Sutton SET Mathematics Mock Paper 3

A

Rounding to the nearest thousand means picking the multiple of 1000 the number sits closest to, and the hundreds digit decides it. Here the hundreds digit is 4, which is less than 5, so you round down to 27,000.

Two options can go before you think at all: an answer to the nearest thousand has to end in three zeros, so 27,400 and 27,500 are not even candidates. That leaves 27,000, 28,000 and 30,000.

28,000 is the tempting one, because 486 feels nearly 500. It is not 500, and 27,486 is 486 above 27,000 but 514 below 28,000. 30,000 is the answer to the nearest ten thousand.

B

Deal with the bracket first, and inside the bracket multiplying still comes before subtracting: 4 x 2 = 8, so 12 - 8 = 4.

The calculation is now 7 + 6 x 4. Multiply before you add: 6 x 4 = 24, then 7 + 24 = 31.

A parity check gets you most of the way for free. 6 x something is always even, and even plus 7 is odd, so the answer must be odd. That rules out 24 and 52 straight away.

52 comes from adding the 7 and the 6 first, 103 from working the bracket left to right as (12 - 4) x 2, 71 from ignoring the bracket altogether, and 24 from finding 6 x 4 and forgetting to add the 7.

D

Build 15% out of 10% and 5%. 10% of 240 is 24, and 5% is half of that, so 12. Together, 24 + 12 = 36 punnets.

A size check does most of the work: 15% is about a seventh, and a seventh of 240 is somewhere near 35. Anything tiny like 3.6, or as big as 48, is the wrong size.

24 is the answer if you stop at 10%, 12 if you find only the 5%, and 48 is 20%. 3.6 is 10% of 36, which is what you get if a decimal point slips.

C

There are 1000 millilitres in 1 litre, so multiply by 1000: 2.35 x 1000 = 2350 ml.

Rough size settles it before you multiply. 2.35 litres is a little over 2 litres, so the answer must be a little over 2000 ml. Only 2350 ml is in that range.

235 ml comes from multiplying by 100, and 23,500 ml from multiplying by 10,000. 2035 ml is what you get if you read 2.35 litres as 2 litres and 35 millilitres, but the 0.35 is 35 hundredths of a litre, which is 350 ml.

A

The three angles in any triangle add up to 180 degrees. Add the two you have: 47 + 68 = 115. Then 180 - 115 = 65 degrees.

Rough size throws out two options immediately. 245 degrees is more than a straight line all on its own, and 115 degrees added to the 115 you already have is 230, which is past 180.

133 degrees is 180 - 47, so one of the given angles has been forgotten, and 112 degrees is 180 - 68 for the same reason. 115 degrees is just the two given angles added together.

D

Count the parts first: 3 + 5 = 8 parts. Then 64 divided by 8 gives 8 sheets in one part.

The larger share is 5 parts, so 5 x 8 = 40 sheets. The other stand gets 3 x 8 = 24, and as a check 40 + 24 = 64.

You can spot the answer by pairing: the two shares must add to 64, and the only pair here that does is 24 and 40. 24 is the smaller share, so choosing it means the ratio has been read the wrong way round. 8 is one part, 32 is half of everything, and 56 is 64 with one part taken off.

C

A mean of 42 minutes across four rehearsals means the four lengths add to 4 x 42 = 168 minutes.

The three you know add to 36 + 45 + 39 = 120 minutes, so the fourth is 168 - 120 = 48 minutes.

Rough size rules out most of the list at a glance. One rehearsal cannot be 120 or 168 minutes when the mean is only 42, and it must be longer than the mean because two of the three you were given are shorter than it.

40 minutes is the mean of the three you were given, and 42 minutes is the trap of assuming the missing one matches the overall mean.

E

Sketch the three points. (2, 1) and (2, 5) are one above the other on the line x = 2, and (6, 5) is level with (2, 5) on the line y = 5.

The missing corner has to be below (6, 5) and level with (2, 1), so it takes the 6 from one and the 1 from the other: (6, 1).

