Consecutive Day Sums as Powers of 2
XAT 2018 · Quantitative Ability & Data Interpretation · Hard · Quantitative Aptitude
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 where N is a natural number. What can be the possible value(s) of N?
- A.
5
- B.
6
- C.
7
- D.
8
- E.
N can have more than one value
Answer
B
Explanation
Sum of 4 consecutive days in same month = . Setting :
- (not integer).
- (not integer, but across two month boundaries: e.g., 30th, 31st, 1st, 2nd gives ). This occurs in 6 months of a year. Thus is uniquely possible.
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