A number gives a remainder of 1 when divided by 2, 3 or 6, and a remainder of 4 when divided by 5. If this number is divisible by 7, find the smallest such whole number.
Rohit can go home on Diwali, which falls on Thursday, 12 November in the year described. Diwali is 45 days later. What day is today? Treat these as the calendar facts of the original question; “this year” does not mean the 2027 edition year.
Some chocolates weigh 1120 grams. After 13 are removed, the remaining chocolates weigh 600 grams. How many were there at first? Assume every chocolate has the same weight.
Sixty potatoes weigh 4 kg. Potatoes cost 30 dollars per kilogram. What is the price, in dollars, of two dozen potatoes? Assume all the potatoes have equal weight.
Brian takes a day off from work every 4th day and David takes a day off on every 5th day. If they have a day off today and their next day off falls on a Monday, what day is today?
**Editorial note:** Interpret “their next day off” as their next shared day off after today. Today is day 0; Brian’s future days off are 4, 8, 12, … and David’s are 5, 10, 15, … days later. Choose one option.
A prime number is a whole number with exactly two positive factors: 1 and itself. For example, 2 and 7 are prime numbers. Two prime numbers sum to 55. Find their product.
There are 5 pairs of different colours of socks in a drawer. What is the least number of socks Jeena must take out without looking to be sure that she has a pair of the same colour?
If the cells are added in the same pattern, which row will have the number 25?
**Editorial note:** Keep the printed fifth row exactly as shown. For this exercise, continue after 35 with 34, 33, 32, …, and put one more cell in each new row. Count the top row as row 1. Choose one option.
The letters a a b b b c c d repeat in this order: a a b b b c c d a a b b b c c d … . How many b’s appear before the 1000th letter? “Before” excludes the 1000th position.
