Question
The $2^{\text{nd}}$ of June is a Thursday in a certain year. Which day of the week is the $3^{\text{rd}}$ of July in that year?
The correct answer is
Sunday
Day of Week Calculation: June to July
The question asks for the day of the week for July 3rd, given that June 2nd is a Thursday in the same year.
Calculating Total Days
First, determine the number of days between June 2nd and July 3rd.
- Days remaining in June: June has 30 days. So, $30 - 2 = 28$ days.
- Days in July until the target date: 3 days (July 1st, 2nd, 3rd).
- Total number of days = Days remaining in June + Days in July = $28 + 3 = 31$ days.
Determining the Day Shift
To find the day of the week, calculate the number of full weeks and remaining days in the total period.
- Divide the total days by 7 (days in a week): $31 \div 7$.
- The result is 4 weeks with a remainder of 3 days ($31 = 4 \times 7 + 3$).
Finding the Final Day
The remainder of 3 days indicates how many days the week shifts forward from the starting day (Thursday).
- Starting day: Thursday.
- Add the remainder days: Thursday + 3 days = Sunday.
Therefore, July 3rd is a Sunday.
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Important Questions from Numerical Reasoning
- $P, Q, R, S, X$, and $Y$ are distinct single-digit whole numbers taking values from 0 to 9.
$PQ$ is a two-digit number with $Q$ being in the units place and $P$ in the tens place. Similarly, $RS$ is a two-digit number.
It is known that $PQ$ and $RS$ are consecutive numbers and
$(PQ)^2 + (RS)^2 = XYP$, with $XYP$ being a three-digit number.
The value of $Y$ is __________ - Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$?
If $\oplus \div \odot = 2$, $\oplus \div \triangle = 3$, $\odot + \triangle = 5$, and $\Delta \times \otimes = 10$,
then the value of $(\otimes - \oplus)^2$ is:- The remainder when $98!$ is divided by $101$ is equal to ________
- A 'frabjous' number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?
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