Logic problems for Grade 6

5 problems with worked solutions.

№ 1 · Logic · Grade 6

Find the smallest positive integer that leaves a remainder of 2 when divided by 5 and a remainder of 4 when divided by 7.

№ 2 · Logic · Grade 6

Two ribbons of 84 and 126 centimeters must be cut into equal pieces of the greatest possible length with no remainder. How long is each piece?

№ 3 · Logic · Grade 6

One beacon flashes every 18 seconds and another every 24 seconds. They flash together now. After how many seconds will they flash together again?

№ 4 · Logic · Grade 6

There are chickens and rabbits in a yard. Altogether there are 18 heads and 50 legs. How many rabbits are there?

№ 5 · Logic · Grade 6

There are three closed boxes labeled 'apples', 'pears', and 'apples and pears'. All three labels are wrong. How many fruits must be taken from one chosen box to determine all the contents?