Sutton SET Mathematics Mock Paper 1

D

Break the number into its columns starting from the right: 2 units, 9 tens, 5 hundreds, 7 thousands, 0 ten thousands and 4 hundred thousands.

The digit in the hundreds column is therefore 5.

The tempting answer is 7, which is one column too far to the left and belongs to the thousands. Counting the columns from the right every time is what stops that.

The 9 is in the tens column, and the 0 is worth nothing on its own, although it is holding the ten thousands column open, which is why it cannot be left out of the number.

B

Multiplication is done before addition and subtraction, so deal with 5 x 4 = 20 first.

The calculation now reads 7 + 20 - 3, which is 27 - 3 = 24.

Even before you start you can see that the answer must be somewhere near 20, because the multiplication is the biggest part of it. That rules out 45 and 48 at a glance.

Both of those come from working left to right: 7 + 5 = 12, then 12 x 4 = 48, then 48 - 3 = 45. The answer 12 comes from doing the subtraction first, and 27 from forgetting to take the 3 away at the end.

B

Divide by the bottom number first: 64 divided by 8 = 8, so one eighth is 8 conkers.

Three eighths is three of those: 3 x 8 = 24 conkers.

Three eighths is less than a half, so the answer has to be smaller than 32. That one thought rules out 32, 40 and 192 before any working at all.

40 is the five eighths she keeps rather than the part she hands over, 8 is one eighth left on its own, and 192 comes from multiplying by 8 instead of dividing by it.

E

There are 1000 millilitres in 1 litre, so multiply by 1000: 2.4 x 1000 = 2400 millilitres.

A millilitre is a far smaller unit than a litre, so the number in front of it must be far bigger than 2.4. That single thought rules out every option except 2400, without any multiplying at all.

24 comes from multiplying by 10 and 240 from multiplying by 100, so both stop short of the full thousand.

0.24 divides by 10 instead of multiplying, and 2.4 keeps the number exactly as it was and simply writes a new unit after it. That last one is the slip to watch for, because changing the unit always changes the number.

A

The angles in a triangle add up to 180 degrees, so the two equal angles share whatever is left once the 110 degrees is taken off: 180 - 110 = 70 degrees.

That 70 degrees is split evenly between the two of them, so each one is 70 divided by 2 = 35 degrees. Check by adding all three: 110 + 35 + 35 = 180 degrees.

A sense check clears two options away first. Each equal angle has to be well under 110 degrees, or the three together would come to more than 180, so 110 and 250 degrees are impossible.

70 degrees is the trap. It is what the two equal angles come to together, not what each one measures, so it is the working stopped one step early.

55 degrees halves the 110 instead of halving what is left over, 110 degrees simply repeats the angle you were given, and 250 degrees works from 360 degrees rather than 180.

E

A ratio of 1 to 4 means 4 parts of water for every 1 part of squash.

One part is the 250 ml of squash, so the water is 4 x 250 = 1000 ml.

Four options disappear before any arithmetic. There must be more water than squash, so the answer has to be bigger than 250 ml, and only one option is.

250 ml is the amount of squash rather than the amount of water, and 62.5 ml comes from dividing by 4 instead of multiplying, which turns the ratio the wrong way round.

50 ml shares the squash into 5, and 200 ml treats the 250 ml as the whole drink and takes four fifths of it.

B

Add the four numbers: 14 + 9 = 23 and 21 + 16 = 37, so the total is 60 lengths.

The mean shares that total between the four swimmers: 60 divided by 4 = 15.

A mean always lands somewhere between the smallest value and the largest, so it has to be between 9 and 21. That rules out 30 and 60 on sight.

60 is the total rather than the mean, which is the easiest mark to throw away here. 12 comes from dividing by 5 and 20 from dividing by 3.

C

Both points have a y coordinate of 5, so the line from P to Q is flat and M must have a y coordinate of 5 as well.

For the x coordinate, find the number halfway between 2 and 8. The gap is 6, so halfway is 3 squares along from 2, which is 5.

M is at (5, 5).

(3, 5) is the trap. It works out correctly that M is 3 squares along from P, and then writes that 3 down instead of counting those 3 squares on from 2.

(5, 10) and (10, 10) add the coordinates together rather than finding the middle of them, and (5, 2.5) halves the y coordinate even though it never changes.

B

To round to the nearest hundred, see how many whole hundreds there are and what is left over. This is 67 hundreds with 48 left over.

