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06 Mar 2017, 01:37
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (01:54) correct
27%
(02:07)
wrong
based on 400
sessions
History
Date
Time
Result
Not Attempted Yet
Warren has five vehicles: a blue convertible, a black sedan, a red coupe, a silver station wagon, and a blue SUV. If he drives a different car to work each day from Monday through Friday, in how many orders could he drive his five cars during a week if he always drives the convertible on Friday and won’t drive the same color vehicle on consecutive days?
A. 6
B. 18
C. 24
D. 120
E. 144
A. 6
B. 18
C. 24
D. 120
E. 144
06 Mar 2017, 02:53
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Restrictions:
1. He always drives the convertible on Friday
2. Won’t drive the same color vehicle on consecutive days -> He will not drive the blue SUV on Thursday, as on Friday he always drives the Blue Convertible.
Based on the above restrictions, below are the options what he can drive on each day.
Friday - Blue Convertible
Thursday - Black sedan/Red coupe/Silver station wagon
Wednesday - Black sedan/Red coupe/Silver station wagon/Blue SUV
Tuesday - Black sedan/Red coupe/Silver station wagon/Blue SUV
Monday- Black sedan/Red coupe/Silver station wagon/Blue SUV
Therefore to calculate the order =
Friday - he can select only 1
Thursday - he can select only 3
Wednesday - he can select any vehicle out of the remaining 3
Tuesday - he can select any vehicle out of the remaining 2
Monday - he can select only the 1 remaining vehicle
Total ways - 1 * 3 *3 *2 * 1 = 18
Answer is B. 18
1. He always drives the convertible on Friday
2. Won’t drive the same color vehicle on consecutive days -> He will not drive the blue SUV on Thursday, as on Friday he always drives the Blue Convertible.
Based on the above restrictions, below are the options what he can drive on each day.
Friday - Blue Convertible
Thursday - Black sedan/Red coupe/Silver station wagon
Wednesday - Black sedan/Red coupe/Silver station wagon/Blue SUV
Tuesday - Black sedan/Red coupe/Silver station wagon/Blue SUV
Monday- Black sedan/Red coupe/Silver station wagon/Blue SUV
Therefore to calculate the order =
Friday - he can select only 1
Thursday - he can select only 3
Wednesday - he can select any vehicle out of the remaining 3
Tuesday - he can select any vehicle out of the remaining 2
Monday - he can select only the 1 remaining vehicle
Total ways - 1 * 3 *3 *2 * 1 = 18
Answer is B. 18
General Discussion
06 Mar 2017, 22:11
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Bunuel
I - a blue convertible, II - a black sedan, III - a red coupe, IV - a silver station wagon, V - a blue SUV
I*1 the convertible can come only in one order on Friday and its place is fixed during the week.
V*3 there are three different places/days in a week the blue SUV can come and its place is also fixed in one of those three orders/days.
II*3 After fixing places for the convertible and the SUV, there are three different days/orders remaining for the next car - in my case for the black sedan.
III*2 After fixing places for the above three cars, there are two different days/orders remaining for the next car - in my case for the red coupe.
IV*1 After fixing places for the above four cars, there is only one day/order remaining for the last car - in my case for the silver station wagon.
Altogether 1*3*3*2*1=18 different ways that Warren can drive his cars under the given requirements.
Answer B.
