Amcat Quatitative Ability Previous Paper 8

71.      Find the remainder when 2²¹ is divided by 6. A.        0          B.        1          c.         2          D.        3

72.      Which of the following numbers is the smallest number? A.        1/12   B.        1/6     C.        ¼         D.        1/3 Ans: (A) 

73.      A phone company offers 5 phone plan options: call waiting, call forwarding, voice mail, conferencing, and caller ID. A customer can   choose 3 options. The number of ways one can avail the plan options        is: A.        5          B.        10       C.        3          D.        20 Solution: 5c3 =10 is correct answer

74.      If log₃₂ x + log₃₂ (1/8) = 1/5, then the value of x is equal to: A.        8          B.        5          C.        16       D.        32 Solution: log _b x+ log _b y = log _b xy so log₃₂ x + log₃₂ (1/8) = 1/5 log ₃₂ x(1/8) = 1/5 x/8 = 32^1/5 x/8 = 2 x= 16

75.      Length and breadth of a rectangle are directly proportional. If length increases from 6 cm to 21 cm and if breadth now is 14 cm, then what    was the breadth before any change in length occurred?    
 A.        4 cm   B.        1.5 cm           C.        2 cm               D.        3 cm 

Solution:

since they are directly proportional

6/21=x/14

x=(14*6)/21=4

breadth=4cm..

76.      At an election there are 5 candidates among which 3 members are to be elected and a voter may vote for any number of candidates not greater than the number to be elected. Then the number of ways in     which a voter may vote are ? A.        25       B.        30       C.        32       D.        None of the above

Solution:

77.      One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is '9' of hearts. A.        1/13               B.        1/26               C.        1/52               D.        3/52

Solution:

78.      If 2^x * 3^y = 18 and 2^2x * 3^y =36, the value of x is A.        0          B.        1          C.        2          D.        3          E.         None of the above Solution: second equation can be written as, 2^x*2^x*3^y=36. substituting the first equation value, 2^x*18=36. 2^x=2^1; a^m=a^n, then m=n, so we get x=1

79.      An unbiased coin is tossed 5 times. If tail appears on first 4 tosses,        then probability of tail appearing on the fifth toss is:     A.        ½         B.        1          C.        0          D.        4/5

Solution: (A) Appearing tail on fifth toss is independent of first 4 tosses.

80.      In a single throw of dice, what is the probability to get a number greater than or equal to 4 A.        1/3                 B.        2/3                 C.        ½         D.        None of the above
Solution: Getting number greater than or equal to 4 means 4,5 and 6 are possibilities. Total case for a dice is 6. ans: 3/6 = 1/2