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

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Senior Manager
Joined: 02 Jul 2017
Posts: 293
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and  [#permalink]

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06 Nov 2017, 08:39
1
00:00

Difficulty:

55% (hard)

Question Stats:

38% (02:51) correct 63% (02:34) wrong based on 18 sessions

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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
Math Expert
Joined: 02 Aug 2009
Posts: 7036
An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and  [#permalink]

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06 Nov 2017, 08:49
Nikkb 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

let Lily take x set and Anthony take y...

lily has 6x gizmos and 9x gadgets
Anthony has 6y gizmos and 9y gadgets...

after the exchange.....

Lily has $$\frac{1}{3}*6x=2x$$ gizmos and $$9x+\frac{2}{3}*9y=9x+6y$$ gadgets
given that difference is 92 so $$9x+6y-2x=7x+6y=92$$

A has $$\frac{1}{3}*9y=3y$$ gadgets and $$6y+\frac{2}{3}*6x=4x+6y$$ gadgets
given that difference is 50 so $$4x+6y-3y=4x+3y=50$$

so $$7x+6y=92$$.....................(i)
$$4x+3y=50.......8x+6y=100$$..(ii)
subtract i from ii
$$8x+6y-7x-6y=100-92........x=8$$
ans 8

D
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Senior Manager
Joined: 02 Jul 2017
Posts: 293
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
Re: An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and  [#permalink]

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06 Nov 2017, 09:33
Attaching solution again as someone deleted my earlier post.. not sure why....

emockus , Tridhipal and dave13

Guys here is the solution :

Tool-kit = 6 gizmos + 9 gadgets

Let Anthony bought Toolkits = a
and Lily bought Toolkits = b
Attachments

Toolkit question.JPG [ 1.99 MiB | Viewed 433 times ]

Re: An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and &nbs [#permalink] 06 Nov 2017, 09:33
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