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# Alex has 75 red tokens and 75 blue tokens. There is a booth where Alex

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Math Expert
Joined: 02 Sep 2009
Posts: 59589
Alex has 75 red tokens and 75 blue tokens. There is a booth where Alex  [#permalink]

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20 Mar 2019, 04:56
00:00

Difficulty:

55% (hard)

Question Stats:

56% (03:31) correct 44% (03:32) wrong based on 16 sessions

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Alex has 75 red tokens and 75 blue tokens. There is a booth where Alex can give two red tokens and receive in return a silver token and a blue token, and another booth where Alex can give three blue tokens and receive in return a silver token and a red token. Alex continues to exchange tokens until no more exchanges are possible. How many silver tokens will Alex have at the end?

(A) 62
(B) 82
(C) 83
(D) 102
(E) 103

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Math Expert
Joined: 02 Aug 2009
Posts: 8281
Re: Alex has 75 red tokens and 75 blue tokens. There is a booth where Alex  [#permalink]

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20 Mar 2019, 06:00
Bunuel wrote:
Alex has 75 red tokens and 75 blue tokens. There is a booth where Alex can give two red tokens and receive in return a silver token and a blue token, and another booth where Alex can give three blue tokens and receive in return a silver token and a red token. Alex continues to exchange tokens until no more exchanges are possible. How many silver tokens will Alex have at the end?

(A) 62
(B) 82
(C) 83
(D) 102
(E) 103

You can do simple calculations as the calculations are not too cumbersome, even though it may contain 4-5 steps..

(I) Let Alex go to booth where he gives blue tokens.. so 75 B will give 25 S and 25R
(II) total R now is 75R=25R=100R, these 100R will give 50S and 50B
(III) Out of 50B, 48B will give 16S and 16R
(IV) now 16R will give 8S and 8B
(V) Add 2B left in step (III) to 8B to get 10B, Now 10B will give 3S and 3R.
(VI) 2R out of 3R will give 1S and 1B
(VII) Left in the end are 1R and 1B, and there is no more transaction possible.
Silver earned are 25+50+16+8+3+1=103

E
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Re: Alex has 75 red tokens and 75 blue tokens. There is a booth where Alex  [#permalink]

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20 Mar 2019, 08:12
1
Bunuel wrote:
Alex has 75 red tokens and 75 blue tokens. There is a booth where Alex can give two red tokens and receive in return a silver token and a blue token, and another booth where Alex can give three blue tokens and receive in return a silver token and a red token. Alex continues to exchange tokens until no more exchanges are possible. How many silver tokens will Alex have at the end?

(A) 62
(B) 82
(C) 83
(D) 102
(E) 103

solve using given info

2 Red coins = 1 silver + 1 Blue
so for 75 Red coints = 37 silver + 37 Blue coins
now add these 37 blue coins to 75 blue coins = 112 blue coins
where 3 Blue coin = 1 silver + 1 red
so 112 blue coints= 37 silver + 37 red
again
37 red = 18 silver + 18 blue
again 18 blue = 6 silver + 6 red
then 6 red = 3 silver + 3 blue
3 blue = 1 silver + 1 red
1 Red =
add all silver = 37+37+18+6+3+1 +1= 103
IMO E
Re: Alex has 75 red tokens and 75 blue tokens. There is a booth where Alex   [#permalink] 20 Mar 2019, 08:12
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