48 is less than 50, so it does not reach the next hundred. The answer stays at 67 hundreds, which is 6700.

A number rounded to the nearest hundred always ends in two zeros, so 6750 is not even a possible answer. It is this number rounded to the nearest ten instead.

6800 rounds up because 48 feels close to 50, but close is not the same as past halfway. 6000 and 7000 round to the nearest thousand rather than the nearest hundred.

E

Split the 15 into 10 and 5. Ten crates hold 24 x 10 = 240 satsumas, and five crates hold half of that, which is 120.

Add the two parts: 240 + 120 = 360 satsumas.

The last digit helps too. Since 4 x 5 = 20, the answer has to end in a zero, so 288 can go without a single multiplication.

120 and 240 are the two halves of the working left unfinished, five crates and ten crates, and 288 is 12 crates rather than 15.

300 comes from rounding 24 down to 20 and then forgetting to put the extra 4 satsumas per crate back in.

B

Multiply the top and the bottom by the same number and the value does not change. Times 3 turns three fifths into 9/15.

There is a faster way in. Three fifths is 0.6, which is more than a half, and 6/15, 12/25 and 30/100 are all less than a half, so none of them can be right and none of them needs testing properly.

6/15 multiplies the bottom by 3 but doubles the top instead of trebling it, which is the mistake to watch for.

12/25 multiplies the top by 4 and the bottom by 5, 15/20 is three quarters and 30/100 is three tenths.

C

One hour is 60 minutes, so three hours is 3 x 60 = 180 minutes.

Half an hour is 30 minutes, so the total is 180 + 30 = 210 minutes.

You can fence the answer in first. It must be more than 180, which is three hours, and less than 240, which is four hours. Only 190 and 210 are left, and 190 is wrong because half an hour is 30 minutes, not 10.

350 comes from treating an hour as 100 minutes and working out 3.5 x 100.

E

Parallel sides run in the same direction and stay the same distance apart, so they would never meet however far you carried them on.

A trapezium has one pair of sides that are parallel and one pair that are not, so it is the only shape here that fits.

A rhombus, a parallelogram and a square all have two pairs of parallel sides, so they have too many rather than the right number, and a kite has none at all.

The tempting answer is the parallelogram, because the word parallel is sitting inside its name. The name tells you that its sides are parallel, but not how many pairs there are.

E

Ten per cent of 240 is 24, because finding a tenth means dividing by 10. Five per cent is half of that, which is 12.

15 per cent is 10 per cent plus 5 per cent: 24 + 12 = 36 members.

15 per cent is more than a tenth of the club, and a tenth is 24, so the answer has to be bigger than 24. Every other option fails that test.

24 is 10 per cent and 12 is 5 per cent, so both are the working left unfinished, and 3.6 is 1 per cent.

15 is the trap for a reader in a hurry. It is a number printed in the question, but it is a percentage, not a number of members.

D

Divide first. Eight twenties are 160, leaving 22, which is another 2 boxes with 6 pencils spare. So 182 divided by 8 is 22 remainder 6.

Twenty-two boxes hold only 176 pencils, so those last 6 pencils need a box of their own. That makes 23 boxes.

22.75 cannot be the answer whatever the arithmetic says, because nobody can fill three quarters of a box. Spotting that a remainder question needs a whole number is half the work.

22 is the real trap. It is the number of full boxes, and it leaves 6 pencils sitting on the table.

C

Start at -6 on a number line and count 9 steps to the right. Six of those steps bring you up to 0, and the other three carry on to 3.

The temperature at noon is 3 degrees Celsius.

A rise of 9 from -6 has to take you past zero, so the answer must be a small positive number. Both negative options go straight away, and 15 would need a rise of 21 degrees.

-15 adds the two numbers as though the temperature had fallen, -3 works out 6 - 9 the wrong way round, and 9 forgets where the temperature started.

A

Add the three clubs you are told about: 18 + 12 = 30, and 30 + 14 = 44 pupils.

Take that away from the whole year group: 60 - 44 = 16 pupils chose athletics.

44 is the total of the three clubs rather than what is left over, so it is the answer you reach by stopping one step early.

28 leaves netball out of the adding and 30 leaves swimming out, so both come from using only two of the three figures, and 46 takes away only the 14.

D

Work out one person first: 300 divided by 4 = 75 g each.

Then ten people need 10 x 75 = 750 g.

Ten people is more than twice as many as four, so the answer must be more than twice 300 g. Only 750 g and 3000 g get past that.