You do not need the sketch to rule options out. The fourth corner must have an x you have already seen and a y you have already seen, so anything containing a 6 in the second place is out.

(1, 6) is the right pair of numbers written the wrong way round, which is the commonest slip with coordinates. Remember: along the corridor, then up the stairs.

C

Count up the number line from -6. Going up 6 takes you to 0, and you still have 5 of the 11 degrees left, so you land on 5 degrees Celsius.

The temperature rose, so the answer must be higher than -6. That alone removes -17 immediately.

6 degrees is what you get if you count only as far as zero and stop. -17 comes from subtracting instead of adding, and 17 from adding 6 and 11 while ignoring the minus sign altogether.

E

Split the 26 into 20 and 6. 34 x 20 = 680, and 34 x 6 = 204. Add them: 680 + 204 = 884 seats.

The last digit does most of the sorting here. 4 x 6 = 24, so the answer must end in 4, which leaves only 204 and 884. A quick size check finishes the job: 34 rows of about 25 is somewhere near 850, so 204 is far too small.

680 is what you get if you multiply by the 20 and forget the 6, 204 if you multiply by the 6 and forget the 20, and 780 is 30 x 26, where the 4 in 34 has been lost. 60 is 34 + 26.

D

To find three eighths, first find one eighth: 96 divided by 8 is 12 kg. Then multiply by 3: 12 x 3 = 36 kg.

Three eighths is just under a half, so the answer has to be a bit under 48 kg. That rules out 60 kg without any working, and shows 12 kg and 24 kg are far too small.

12 kg is only one eighth, 24 kg is one eighth doubled instead of trebled, 32 kg is a third of the sack rather than three eighths, and 60 kg is the five eighths that is left in the sack.

E

Add the hours first: 19:45 plus 2 hours is 21:45. Now add the 50 minutes in two steps. 15 minutes takes you to 22:00, and the remaining 35 minutes takes you to 22:35.

Two options can be crossed off on sight, because a clock never shows more than 59 minutes. 21:95 and 22:95 come from adding 45 and 50 to get 95 and writing it down as if it were a time.

22:15 is the trap of reading 2 hours 50 as two and a half hours, and 21:35 comes from adding only 1 hour 50.

A

A parallelogram has two pairs of parallel sides, and that forces opposite angles to be equal. Draw a leaning one and you can see the two sharp corners match each other and the two blunt corners match each other.

Test the others on a leaning parallelogram rather than a rectangle, because a rectangle is a parallelogram and will make almost anything look true. Once it leans, the sides are not all equal, the diagonals are different lengths, no angle is a right angle, and folding it in half never matches.

All four sides the same describes a rhombus, and equal diagonals with right angles describe a rectangle. Both are special parallelograms, not every parallelogram.

B

Work up in chunks of 15. Ten bags take 150, twenty bags take 300, and five more bags take 75, giving 375 for 25 bags. One more bag takes it to 390, and only 10 screws are left, which is not enough for another bag.

So 26 bags can be filled completely, with 10 screws left over.

Rough size kills two options instantly: 6000 is what you get by multiplying instead of dividing, and 390 is the number of screws used, not the number of bags. 10 is the leftover screws.

27 is the tempting one. There are enough screws to start a 27th bag, but it would hold only 10, and the question asks for bags that are completely full.

E

Compare the tenths column first, because tenths are worth more than anything to their right. Four of the numbers have 5 or 7 tenths, but 0.075 has 0 tenths, so it is smaller than all of them.

That one column decides the question, and you never need to look at the rest of the digits.

0.507 is the trap for anyone who thinks a longer number must be a smaller one. It has 5 tenths, so it is worth about a half, while 0.075 is worth less than a tenth.

A

The mix is made of 1 + 4 = 5 parts. Divide the whole mix into those 5 parts: 35 divided by 5 is 7 kg per part.

Cement is 1 part, so the answer is 7 kg. The sand is the other 4 parts, 28 kg, and 7 + 28 = 35 as a check.

