Video: KS2-M17 • Paper 3 • Question 19

Dev thinks of a whole number. He multiplies it by 4. He rounds his answer to the nearest 10. The result is 50. Write all the possible numbers Dev could have started with.

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Video Transcript

Dev thinks of a whole number. He multiplies it by four. He rounds his answer to the nearest 10. The result is 50. Write all the possible numbers Dev could have started with.

We know that Dev starts with a whole number and multiplies it by four. So we know this answer is a multiple of four. We also know that he rounds this answer to the nearest 10 and the result is 50. So we need to work out what number or what numbers we could multiply by four and round to the nearest 10 to get a result of 50.

We know that 10 times four is 40 and 11 times four is 44. But these numbers are both less than 45. If we were to round 44 to the nearest 10, the result would be 40. So we know that 10 and 11 are not the numbers that Dev started with.

Let’s try 12 multiplied by four. 12 times four is 48. And if we round 48 to the nearest 10, the result is 50. So 12 is one of the possible numbers that Dev could have started with. 13 times four is 52. And if we round 52 to the nearest 10, the result is also 50. So 13 is also a possible number that Dev could have started with. 14 times four is 56. If we round 56 to the nearest 10, the result is 60. This means there are no more possible numbers that Dev could have started with.

12 and 13 are the possible numbers that Dev could have started with. If we multiply 12 by four, the result is 48. And then if we round 48 to the nearest 10, the result is 50. 13 times four is 52. 52 rounded to the nearest 10 is 50. The possible numbers are 12 and 13.