a=420-150=270.....a=9 so >5
If b=4, 30a=420-300=120....a=4 and b=c=2 so none is greater than 5
Insufficient


(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.
So a=c and b>c
So 30a+35b+40c=420......70a+35b=420.....you can divide entire equation by 35
2a+b=12.....
Max value of a is 5 and therefore max value of c is 5 and b cannot be greater than c
No combination of a,b,c greater than 5 is possible..
So sufficient

B


Hi chetan2u,
Could you please correct me? I think it's \(b\leq{c}\).
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Manager
Manager
User avatar
S
Joined: 22 Jan 2014
Posts: 176
WE: Project Management (Computer Hardware)
Re: Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40  [#permalink]

Show Tags

New post 14 Jul 2018, 05:17
PKN wrote:
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.


PKN wrote:
Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 cent stamps. She spent a total of $4.20 in buying these stamps. Did she buy more than 5 stamps of any of the three values?

(1) The number of 35 cent stamps and 40 cent stamps that Alice bought are equal.
(2) The number of 30 cent stamps and 40 cent stamps that Alice bought are equal. The number of 35 cent stamps that she bought was not more than the number of 40 cent stamps that she bought.


B.

let x,y,and z be # of 30,35,and 40 cent stamps respectively
so, 30x+35y+40z = 420

1) y=z
=> 30x+75k = 420
(k,x) = (2,9) & (4,4)
or (x,y,z) = (9,1,1) & (4,2,2)
insufficient.

2) x=z
=> 35y+70k = 420
(k,y) = (2,8) , (4,4) & (6,0)
or (x,y,z) = (1,8,1) , (2,4,2) & (3,0,3)
(1,8,1) is discarded since y =< z
so Alice did not purchase any value stamp in a quantity more than 5. sufficient.
_________________

Illegitimi non carborundum.

GMAT Club Bot
Re: Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40 &nbs [#permalink] 14 Jul 2018, 05:17
Display posts from previous: Sort by

Alice bought a certain number of 30 cent stamps, 35 cent stamps and 40

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

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.