Latest CAT Aptitude Question SOLUTION: There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The m

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(#M40010184) CAT question Keep an EYE

There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus?
A)0 B)1/6 C)1/4 D)1/3 E)1

Asked In CAT Devendra Marghade (12 years ago)

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vishnu  (12 years ago)

E)1
As it takes only 6 min to identify.
there are 12 minute to find the faulty machine . so he can easily find out the faulty machine in 12 min and can walk to bus stop in remaing 20 minutes.

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kiran ks  (12 years ago)

ANS: 1/2

time to walk to bus stop=20min
time to check a machine=6min

As there are 4 machines and out of which 2 are faulty, so if he checks 2 machines it is 'not' enough. Because,
if,
1st 2 are faulty then OK
1st 2 are not faulty then it is OK because remaining 2 are faulty
1st one is faulty and 2nd one is not faulty then he has to check for 3rd one
1st one is not faulty and 2nd one is faulty then he has to check for 3rd one

so, the total number of cases = 4
and number of favorable cases = 2
hence, the probability of catching the bus = 2/4
= 1/2 (ANS)

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