NIMCET 2010 — Reasoning PYQ

• 30-day month: $30÷7$ gives a remainder of $2$ odd days.

• 31-day month: $31÷7$ gives a remainder of $3$ odd days.

• February: $0$ odd days (ordinary year) or $1$ odd day (leap year).

2. Checking the Options:

• Option (a) June to October:

  June ($2$) + July ($3$) + August ($3$) + September ($2$) = $10$ odd days.

  $10÷7=3$ remainder. (Incorrect)

• Option (b) April to November:

  April ($2$) + May ($3$) + June ($2$) + July ($3$) + August ($3$) + September ($2$) + October ($3$) = $18$ odd days.

  $18÷7=4$ remainder. (Incorrect)

• Option (c) April to July:

  April ($2$) + May ($3$) + June ($2$) = $7$ odd days.

  $7÷7=0$ remainder. (Correct)

  Since the total odd days are exactly $7$ (a multiple of $7$), April 1st and July 1st will fall on the same day of the week.

• Option (d) October to December:

  October ($3$) + November ($2$) = $5$ odd days.

  $5÷7=5$ remainder. (Incorrect)

Final Answer:

April and July have the same calendar in any given year.

The correct option is (c).