Question

Oliver has a box of toy cars, but he is not sure how many he has. If he arranges the cars in groups of
four, he has three left over. If he arranges them in groups of 3, he has two left over and there are
three left over when he puts them in groups of five. Oliver definitely doesn’t have any more than 30
cars, so how many does he have?

Answer 1

Given :- Oliver has a box of toy cars, but he is not sure how many he has. If he arranges the cars in groups off our, he has three left over. If he arranges them in groups of 3, he has two left over and there are three left over when he puts them in groups of five. Oliver definitely doesn’t have any more than 30 cars, so how many does he have ?

Answer :-

Let us assume that, oliver has total x toy cars .

so,

→ x = 4p + 3

→ x = 3q + 2

→ x = 5r + 3

or we can see that, we have to find the smallest number less than 30 which when divided by 4 ,3 and 5 gives remainder 3 , 2 and 3 respectively .

so, lets check with 5 first ,

• 8 ÷ 5 = 3 remainder .
• 8 ÷ 4 = 0 remainder .
• not correct .

next,

• 13 ÷ 5 = 3 remainder .
• and, 13 ÷ 4 = 1 remainder .
• not correct .

next ,

• 18 ÷ 5 = 3 remainder .
• and, 18 ÷ 4 = 2 remainder .
• not correct .

next ,

• 23 ÷ 5 = 3 remainder .
• 23 ÷ 4 = 3 remainder .
• also, 23 ÷ 3 = 2 remainder .
• All satisfy .

therefore, we can conclude that, 23 is the required number less than 30 .

Hence, Oliver has 23 number of toy cars .

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