300 g is the amount printed in the question, used for ten people without any scaling at all, and 600 g is the amount for 8 people.

3000 g multiplies by 10 without ever dividing by 4, and 75 g is one person's share left on its own.

A

The three angles inside any triangle add up to 180 degrees.

Add the two you are given: 47 + 68 = 115 degrees.

Take that from the total: 180 - 115 = 65 degrees.

Here is the quick way to shorten the list. Angle B alone takes 68 degrees, so the other two angles have only 112 degrees left to share between them, and angle C must be smaller than that. Every option except 65 degrees is impossible.

115 degrees is the two given angles added together, 112 and 133 degrees each use only one of them, and 245 degrees works from 360 degrees instead of 180.

E

Fractions can only be added once the pieces are the same size. Sixths suit both: one half is 3/6 and one third is 2/6.

Now add the top numbers and keep the bottom the same: 3/6 + 2/6 = 5/6 of the pizza.

One check kills four options at once. The answer must be more than one half, because Jonah ate a half on his own, and 1/6, 2/5, 2/6 and 5/12 are all smaller than a half.

2/5 adds the tops and the bottoms together, which is the classic error. 5/12 changes the fractions correctly and then adds the bottoms as well, 2/6 keeps the tops as 1 and 1 without changing them, and 1/6 multiplies instead of adding.

E

A number in both times tables has to be a multiple of 12, because 12 is the smallest number that both 4 and 6 divide into. The numbers that work are 12, 24, 36, 48 and so on.

36 is 4 x 9 and also 6 x 6, so it is the one.

You can sieve the list rather than test it. A multiple of 6 must be even, and its digits must add up to a multiple of 3. Both 16 and 26 fail that digit test, since 1 + 6 = 7 and 2 + 6 = 8.

That leaves 18, 30 and 36, which are all multiples of 6, and only 36 also divides exactly by 4. 18 and 30 are the tempting ones for exactly that reason: passing half the test is not passing it.

C

Change the measurements into metres first. There are 100 cm in a metre, so 180 cm is 1.8 m and 120 cm is 1.2 m.

The perimeter is all four sides added together: 1.8 + 1.2 + 1.8 + 1.2 = 6 m.

Picture the rug before choosing. It is not much longer than you are tall, so 60 m or 600 m describes a running track rather than a rug. Those two come from dividing by 10, or from not converting at all.

3 m adds one length and one width only, which is half of the perimeter, and 2.16 m is the area of the rug in square metres, which is a different measurement altogether.

A

Brackets always come first: 4 + 2 = 6.

That leaves 48 divided by 6 x 3. Dividing and multiplying rank equally, so work along from the left: 48 divided by 6 = 8, then 8 x 3 = 24.

Every wrong option here is bigger than the right one, and that is a clue in itself. Dividing by the whole bracket cuts 48 right down before anything else happens, so a large answer means the bracket was not used properly.

36 drops the 2 out of the bracket and works out 48 divided by 4, then times 3, and 72 divides by the 2 only and forgets the 4.

144 loses the division and simply works out 48 x 3, and 288 multiplies by the bracket instead of dividing by it.

E

A reflection in the vertical axis flips the shape from side to side. Left becomes right and right becomes left, but nothing moves up or down.

So the second number stays at 2 and the first changes from 3 to -3, giving (-3, 2).

(3, -2) is the answer to a reflection in the horizontal axis instead, and that mix-up is the commonest one on this topic.

(-3, -2) reflects in both axes at once, which is a half turn rather than a flip.

(-2, 3) and (2, 3) swap the two numbers over. Read a coordinate pair as along the corridor first, then up the stairs.

B

25 per cent is one quarter, and a quarter of 40 pounds is 10 pounds.

That 10 pounds comes off the price: 40 - 10 = 30 pounds.

Taking a quarter off leaves you paying three quarters, so the answer has to be under 40 pounds but comfortably over half of it. 10 pounds and 50 pounds both fail that.

10 pounds is the money saved rather than the money handed over, and that is the trap here.

32 pounds takes off 20 per cent instead of 25, 39.75 pounds takes off 25 pence by confusing per cent with pence, and 50 pounds adds the quarter on instead of taking it off.

A

The mode is the value that turns up most often. Count them: 9 appears three times and every other temperature appears once, so the mode is 9 degrees.

11 degrees is the median, the middle value once the readings are put in order, and 11.3 degrees is the mean, rounded to one decimal place. Those two averages are the ones most often muddled with the mode.

