CAT 2003 Slot 1 — QA Question 18
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.
How many even integers n, where 100 ≤ n ≤ 200, are divisible neither by seven nor by nine?
Answer & solution
- A
40
- B
37
39
- D
38
Number of even integers satisfying inequality i.e. 100 ≤ n ≤ 200 = 51
Total even integers divisible by 7 = 112, 126, 140, 154, 168, 182, 196 = 7
Total even integers divisible by 9 = 108, 126, 144, 162, 180, 198 = 6
The number 126 is repeated in both the sets.
∴ Total number of positive even numbers between 100 and 200 which are either divisible by 7 or 9 = 7 + 6 − 1 = 12
∴ Total number of positive even numbers between 100 and 200 which are divisible neither by 7 nor by 9 = 51 − 12 = 39
Hence, option (c).