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

It is currently 13 Dec 2019, 16:07

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

A man purchased $510 worth savings bonds in denominations of

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

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
User avatar
B
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 400
Location: United States (NY)
GPA: 3.82
WE: Account Management (Retail Banking)
A man purchased $510 worth savings bonds in denominations of  [#permalink]

Show Tags

New post 16 Oct 2012, 10:39
3
7
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

61% (03:02) correct 39% (02:47) wrong based on 155 sessions

HideShow timer Statistics

Kaplan's Daily Question

A man purchased $510 worth savings bonds in denominations of $15 and $30, including at least 1 of each denomination. He gave away 8 of the bonds as gifts but then lost all the rest of the bonds he had purchased. If the number of $30 bonds he gave away was a multiple of the number of $15 bonds he gave away, what was maximum possible value of the bonds that he lost?

A.180
B.225
C.285
D.300
E.330

Spoiler: :: OE
The value of the bonds that the man lost will be the total amount he purchased ($510) minus the value of the bonds he gave away. The less he gave away, the more he must have lost, so we can find the maximum he could have lost by finding the minimum he could have given away. We can try to do so using the information we are given about the number of bonds he gave away.

If t = the number of $30 bonds given away, and f = the number of $15 bonds given away, we know that t + f = 8, and t is a multiple of f. We want to find the minimum amount he could have given away. That means we want the smaller denomination, f, the number of $15 bonds, to be as large as possible. So, if t + f = 8, and t is a multiple of f, what are the possible values of t and f? There are three possibilities



If t = 5 and f = 3, 5 + 3 = 8 but 5 is not a multiple of 3, so this is not possible. Also, if t is less than 4, f must be greater than 4, so t could not be a multiple of f.

So, the largest possible value of f is 4. In this case, t is also 4, and the amount given away will be $30t + $15f = ($30 × 4) + ($15 × 4) = $120 + $60 = $180. If he gave away $180, then he must have lost $510 - $180 = $330, which is choice (E).

Note the trap answers: (A) represents the minimum he could have given away; (B) represents the amount lost if f = 1; and (C) represents the amount lost if f = 2.


Spoiler: :: Kudos
Press Kudos if you liked this post :idea:
Intern
Intern
avatar
Joined: 14 Oct 2012
Posts: 1
Re: A man purchased $510 worth savings bonds in denominations of  [#permalink]

Show Tags

New post 16 Oct 2012, 14:09
If the man gives away 180=(4*30+15*30), this means that he would have 510-180=230 left. But since 230 is not a multiple of 15 or 30 he cannot have bought bonds for 510. That is (4,4) cannot be the answer.

I go for D. The man gives (6*30+2*15)=210 leaving him 300 left to spend on bonds. And 300 is a multiple of 15 and 30 so he can actually spend 510 in total.
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India
Re: A man purchased $510 worth savings bonds in denominations of  [#permalink]

Show Tags

New post 16 Oct 2012, 22:00
cqwejie wrote:
If the man gives away 180=(4*30+15*30), this means that he would have 510-180=230 left. But since 230 is not a multiple of 15 or 30 he cannot have bought bonds for 510. That is (4,4) cannot be the answer.

I go for D. The man gives (6*30+2*15)=210 leaving him 300 left to spend on bonds. And 300 is a multiple of 15 and 30 so he can actually spend 510 in total.


Actually, you have a typo.
510 - 180 = 330 which is a multiple of 15 and 30.
_________________
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 >
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India
Re: A man purchased $510 worth savings bonds in denominations of  [#permalink]

Show Tags

New post 16 Oct 2012, 22:01
thevenus wrote:
Kaplan's Daily Question

A man purchased $510 worth savings bonds in denominations of $15 and $30, including at least 1 of each denomination. He gave away 8 of the bonds as gifts but then lost all the rest of the bonds he had purchased. If the number of $30 bonds he gave away was a multiple of the number of $15 bonds he gave away, what was maximum possible value of the bonds that he lost?