The cement is the small share, one fifth of the mix, so it must be well under half of 35 kg. That rules out 17.5 kg, 28 kg and 140 kg before you calculate anything.

28 kg is the sand rather than the cement, which is the ratio read backwards. 8.75 kg comes from dividing by 4 instead of by 5 parts, and 17.5 kg from sharing the mix equally instead of in the ratio.

B

The range is the difference between the largest and smallest values, so it is one subtraction: 24 - 9 = 15.

A range is a gap, so it can never be bigger than the largest value in the set. That rules out 24 and 33 at once, and 18 is suspicious because it is one of the values rather than a gap.

18 is in fact the mean of the four numbers, since 18 + 24 + 9 + 21 = 72 and 72 divided by 4 is 18. 33 is the largest and smallest added instead of subtracted.

B

Break the numeral into chunks. M is 1000. CM is a smaller letter before a larger one, so it means 1000 - 100 = 900. XL means 50 - 10 = 40. VII is 7.

Add them: 1000 + 900 + 40 + 7 = 1947.

Getting MCM to 1900 rules out three options in one move, because only 1907, 1947 and 1967 start there.

1967 comes from adding X and L to make 60 instead of subtracting to make 40, 1907 from missing the XL out, and 2147 from reading CM as 1100 by adding rather than subtracting. 2047 treats both Ms as thousands and drops the C.

B

Angles that fill the space around a point add up to 360 degrees, a full turn. The three you have add to 90 + 115 + 62 = 267 degrees.

So the fourth angle is 360 - 267 = 93 degrees.

Before calculating, notice the three given angles already take up most of the turn, so the one left must be small. 267 degrees and 360 degrees are impossible on that ground alone.

87 degrees comes from using 180 for a full turn instead of 360, and 155 degrees from subtracting only two of the three angles and forgetting the 62.

A

Find the cost first. Six lots of 1 pound 85 is easier as six lots of 2 pounds, which is 12 pounds, minus six lots of 15p, which is 90p. So the strawberries cost 11 pounds 10.

Change from 20 pounds is 20.00 - 11.10 = 8 pounds 90.

Rough size does the sorting. She spends more than 10 pounds, so her change from 20 pounds must be less than 10 pounds. That rules out 10 pounds 75, 11 pounds 10 and 18 pounds 15 in one glance.

11 pounds 10 is what she spent, not her change, and 18 pounds 15 is the change from buying just one punnet. 9 pounds 25 is the cost of five punnets.

C

25% is a quarter, and a quarter of 120 pounds is 30 pounds off. The sale price is 120 - 30 = 90 pounds.

It is quicker to go straight for what is left: taking a quarter off leaves three quarters, and three quarters of 120 is 90 pounds.

The last digit prunes the list for free. A quarter of 120 is a whole number of tens, so the sale price must end in a zero, and 95 pounds and 96 pounds cannot be right.

30 pounds is the discount rather than the price, 95 pounds comes from taking 25 pounds off instead of 25%, and 96 pounds is 20% off.

C

Get both sides into the same unit before you do anything else: 250 cm is 2.5 m.

Perimeter is all the way round, so add one of each side and double: 2.5 + 1.6 = 4.1, and 4.1 x 2 = 8.2 m.

A sanity check on units removes the two big answers instantly. A vegetable bed with a perimeter of 251.6 m or 503.2 m would be longer than a running track. Both come from adding 250 to 1.6 without converting.

4.1 m is right but only half way, because the doubling has been forgotten, and 4 m is 2.5 x 1.6, which is the area in square metres, not the perimeter.

A

Nine tiles out of twelve are green, so the fraction is 9/12. Simplest form means dividing top and bottom by the largest number that goes into both, which is 3: 9 divided by 3 is 3, and 12 divided by 3 is 4, giving 3/4.

9/12 is the same amount but it is not in its simplest form, so it does not answer the question that was asked. Simplifying is the whole task here.

