CAT 2003 Slot 1 — QA Question 19
Answer the following question based on the information given below.
A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1, the south end point of OR to E2, the east endpoint of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and km/hr on all the chord roads.
A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals
Answer & solution
- A
31
- B
63
- C
75
91
Of the four given options 63 and 75 are multiples of 3. Their remainder cannot be 1.
∴ The last digit cannot be 1. Thus, 63 and 75 are eliminated.
For the options 31 and 91, the remainder is 1. Thus, the last digit is 1.
31 = (11111)2 = (1011)3 = (111)5
91 = (1011011)2 = (10101)3 = (331)5
91 has 1 as the first digit in only 2 of the notations.
Hence, option (d).