15 degrees is simply the highest reading and 12 degrees is the first one written down.

Learn the word itself: mode means most often. You find it by counting how many times each value appears, not by calculating anything.

E

There are 2 + 3 = 5 shares altogether, so one share is 45 divided by 5 = 9 stickers.

Martha takes 3 of those shares: 3 x 9 = 27 stickers.

There is a one-line check that finishes the question. Martha has the bigger share, so she must have more than half of 45, which is more than 22.5. Only 27 clears that bar, and you can mark it without finishing the arithmetic.

18 is Ravi's share, so it is the right number handed to the wrong person, and it is what you get by using the ratio the wrong way round. 9 is a single share and 15 is 45 divided by 3.

C

The units have to match before anything is added. There are 1000 g in a kilogram, so 850 g is 0.85 kg.

Now add them: 2.4 + 0.85 = 3.25 kg.

Rough size does most of the work here. The total must be more than 2.4 kg and clearly less than 4 kg, so 1.55 kg, 10.9 kg and 852.4 kg can all go before you add a thing.

852.4 kg adds the 850 straight on to the 2.4 as though grams and kilograms were the same unit. 10.9 kg turns 850 g into 8.5 kg, 2.485 kg turns it into 0.085 kg, and 1.55 kg subtracts instead of adding.

D

A parallelogram has two pairs of parallel sides, and that is all you are promised. From those parallel sides you get opposite sides equal in length and opposite angles equal in size, so the statement about opposite angles is true of every single one.

Each of the other statements describes a special parallelogram rather than all of them. Four equal sides belongs to a rhombus, and four right angles belongs to a rectangle.

Equal diagonals also belongs to a rectangle, and four lines of symmetry belongs to a square.

The way to test a statement like this is to picture a long, leaning parallelogram, the sort that looks like a rectangle that has been pushed over. Every wrong option here fails on that one shape, and a single shape that breaks a statement is enough to rule it out.

A

Take the seats sold away from the seats there are: 1250 - 867.

Counting on is easier than exchanging here. From 867 up to 900 is 33, and from 900 up to 1250 is 350, so the answer is 33 + 350 = 383 empty seats.

The last digit rules two options out on sight. Taking 7 away from a number ending in 0 must leave a 3 at the end, so 617 and 2117 are impossible, and 2117 is what you get by adding rather than subtracting.

393 misses one of the exchanges in the tens column, and 483 takes away 767 instead of 867, which is a place-value slip rather than an arithmetic one.

E

Nine squares out of twelve are shaded, so the fraction starts as 9/12.

The question asks for the simplest form, so divide the top and the bottom by 3: 9/12 becomes 3/4.

9/12 is the trap. It describes exactly the right amount of shading, but it has not been simplified, so it does not answer the question that was asked.

1/4 and 3/12 are both the white part rather than the grey part, one simplified and one not, and 3/9 compares the white squares with the grey ones instead of with the whole rectangle.

D

Compare decimals by place value, not by how many digits they have. All five begin with a zero and a point, so start with the tenths.

The tenths are 7, 6, 6, 7 and 0. That leaves 0.7 and 0.71 in the running, and 0.71 has an extra hundredth on top, so it is the longest.

0.605 is the tempting answer, because 605 is the biggest string of digits on the page, and 0.099 has the most digits of all. Neither of those things makes a decimal bigger.

0.7 comes very close indeed, but 0.7 is the same as 0.70, which is one hundredth short of 0.71.

B

Put both measurements into the same unit first: 250 cm is 2.5 m.

Area is length times height: 4 x 2.5 = 10 square metres.

1000 multiplies 4 by 250 and so mixes metres with centimetres in the same sum, and 100 divides 250 by 10 instead of 100 and works out 4 x 25. A sense check settles both: a classroom wall is about the size of a few doors, not the size of a field.

6.5 adds the two measurements instead of multiplying them, and 13 is the perimeter of the wall rather than its area. An area always comes from a multiplication.

A

The angles inside any quadrilateral add up to 360 degrees.

Add the three you are given: 85 + 95 = 180, and 180 + 100 = 280 degrees.

Take that from the total: 360 - 280 = 80 degrees.

280 degrees is the total of the three known angles and 360 degrees is the total for the whole shape, so both are numbers you meet on the way rather than answers. Stopping at one of them is the commonest way to lose this mark.