1/4 is the cream fraction rather than the green one, and 4/3 is the right fraction turned upside down. Any fraction bigger than 1, like 4/3, is impossible when you are describing part of a whole.

E

A triangular prism has a triangle at each end and three rectangles joining them, so 5 faces. Each triangle has 3 edges, making 6, and 3 more edges join the ends together, making 9. The two triangles have 3 corners each, so 6 vertices.

Counting faces first is the fast route. A cube and a cuboid both have 6 faces, and a triangle-based pyramid has 4, so three options go at once. Only the square-based pyramid and the triangular prism have 5 faces.

The square-based pyramid is the near miss: it has 5 faces too, but only 8 edges and 5 vertices, because its four sloping faces meet at a single point on top.

C

Round each number to something friendly: 39 is nearly 40, and 21 is nearly 20. Then 40 x 20 = 800, so the total is close to 800.

The exact answer is 819, which confirms it, but the point of the question is that you never needed to find it.

600 is 30 x 20, where 39 has been rounded too far down, and 1200 is 40 x 30, where 21 has been rounded up to the wrong ten. 80 is 39 + 21 rounded, and 8000 is ten times too big.

E

The denominators 4 and 5 both go into 20, so rewrite both fractions in twentieths: 3/4 is 15/20 and 2/5 is 8/20.

Now add the numerators: 15 + 8 = 23, giving 23/20. That is more than a whole one, so write it as 1 3/20.

Rough size answers this on its own. 3/4 is more than a half and 2/5 is nearly a half, so the total must be more than 1. Every option below 1 can be crossed off without any adding at all.

5/9 is the classic error of adding the tops and the bottoms, and 3/10 is 3/4 multiplied by 2/5 instead of added.

C

Find the cost of one first: 78 divided by 6 is 13 pounds.

Then ten of them cost 13 x 10 = 130 pounds.

Ten pads must cost more than six pads but nothing like ten times as much, so the answer sits between 78 and about 200 pounds. That removes 13 pounds, 46 pounds 80 and 780 pounds without a single calculation.

156 pounds is the cost of twelve pads, from doubling six instead of scaling to ten, and 780 pounds is 78 multiplied by 10, which would be right only if each pad cost 78 pounds.

B

Convert first: 3.6 m is 360 cm. Four shelves at 65 cm each take 4 x 65 = 260 cm.

What is left is 360 - 260 = 100 cm.

The unit is the trap and also the shortcut. 1 cm is the right number in the wrong unit, since the answer is 1 metre, and the question asked for centimetres. If a leftover of 1 cm looks odd to you, that instinct is correct.

260 cm is the piece that was cut off rather than what is left, and 295 cm is 360 - 65, where only one shelf has been taken. 165 cm counts three shelves instead of four.

D

24 out of 60 is the fraction 24/60. Divide top and bottom by 12 and it becomes 2/5, and 2/5 is 40%.

You can also work in tenths: 6 pupils are 10% of 60, and 24 is four lots of 6, so 24 pupils are 40%.

Drums is the biggest group but it is not half the pupils, so the answer has to be between 25% and 50%. That leaves 36% and 40%, and 36 is simply the 60 - 24 pupils who chose something else, written as if it were a percentage.

24% is the count copied straight into a percentage, 25% is the violin group's share, and 60% is the total number of pupils, not a percentage at all.

E

A right angle is 90 degrees. Think of it as 3 equal parts, because one angle is 1 part and the other is 2 parts. Each part is 90 divided by 3 = 30 degrees.

The larger angle is 2 parts, so 2 x 30 = 60 degrees, and the smaller is 30 degrees. Check: 60 + 30 = 90.

Both angles are pieces of a right angle, so neither can be 90 degrees or more. 120 degrees and 240 degrees are impossible on sight, and they come from splitting a straight line or a full turn instead.

30 degrees is the smaller of the two angles, and 45 degrees is what you get by splitting the right angle equally, which ignores the word twice.

