Video: GCSE Mathematics Foundation Tier Pack 5 • Paper 2 • Question 3

GCSE Mathematics Foundation Tier Pack 5 • Paper 2 • Question 3

04:05

Video Transcript

Five digits are shown in the grid below: seven, two, nine, five, three. Part a) Write down the largest three-digit number that can be made by arranging three of these digits without repeating any digit. Part b) Write down the closest number to 3000 that can be made by arranging four of these digits without repeating any digit.

So the first thing I’m gonna do before I answer any of the parts of this question, so a) or b), is rearrange our numbers or our digits from smallest to largest. So the smallest digit is two. Then we have three, then five, then seven, and finally the digit nine.

Okay, so now let’s look at part a). What we want to do is write down the largest three-digit number that can be made by arranging three of these digits without repeating any digit. So to enable us to do this, what I want to do is use the three largest digits. So we’ve got five, seven, and nine. And then what I want to do is rearrange these three digits to have the largest digit first and the smallest digit of of these three last. And when we do that, we’re gonna have nine in the hundreds place value, seven in the tens place value, and five in the ones place value or units place value. So therefore, the largest three-digit number that we can make by arranging three of these digits without repeating any is 975.

So now what we want to do is answer part b). And for part b), we need to write down the closest number to 3000 that could be made by arranging four of the digits without repeating any digit. So what we want to do, because we want to get the number that’s closest to 3000, is write down the greatest number we can write down that is in the 2000s and the smallest that is in the 3000s. And then we want to compare them to see which is actually closer to 3000 itself.

So I’m gonna start with the largest number in the 2000s. So we’re gonna start with the number two. And then we’re gonna select the three largest digits. And then again, as we did in part a), we’re gonna arrange them from the largest digit to the smallest digit. And when we do that, we’re gonna get 2975. And then what we can see is how close this is to 3000. Well, we can see that we’d have to add 25 to 2975 to get to 3000. And we can work that out by counting up, because to go from 2975, if you add five, you get to 2980, then add 20 we get to 3000.

So now what we want to do is list the smallest number in the 3000s. So first of all, we’re gonna start with three. And then what we want are the next three smallest digits, because we want it to be the lowest number in the 3000s. And those three digits are two, five, and seven. And this time, we’re gonna put the digits in order from smallest to largest, because we want to make the smallest number that’s in the 3000s. So when we do that, we get 3275 [3257]. So again, what we do is we compare it to the 3000. And we can see that we’d have to add 257 to 3000 to get to 3257.

Well, if we now compare the differences, we can see that 25 is less than 257. So therefore, the closest number to 3000 that could be made by arranging four of the digits without repeating any digit is 2975.

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