Probability, Permutation Combination : Test 005

1. 

    A shop sells two kinds of rolls-egg roll and mutton roll. Onion, tomato, carrot, chilli sauce and tomatosauce are the additional ingredients. You can have any combination of additional ingredients, or have standard rolls without any additional ingredients subject to the following constraints:

(a)    You can have tomato sauce if you have an egg roll, but not if you have a mutton roll.

(b)   If you have onion or tomato or both you can have chilli sauce, but not otherwise.

How many different rolls can be ordered according to these rules?

a) 21          b)         33        c)         40        d)         42        e)         None of the above

2.   

          A student wants to make up a schedule for a 7-day period during which she will study one subject each day. She is taking four subjects: mathematics, physics, chemistry and economics. The total number of different schedules is 4⁷. The number of schedules that devote at least one day to each subject is

a)      8400                      b)   8404             c)   8748          d)   None of the above

1308: Number System - Remainder - CAT 2000

The integers 34041 and 32506, when divided by a three-digit integer n, leave the same remainder.
What is the value of n?

a. 289          b. 367         c. 453     d. 307
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Let r be the remainder. Then 34041 – r and 32506 – r are perfectly divisible by n.
Hence, their difference should also be divisible by the same.
(34041 – r) – (32506 – r) = 1535, which is divisible by only 307.
Answer : D