Basic Numeracy/Quantitative Aptitude

Detailed Solution

53. d: The total number N of different ways that someone can go from city A to city C, passing by city B is N = 3 * 2 = 6

54. d: The total number N of different ways that this man can wear one of his suits, one of his shirts and a pair of his shoes is N = 3 * 4 * 5 = 60

55. d: In the diagram below, any of the 5 digits of the number to be formed can be any of the 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Hence the 10 choices for each digit of the number to be formed since repetition of the digits from 0 to 9 is allowed. When repetition is allowed, the total number N of ID cards is given by the total numbers of 5 digit numbers that can formed and is given by:

56. In the diagram below, the first digit of the number to be formed can be any of the 10 digits, hence the 10 choices. The second digit can be any of the 10 digits except the digit used in position 1 since no repetition of the digits is allowed, hence the 9 choices. The third digit can be any of the 10 digits excepts the two already used in positions 1 and 2 since repetition is not allowed, hence the 8 choices and so on.

The number N of ID cards is given by
N = 10 * 9 * 8 * 7 * 6 = 30,240

57. d: 26 (all letters in the alphabet) choices are possible for each of the 3 letters to be used to form the licence number. 10 choices (0,1,2,3,4,5,6,7,8,9) are possible for each of the 4 digits. The total number of license numbers is given by N = 26 * 26 * 26 * 10 * 10 * 10 * 10 = 175,760,000

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