XAT 2011 — QA & DI Question 27
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 0030l6?
Answer & solution
2201
- B
2202
- C
2600
- D
2960
- E
None of the above options
Skipping the digit 5 converts the counting base system to 9 from 10.
Actual values of digits greater than 5 will change i.e. face value of 6 will be 5, 7 will be 6, and so on.
Hence, 3016 displayed by micromanometer is actually 3015 in base 9
Now, (3015)9 = 3 × 93 + 0 × 92 + 1 × 9 + 5 = 2201
Hence, option (a).