Question:
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 ______.
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 ______.
Show Hint
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
Step 1: Work out how many times each weekday appears in April.
April has 30 days. Since \( 30 = 4 \times 7 + 2 \), April is exactly four full weeks plus 2 extra days. Every weekday appears at least 4 times in those four full weeks, and the 2 extra days (the 29th and 30th) add one more occurrence to whichever two weekdays they fall on. So exactly 2 weekdays occur 5 times in the month, and the other 5 weekdays occur only 4 times.
Step 2: Use the "4 Mondays and 4 Fridays" clue.
We are told both Monday and Friday occur only 4 times, not 5. That means Monday and Friday must both be outside the pair of weekdays that gets the extra 5th occurrence. Since the 29th falls on the same weekday as the 1st, and the 30th falls on the same weekday as the 2nd, the two "extra" weekdays are always the weekday of the 1st and the very next weekday after it. So we need a pair of two consecutive weekdays that includes neither Monday nor Friday.
Step 3: Test each possible starting weekday for the 1st.
If the 1st is Sunday, the pair is Sunday-Monday, which includes Monday, ruled out.
If the 1st is Monday, the pair is Monday-Tuesday, includes Monday, ruled out.
If the 1st is Tuesday, the pair is Tuesday-Wednesday, includes neither Monday nor Friday, allowed.
If the 1st is Wednesday, the pair is Wednesday-Thursday, includes neither Monday nor Friday, allowed.
If the 1st is Thursday, the pair is Thursday-Friday, includes Friday, ruled out.
If the 1st is Friday, the pair is Friday-Saturday, includes Friday, ruled out.
If the 1st is Saturday, the pair is Saturday-Sunday, includes neither Monday nor Friday, allowed.
Step 4: Match against the given options.
The options offered are Saturday, Sunday, Wednesday and Thursday. Of these, Saturday and Wednesday both satisfy "four Mondays and four Fridays" by our test above; Sunday and Thursday do not. Among the two valid choices, the XAT 2007 answer key marks Wednesday as the intended answer. We flag that Saturday also passes the same test, as a matter of completeness.
Final Answer:
If 1st April falls on a Wednesday, the extra 5th occurrence lands on Wednesday and Thursday, leaving Monday and Friday at exactly 4 occurrences each, matching the clue. \[ \boxed{\text{Wednesday}} \]
April has 30 days. Since \( 30 = 4 \times 7 + 2 \), April is exactly four full weeks plus 2 extra days. Every weekday appears at least 4 times in those four full weeks, and the 2 extra days (the 29th and 30th) add one more occurrence to whichever two weekdays they fall on. So exactly 2 weekdays occur 5 times in the month, and the other 5 weekdays occur only 4 times.
Step 2: Use the "4 Mondays and 4 Fridays" clue.
We are told both Monday and Friday occur only 4 times, not 5. That means Monday and Friday must both be outside the pair of weekdays that gets the extra 5th occurrence. Since the 29th falls on the same weekday as the 1st, and the 30th falls on the same weekday as the 2nd, the two "extra" weekdays are always the weekday of the 1st and the very next weekday after it. So we need a pair of two consecutive weekdays that includes neither Monday nor Friday.
Step 3: Test each possible starting weekday for the 1st.
If the 1st is Sunday, the pair is Sunday-Monday, which includes Monday, ruled out.
If the 1st is Monday, the pair is Monday-Tuesday, includes Monday, ruled out.
If the 1st is Tuesday, the pair is Tuesday-Wednesday, includes neither Monday nor Friday, allowed.
If the 1st is Wednesday, the pair is Wednesday-Thursday, includes neither Monday nor Friday, allowed.
If the 1st is Thursday, the pair is Thursday-Friday, includes Friday, ruled out.
If the 1st is Friday, the pair is Friday-Saturday, includes Friday, ruled out.
If the 1st is Saturday, the pair is Saturday-Sunday, includes neither Monday nor Friday, allowed.
Step 4: Match against the given options.
The options offered are Saturday, Sunday, Wednesday and Thursday. Of these, Saturday and Wednesday both satisfy "four Mondays and four Fridays" by our test above; Sunday and Thursday do not. Among the two valid choices, the XAT 2007 answer key marks Wednesday as the intended answer. We flag that Saturday also passes the same test, as a matter of completeness.
Final Answer:
If 1st April falls on a Wednesday, the extra 5th occurrence lands on Wednesday and Thursday, leaving Monday and Friday at exactly 4 occurrences each, matching the clue. \[ \boxed{\text{Wednesday}} \]
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