NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 02:10 It is currently 26 Apr 2024, 02:10
Decision Tracker
My Rewards
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

An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Li

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92929
Own Kudos [?]: 619095 [17]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Li [#permalink] New post   17 Dec 2019, 00:50
2
Kudos
15
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

66% (02:47) correct 34% (03:01) wrong based on 93 sessions
Hide Show timer Statistics
An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Lily each buy some tool-kits. After both of them complete their purchases, Lily trades two-thirds of her gizmos with Anthony for two-thirds of his gadgets. After the trade, Lily has 92 more gadgets than she has gizmos, and Anthony has 50 more gizmos than he has gadgets. How many tool-kits did Lily buy?

A. 4
B. 5
C. 6
D. 8
E. 10


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
D
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1878
Own Kudos [?]: 6296 [2]
Given Kudos: 704
Location: India
Send PM
Re: An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Li [#permalink] New post   17 Dec 2019, 04:33
1
Kudos
1
Bookmarks
Assume Lily buys 'x' tool kits and Anthony buys y

Before transfer
Number of Gadgets Lily has= 9x
Number of Gadgets Anthony has= 9y

Number of Gizmos Lily has= 6x
Number of Gizmos Anthony has= 6y

After Transfer

Number of Gadgets Lily has= 9x+6y
Number of Gadgets Anthony has= 3y

Number of Gizmos Lily has= 2x
Number of Gizmos Anthony has= 6y+4x


Lily has 92 more gadgets than she has gizmos
7x+6y=92....(1)

Anthony has 50 more gizmos than he has gadgets
3y+4x=50......(2)

From (1) and (2)

x=8 and y= 6


Bunuel wrote:
An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Lily each buy some tool-kits. After both of them complete their purchases, Lily trades two-thirds of her gizmos with Anthony for two-thirds of his gadgets. After the trade, Lily has 92 more gadgets than she has gizmos, and Anthony has 50 more gizmos than he has gadgets. How many tool-kits did Lily buy?

A. 4
B. 5
C. 6
D. 8
E. 10


Are You Up For the Challenge: 700 Level Questions
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22055 [1]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Li [#permalink] New post   21 Dec 2019, 21:09
1
Kudos
Expert Reply
Bunuel wrote:
An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Lily each buy some tool-kits. After both of them complete their purchases, Lily trades two-thirds of her gizmos with Anthony for two-thirds of his gadgets. After the trade, Lily has 92 more gadgets than she has gizmos, and Anthony has 50 more gizmos than he has gadgets. How many tool-kits did Lily buy?

A. 4
B. 5
C. 6
D. 8
E. 10


Are You Up For the Challenge: 700 Level Questions


We can let A and L be the number of toolkits Anthony and Lily bought, respectively. Thus, Anthony has 6A gizmos and 9A gadgets, and Lily has 6L gizmos and 9L gadgets. After Lily trades two-thirds of her gizmos (i.e., 4L gizmos) with Anthony for two-thirds of his gadgets (i.e., 6A gadgets), Anthony has 6A + 4L gizmos and 9A - 6A = 3A gadgets, and Lily has 6L - 4L = 2L gizmos and 9L + 6A gadgets.

Since Lily has 92 more gadgets than she has gizmos and Anthony has 50 more gizmos than he has gadgets after the trade, we have:

9L + 6A = 2L + 92

and

6A + 4L = 3A + 50

Simplifying the equations, we have:

7L + 6A = 92

3A + 4L = 50

Multiplying the latter equation by -2, we have -6A - 8L = -100. Adding this equation to 7L + 6A = 92, we have:

-L = -8

L = 8

We see that Lily bought 8 toolkits.

Answer: D
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3965 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Li [#permalink] New post   18 Mar 2024, 21:59
Given: An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Lily each buy some tool-kits. After both of them complete their purchases, Lily trades two-thirds of her gizmos with Anthony for two-thirds of his gadgets. After the trade, Lily has 92 more gadgets than she has gizmos, and Anthony has 50 more gizmos than he has gadgets.

Asked: How many tool-kits did Lily buy?

Let toolkit bought by Lily be x and bought by Anthony be y.

Before trade:
Gizmos with Lily = 6x
Gadgets with Lily = 9x
Gizmos with Anthony = 6y
Gadgets with Anthony = 9y

After trade:
Gizmos with Lily = 6x -2/3*6x + = 2x
Gadgets with Lily = 9x + 2/3*9y = 9x +6y
Gizmos with Anthony = 6y + 4x
Gadgets with Anthony = 9y - 6y = 3y

(9x +6y) - 2x = 92
7x + 6y =92

(6y + 4x) - 3y = 50
3y + 4x = 50

x =8
y= 6

Toolkits bought by Lily = x = 8

IMO D

Posted from my mobile device
GMAT Club Bot
gmatclubot
Re: An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Li [#permalink]
18 Mar 2024, 21:59
Moderators:
Bunuel
Math Expert
92921 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions