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No. of Machines

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No. of Machines

by tonebeeze » Mon Mar 14, 2011 1:36 pm
Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 4 steel parts and 7 chrome parts. If a certain group of type A and type B machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group

a. 2
b. 3
c. 4
d. 6
e. 9

OA = 6
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by force5 » Mon Mar 14, 2011 2:16 pm
Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 4 steel parts and 7 chrome parts. If a certain group of type A and type B machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group
IMO- D (6)
steel chrome
A 3 2

B 4 7

x 20 22

the only possible comb is 4A+2B ( 4A= 12 steel, 2B = 8 steel= total 20 steel)
hence 6 machines.
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by Night reader » Mon Mar 14, 2011 2:23 pm
x-machine A steel parts, y-machine B steel parts
3x+4y=20, x and y must be integers --> 20 can't be divided by 3, so x=4, y=2 OR 4 machines A and 2 machines B

let's check our answer with solving for chrome parts
2x+7y=22, If x=4 then 8+7y=22, y=2 the same answer :) 4 machines A and 2 machines B

total 6 machines

IOM d

tonebeeze wrote:Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 4 steel parts and 7 chrome parts. If a certain group of type A and type B machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group

a. 2
b. 3
c. 4
d. 6
e. 9

OA = 6
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by GMATGuruNY » Mon Mar 14, 2011 2:24 pm
tonebeeze wrote:Each Machine of type A has 3 steel parts and 2 chrome parts. Each machine of type B has 4 steel parts and 7 chrome parts. If a certain group of type A and type B machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group

a. 2
b. 3
c. 4
d. 6
e. 9

OA = 6
Steel parts in A + Steel Parts in B = Steel Parts in A+B:
3A + 4B = 20.

Chrome parts in A + Chrome Parts in B = Chrome Parts in A+B:
2A + 7B = 22.

Multiplying 2A + 7B = 22 by 3, we get:
6A + 21B = 66.
Multiplying 3A + 4B = 20 by 2, we get:
6A + 8B = 40.

Subtracting the bottom equation above from the top equation above, we get:
13B = 26.
B = 2.

Plugging B=2 into 3A+4B = 20, we get:
3A + 4*2 = 20
3A = 12.
A = 4.

A+B = 4+2 = 6.

The correct answer is D.
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