A.180
B.225
C.285
D.300
E.330



We know that 0 is a multiple of every integer. If I were to ignore the options, I would say that he gifted 8 of the $15 bonds and 0 of the $30 bonds so that he gifted only $120 bonds and suffered maximum loss of 510 - 120 = $390.
But 390 is not the options so I can only assume that they mean 'positive multiples only' (in which case, you go for 4 of $15 bonds and 4 of $30 bonds)
I would expect them to write it clearly though.

Not a perfect question.
_________________
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: 12 Dec 2012
Posts: 213
Concentration: Leadership, Marketing
GMAT 1: 540 Q36 V28
GMAT 2: 550 Q39 V27
GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)
A man purchased $510 worth savings bonds in denominations  [#permalink]

Show Tags

New post 26 Mar 2013, 08:33
A man purchased $510 worth savings bonds in denominations of $15 and $30, including at least 1 of each denomination. He gave away 8 of the bonds as gifts but then lost all the rest of the bonds he had purchased. If the number of $30 bonds he gave away was a multiple of the number of $15 bonds he gave away, what was maximum possible value of the bonds that he lost?

180
225
285
300
330

Kaplan 's question of the day :

https://www.freequestionaday.com/gmat?c ... ae3b6fedd2

could not solve it and could not understand the explanation . Any help please ? thanks in advance :)
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1010
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: A man purchased $510 worth savings bonds in denominations  [#permalink]

Show Tags

New post 26 Mar 2013, 09:07
TheNona wrote:
A man purchased $510 worth savings bonds in denominations of $15 and $30, including at least 1 of each denomination. He gave away 8 of the bonds as gifts but then lost all the rest of the bonds he had purchased. If the number of $30 bonds he gave away was a multiple of the number of $15 bonds he gave away, what was maximum possible value of the bonds that he lost?

180
225
285
300
330

Kaplan 's question of the day :

https://www.freequestionaday.com/gmat?c ... ae3b6fedd2

could not solve it and could not understand the explanation . Any help please ? thanks in advance :)


IMO E

To maximise the value of the bonds he lost, we have to minimize the value he gave away

knowing that X(=number 30$ bonds) +Y(=number of 15$ bonds) = 8
and that X is a multiple of Y, to minimize 30X+15Y I use the combination (4,4) since 4 is a multiple of itself. (the other combinations are (7,1) cost = 225; and (6,2) cost = 210; but as you can see they have higher prices)
\(30*4+14*4=180\) = value gave away
\(510-180=330\) = value lost

PS: is (0,8) a valid combination? 0 is a multiple of 8, right?
Verbal Forum Moderator
User avatar
B
Joined: 10 Oct 2012
Posts: 583
Re: A man purchased $510 worth savings bonds in denominations  [#permalink]

Show Tags

New post 26 Mar 2013, 09:26
1
TheNona wrote:
A man purchased $510 worth savings bonds in denominations of $15 and $30, including at least 1 of each denomination. He gave away 8 of the bonds as gifts but then lost all the rest of the bonds he had purchased. If the number of $30 bonds he gave away was a multiple of the number of $15 bonds he gave away, what was maximum possible value of the bonds that he lost?

180
225
285
300
330

Kaplan 's question of the day :

https://www.freequestionaday.com/gmat?c ... ae3b6fedd2

could not solve it and could not understand the explanation . Any help please ? thanks in advance :)


Let the number of 15$ bonds given be x, then the number of 30$ bills given = kx, where k is an integer.

Thus, x+kx = 8 --> x(1+k) = 8. Thus, we could have

x = 1, k=7 --> The value left with him = 510 - (15+210) = 285
x = 8,k =0 --> The value left with him = 510 - (120) = 390
x =4, k =1 --> The value left with him = 510 - (60+120) = 330
x=2,k=3 --> The value left with him = 510 - (30+180) = 300

Thus, the answer is E.
_________________
Intern
Intern
avatar
Joined: 22 Jan 2010
Posts: 24
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)
Re: A man purchased $510 worth savings bonds in denominations of  [#permalink]

Show Tags

New post 27 Mar 2013, 06:07
1
8 => 1+7
=> 2+6
=> 3+5
=> 4+4
so,only possible set for ($15,$30) = (2,6) and (4,4).

