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

_________________

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