XAT 2018 — QA & DI Question 17
David has an interesting habit of spending money. He spends exactly £X on the Xth day of a month. For example, he spends exactly £5 on the 5th of any month. On a few days in a year, David noticed that his cumulative spending during the last 'four consecutive days' can be expressed as 2N where N is a natural number. What can be the possible value(s) of N?
Answer & solution
- A
5
6
- C
7
- D
8
- E
N can have more than one value
Sum of any four consecutive numbers = x + x + 1 + x + 2 + x + 3 = 4x + 3.
This sum is never divisible by 4. But 2N is always divisible by 4 (for N ≥ 2).
∴ The four consecutive days do not fall in the same month. Let’s look at the various possibilities.
Now, there are 4 possibilities for number of days in a month.
The only possibility for cumulative spending during the last 'four consecutive days' to be expressed as 2N = 64 = 26.
∴ N = 6
Hence, option (b).