Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 4

Which of the following numbers is 3 more than a multiple of 6? Circle your answer. [A] 57 [B] 50 [C] 59 [D] 53

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Video Transcript

Which of the following numbers is three more than a multiple of six? Circle your answer. 57, 50, 59, or 53.

The number we’re looking for we could call it 𝑛. 𝑛 is equal to three more. So we’ll be adding three to a multiple of six. And we can represent a multiple of six by saying six times 𝑥. To find out which of these four numbers fit the requirement, we’ll need to subtract three from all of them. And we get 54, 47, 56, and 50. And now, we ask of these four values which of them are a multiple of six. Can we divide any of these values by six and end up with an integer?

If you recognise that 54 equals six times nine, then we know that 54 is a multiple of six. If 54 is a multiple of six, that means 57 is three more than a multiple of six. 57 is three more than a multiple of six. To check the other numbers, let’s use a different method. Let’s write out the multiples of six. Six times one is six, six times two is 12, six times three is 18, six times four is 24, next is 30, then 36, 42, 48, 54, and 60. And it keeps going.

This shows us that 47, 56, and 50 are not multiples of six. 54 is a multiple of six. And when you add three, you get 57, which confirms our choice.

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