5th and 6th Grade, March, 2019

B.1241. There are three different kinds of chocolate you can buy in the candy store around the corner. If you buy a bar of chocolate with peanuts and a bar of chocolate with almond you pay \$3.50. If you buy 4 bars of chocolate with peanuts, 4 bars of chocolate with almond and 3 bars of chocolate with berries, you pay \$18.50. How much does a bar of chocolate with berries cost?

B.1242. Peter’s mom sent him to the store and told him what to buy: milk, seltzer, bread, eggs, and donuts. By the time Peter got to the store he could remember only that he had to buy 1 liter, 6 pieces, a half a kilogram, 10 pieces and 3 liters of the items, but he could not remember which amount belonged to which item. He received \$7.00 from his mom, so he knew it should be enough money to buy everything he had to. He saw in the store that 1 liter of milk costs \$2.00, 1 liter of seltzer costs 59 cents, 1 piece of donut costs 12 cents, 1 egg costs 20 cents, and 1 kg of bread costs \$1.50. How much or how many did Peter have to buy from each item?

B.1243. What is the greatest number of 4 cm x 6 cm cards that can be cut out of a 20 cm x 32 cm sheet of paper? Describe how it can be done.

B.1244. For some numbers the sum of the digits is 2019. How many digits does the smallest such number have?

B.1245. An energy efficient light bulb costs \$18.00. It works for 10,000 hours, and the electricity it uses up every hour costs 0.8 cents. A regular light bulb with the same brightness costs \$0.40. It works for 1,000 hours and the electricity it uses up every hour costs 3.4 cents. How much money do you save during the lifespan of an energy efficient light bulb?

B.1246. What is the largest prime such that the sum of its digits is greater than the number of primes up to it?

B.1247. What is the greatest 2-digit number that can be written as the sum of 2 different primes in 7 different ways?

B.1248. In an increasing order we wrote down all those 3-digit numbers whose digits are not all different.

a) Where in this order is 133?

b) What is the 28th such number?