260 degrees works from 540 degrees, which is the total for a pentagon, and 90 degrees is a guess that the last corner must be a right angle. Nothing in the question says the shape has any right angles at all.

C

Multiply first: 6 bulbs in each of 14 tubs is 6 x 14 = 84 bulbs planted.

The 8 still in the bag were in it at the start as well, so add them on: 84 + 8 = 92 bulbs.

84 is the trap. It is the number that went into the ground, and the bag must have held more than that, because 8 of them never left it.

76 subtracts the 8 instead of adding it, and 112 multiplies the wrong pair of numbers, working out 8 x 14.

132 adds the 8 on to the tubs before multiplying, working out 6 x 22, which quietly plants the leftover bulbs.

B

Turn them all into decimals so that they can be compared fairly. Three fifths is 3 divided by 5, which is 0.6, and 58 per cent is 58 out of 100, which is 0.58. The third one is already 0.55.

In order, smallest first, that is 0.55, then 0.58, then 0.6, which is row B.

Row D reads 58 per cent as 0.058 and so parks it at the front, and row C guesses that three fifths must be a little more than 0.55 without ever converting it.

Row A lines them up by how the digits look on the page, 3 then 55 then 58, and row E has the right idea in the wrong direction, largest first. Converting everything to decimals first is what stops all four.

C

Find the price of one yoghurt: 2.70 divided by 6 = 0.45 pounds, which is 45p.

Ten of them cost 10 x 0.45 = 4.50 pounds.

Ten yoghurts must cost more than six do, so the answer has to be above 2.70 pounds, and 27 pounds is not a supermarket price for ten yoghurts. That leaves only two options to think about.

5.40 pounds is two whole packs, which is twelve yoghurts rather than ten, and that is the trap.

0.45 pounds is the cost of a single yoghurt, 1.80 pounds is the cost of the four extra ones on their own, and 27 pounds multiplies by 10 without ever dividing by 6.

C

Three whole circles stand for 3 x 8 = 24 books.

Half a circle stands for half of 8, which is 4 books.

Altogether that is 24 + 4 = 28 books.

24 counts only the whole circles and throws the half away, and 32 rounds the row up to four circles. The answer has to sit between those two, which leaves 28 as the only possibility on the list.

35 treats each circle as 10 books rather than 8, and 3.5 reads the number of circles as if it were the number of books.

D

A triangular prism has two triangular ends joined by three rectangles.

Each triangle needs 3 straws, which is 6, and then 3 more straws join the corners of one triangle to the corners of the other. That makes 6 + 3 = 9 edges.

5 is the number of faces, two triangles and three rectangles, and 6 is the number of corners. Both are easy to grab when the word edge has not been read carefully.

8 forgets one of the three joining straws, and 12 is the number of edges on a cuboid rather than on a prism with triangular ends.

A

One thousand less means the thousands column goes down by 1. There are 0 thousands here, so you have to exchange one of the ten thousands: 20 304 becomes 19 304.

Check it by adding back: 19 304 + 1000 = 20 304.

Every wrong option changes a different column. 20 004 takes away three hundred, 20 204 takes away one hundred, 20 294 takes away ten and 20 303 takes away one.

20 204 is the tempting one, because taking a thousand from a number with a zero in the thousands column feels awkward, and it is far easier to change a digit that is already sitting there. Reading which column the question asks about is the whole question.

D

Doubling is the quick route: 250 doubled is 500, doubled again is 1000, again is 2000 and again is 4000. Four doublings is the same as multiplying by 16.

You can also see it as 250 x 4 = 1000, and then 1000 x 4 = 4000.

Rough size sorts the list out too. Sixteen boxes is more than ten boxes, which is 2500, and fewer than twenty boxes, which is 5000. Only 3750 and 4000 sit in that gap.

3750 is 15 boxes, one box short, and 2500 is ten boxes. 1500 is 6 boxes, and 40 000 is the right digits with an extra zero on the end.

A

60 kilometres per hour means 60 km in 60 minutes, which is exactly 1 km every minute.

In 45 minutes the coach therefore travels 45 km.

45 minutes is less than an hour, so the distance has to be less than 60 km. Every other option fails that test before any working at all, which is a whole mark won for nothing.

60 km is the distance in a whole hour, and 105 km comes from adding the 60 and the 45 rather than using them together.

2700 km multiplies 60 by 45 as though the minutes were hours, and 80 km scales the wrong way round, working out 60 divided by 45 and then times 60.

D

Three whole ones are worth 15 fifths, because each whole one is 5 fifths.

