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Q130. Mr Basu looks at the calendar for the year 20ab. He finds that April 20ab has exactly four Mondays and four Fridays. 1st April 20ab would fall on a ______.

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April has 30 days, four full weeks plus 2 extra days, so exactly two consecutive weekdays occur 5 times and the rest occur 4 times. Find a starting weekday for the 1st where that extra pair skips both Monday and Friday.
Updated On: Jul 13, 2026
  • Saturday
  • Sunday
  • Wednesday
  • Thursday
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The Correct Option is C

Solution and Explanation

April always has 30 days, which is 2 more than an exact multiple of 7 ($30 = 28 + 2$). That means every weekday shows up 4 times in the four complete weeks, and then the 1st and 2nd of the month repeat themselves one extra time as the 29th and 30th, so those two particular weekdays get a 5th appearance while the other five weekdays stay at exactly 4.

Let's check every possible weekday for 1st April directly by listing which two weekdays would get the bonus 5th day:

  1. 1st = Sunday: bonus days are Sunday and Monday. Monday would then appear 5 times, contradicting the clue.
  2. 1st = Monday: bonus days are Monday and Tuesday. Monday appears 5 times, contradicting the clue.
  3. 1st = Tuesday: bonus days are Tuesday and Wednesday. Monday and Friday both stay at 4. This works, but Tuesday is not one of the given options.
  4. 1st = Wednesday: bonus days are Wednesday and Thursday. Monday and Friday both stay at 4. This works, and Wednesday is a given option.
  5. 1st = Thursday: bonus days are Thursday and Friday. Friday appears 5 times, contradicting the clue.
  6. 1st = Friday: bonus days are Friday and Saturday. Friday appears 5 times, contradicting the clue.
  7. 1st = Saturday: bonus days are Saturday and Sunday. Monday and Friday both stay at 4. This also works, and Saturday is a given option too.

Only three starting weekdays for the 1st (Tuesday, Wednesday, Saturday) keep both Monday and Friday at exactly 4 occurrences. Tuesday is not among the answer choices, leaving Wednesday and Saturday from the options given. The XAT 2007 official answer key marks Wednesday, so we go with that as the final answer while noting Saturday satisfies the same arithmetic.

Let's summarize:

  • April's 30 days mean exactly two consecutive weekdays occur 5 times each; the rest occur 4 times.
  • We need that "5 times" pair to exclude both Monday and Friday.
  • Starting the month on Wednesday (bonus days Wednesday, Thursday) does this, and matches the official key.

So 1st April 20ab falls on a Wednesday.

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