To make value of lost bond maximum,the value of 8 bonds gifted would be minimum => No of $30 bonds has to be minimum.

Value of gifted bonds = (15+30) * 4 = 180.
So,maximum value of lost bonds = 510 -180 = 330
Hence ,option E.
--------------------------------------------------------------
Press Kudos if you liked my post .
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2491
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: A man purchased $510 worth savings bonds in denominations of  [#permalink]

Show Tags

New post 24 Feb 2016, 18:23
since we must have at least 1 of each..suppose he:
gave away x# of 15, and y# of 30
since y must be a multiple of x, and since x+y must be 8, we have these options:
x=1 - y=7
x=2 - y=6
x=4 - y=4
can't have other ones, because y must be a multiple of x.
4 is always a multiple of 4...if we have less x, then we lose more on y...
so 4x15+4x30=180. 510-180=330
330 is the max he could have lost.
Director
Director
User avatar
D
Joined: 08 Jun 2013
Posts: 542
Location: France
Schools: INSEAD Jan '19
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Consulting (Other)
GMAT ToolKit User
Re: A man purchased $510 worth savings bonds in denominations of  [#permalink]

Show Tags

New post 11 Jan 2019, 06:15
The value of the bonds that the man lost will be the total amount he purchased ($510) minus the value of the bonds he gave away. The less he gave away, the more he must have lost, so we can find the maximum he could have lost by finding the minimum he could have given away. We can try to do so using the information we are given about the number of bonds he gave away.

If t = the number of $30 bonds given away, and f = the number of $15 bonds given away, we know that t + f = 8, and t is a multiple of f. We want to find the minimum amount he could have given away. That means we want the smaller denomination, f, the number of $15 bonds, to be as large as possible. So, if t + f = 8, and t is a multiple of f, what are the possible values of t and f?

If t = 5 and f = 3, 5 + 3 = 8 but 5 is not a multiple of 3, so this is not possible. Also, if t is less than 4, f must be greater than 4, so t could not be a multiple of f.

So, the largest possible value of f is 4. In this case, t is also 4, and the amount given away will be $30t + $15f = ($30 x 4) + ($15 x 4) = $120 + $60 = $180. If he gave away $180, then he must have lost $510 - $180 = $330, which is choice (E).

Note the trap answers: (A) represents the minimum he could have given away; (B) represents the amount lost if f = 1; and (C) represents the amount lost if f = 2.

Posted from my mobile device
_________________
Everything will fall into place…

There is perfect timing for
everything and everyone.
Never doubt, But Work on
improving yourself,
Keep the faith and
Stay ready. When it’s
finally your turn,
It will all make sense.
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 971
Location: United States
A man purchased $510 worth savings bonds in denominations of  [#permalink]

Show Tags

New post 04 Oct 2019, 07:06
thevenus wrote:
Kaplan's Daily Question

A man purchased $510 worth savings bonds in denominations of $15 and $30, including at least 1 of each denomination. He gave away 8 of the bonds as gifts but then lost all the rest of the bonds he had purchased. If the number of $30 bonds he gave away was a multiple of the number of $15 bonds he gave away, what was maximum possible value of the bonds that he lost?

A.180
B.225
C.285
D.300
E.330


"max value lost" -> by finding "least money given away"

\(8=x+y…x=15.given…y=30.given…y=x*multiple…y≥x\)
\(8=x+y=[1+7,…2+6,…4+4]…y≥x…min(y)=4…x=4\)
\(gave.away:15(4)+30(4)=60+120=180\)
\(lost:510-180=330\)

Answer (E)
GMAT Club Bot
A man purchased $510 worth savings bonds in denominations of   [#permalink] 04 Oct 2019, 07:06
Display posts from previous: Sort by

A man purchased $510 worth savings bonds in denominations of

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





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