Add on the 2 fifths that are already there: 15 + 2 = 17 fifths, written 17/5.

A size check narrows it down fast. The answer is a little more than 3, so the top number must be a little more than 15. Only 17/5 and 32/5 get past that, and 32/5 works out at 6.4, which is far too big.

32/5 simply writes the digits 3 and 2 side by side, which is the trap. 11/5 multiplies 3 by 3 instead of by 5, 6/5 adds 3 and 2 rather than converting, and 5/17 turns the fraction upside down.

C

An equilateral triangle has three equal sides, so its perimeter is 3 x 12 = 36 cm.

The square shares that same perimeter between four equal sides: 36 divided by 4 = 9 cm.

A square needs more sides to cover the same distance, so each of its sides must be shorter than 12 cm. That makes 12 cm and 16 cm impossible whatever the arithmetic says.

12 cm assumes the two shapes have the same side length, 3 cm divides the 12 cm side by 4 rather than dividing the perimeter, and 16 cm counts four sides on the triangle and then divides 48 by 3.

6 cm halves the 12 cm side, which would be right only for a square with half the perimeter.

A

Three eighths means 3 divided by 8. One eighth is 0.125, so three eighths is 3 x 0.125 = 0.375.

Three eighths is less than a half, so the decimal has to be less than 0.5. Only 0.375 clears that, and it can be marked without dividing anything.

0.625 is five eighths, the part left over rather than the part asked for.

0.38 writes the digits 3 and 8 after a decimal point and 3.8 writes them either side of one. Those are the two most popular wrong answers of all, and neither of them is a division. 2.67 divides 8 by 3 instead of 3 by 8.

D

Percentages are out of 100, and 25 goes into 100 exactly 4 times, so multiply both parts by 4: 15 out of 25 is the same as 60 out of 100.

That is 60 per cent.

More than half the class walks, so the answer has to be over 50 per cent, and three of the five options are gone straight away.

40 per cent is the percentage who do not walk, so it is the right sum about the wrong group, and that is the trap. 15 per cent reads the count of 15 as if it were already a percentage, 10 per cent is the number of pupils who do not walk, and 75 per cent answers 15 out of 20.

B

Work out the cost first. Eight tickets at 7.50 pounds is 8 x 7 = 56 pounds, plus eight half pounds, which is 4 pounds, giving 60 pounds.

She hands over 4 x 20 = 80 pounds.

The change is 80 - 60 = 20 pounds.

60 pounds is the cost of the tickets and 80 pounds is the money she handed over, so both are steps along the way rather than answers to the question asked, and 140 pounds adds the two totals instead of subtracting.

12.50 pounds is the change from one note for one ticket, which answers a much smaller question than the one on the page.

B

Growth is the difference between one reading and the next, not the height itself. Week 1 to week 2 is 7 - 4 = 3 cm, week 2 to week 3 is 13 - 7 = 6 cm, and week 3 to week 4 is 16 - 13 = 3 cm.

The biggest jump is 6 cm, between week 2 and week 3. On the graph that is the steepest part of the line.

Weeks 3 and 4 make the tempting answer, because week 4 is where the plant is tallest, but being tall is not the same as growing quickly.

Weeks 1 to 4 cover the whole four weeks rather than the gap between two readings, and the last option is contradicted by the figures, since the jumps are 3, then 6, then 3.

D

Round each number to something friendly: 397 is about 400, and 21 is about 20.

400 x 20 = 8000, so 8000 is the best estimate.

This is a question to be estimated rather than calculated, and the size of each option is the fastest way in. Four hundreds times two tens lands in the thousands, so 800 and 80 000 are the wrong shape altogether.

800 comes from 400 x 2, 4000 from using 10 minutes instead of 20, 6000 from rounding 397 down to 300, and 80 000 from letting an extra zero creep in.

D

The shorter ribbon is 3 parts and measures 21 cm, so one part is 21 divided by 3 = 7 cm.

The longer ribbon is 7 parts: 7 x 7 = 49 cm.

Since 7 is more than twice 3, the longer ribbon must be more than twice 21 cm, so more than 42 cm. Only 49 cm and 63 cm get that far.

63 cm multiplies 21 by 3 and so uses the ratio the wrong way round, which is the trap here.

7 cm is one single part, 9 cm divides 21 by 7 and then multiplies by 3, using the two numbers in each other's places, and 25 cm simply adds the difference between 3 and 7 on to 21.