D

A multiple of both 6 and 9 must be a multiple of 18, and 18, 36, 54 is the list. Only 54 appears in the options.

Elimination gets there faster than the list does. Every multiple of 6 is even, so 45 and 63 are out at once. Then use the digit-sum test for 9: 2 + 4 = 6 and 4 + 2 = 6, neither of which is a multiple of 9, but 5 + 4 = 9.

24 and 42 are multiples of 6 only, while 45 and 63 are multiples of 9 only. Checking just one of the two conditions is what makes each of them tempting.

C

Work backwards, undoing each step in reverse order. The last thing she did was subtract 14, so add it back: 63 + 14 = 77. Before that she multiplied by 7, so divide: 77 divided by 7 = 11.

Always check a backwards answer forwards: 11 x 7 = 77, and 77 - 14 = 63. Correct.

23 is the trap of undoing the steps in the wrong order, dividing first and then adding 14. 7 comes from subtracting the 14 instead of adding it, 9 from ignoring the 14 altogether, and 77 from stopping half way and forgetting to divide.

B

Ignore the decimal points and multiply the digits: 6 x 4 = 24. Now count the decimal places in the question. 0.6 has one and 0.4 has one, so the answer needs two: 0.24.

Size alone almost finishes the question. Multiplying by a number smaller than 1 always makes something smaller, so the answer must be less than 0.4. That rules out 1, 2.4 and 24 immediately.

1 comes from adding rather than multiplying, and 0.024 has one decimal place too many.

A

Doubling makes this easy: 4.5 x 2 = 9, so ten cans hold 45 litres and twenty cans hold 90 litres. The answer is 20 cans.

You are counting cans, so the answer must be a whole number, and 22.5 goes straight away. So does 405, which is 90 multiplied by 4.5 instead of divided, and 85.5, which is 90 with one can taken off.

22.5 is the near miss to watch: it comes from dividing 90 by 4 rather than 4.5. 45 is simply half of the butt.

C

Two of the sides are easy to measure because they run straight along the grid. From (1, 2) up to (1, 8) is 6 metres, and from (1, 2) across to (7, 2) is 6 metres, and they meet at a right angle.

The triangle is exactly half of the 6 by 6 square that those two sides make, so the area is half of 36, which is 18 square metres.

36 is the whole square, so choosing it means the halving has been forgotten, and 24 is that square's perimeter rather than an area. 12 is just the two side lengths added, and 6 is a single side.

D

Turn everything into decimals so they can be compared in one column. 3/5 is 0.6, 65% is 0.65, and 2/3 is 0.666..., which is the largest of the five.

There is a shortcut worth spotting. 0.6 and 3/5 are exactly the same amount, so neither of them can be the single largest, and both can be crossed off before you convert anything else. 0.58 is smaller than 0.6, so it goes too, leaving only 65% and 2/3.

65% is the tempting final answer because a percentage looks bigger than a fraction. Compare them fairly: 2/3 is 66.6%, which beats 65%.

D

The bracket comes first: 3 + 2 = 5. That leaves 60 / 5 x 4.

Dividing and multiplying rank equally, so work from left to right: 60 / 5 = 12, then 12 x 4 = 48.

A size check rules out the largest option for nothing. You divide 60 by 5 before you do anything else, which makes the running total 12, and multiplying by 4 cannot get it back above 60. So 88 is impossible.

88 comes from bracketing the wrong pair, as (60 / 3 + 2) x 4. 3 comes from doing the multiplication before the division, as 60 / (5 x 4), 28 from ignoring the bracket, and 12 from forgetting the final x 4.

D

Name the columns to the right of the decimal point in order: tenths, hundredths, thousandths. In 12.045 the 0 is in the tenths column, the 4 is in the hundredths column and the 5 is in the thousandths column.

So the 4 is worth 4 hundredths, which is 0.04 kg.

The 0 is the whole point of the question. Skip past it, as though the 4 were the first digit after the point, and you get 4 tenths, which is ten times too big. Counting from the far right instead gives 4 thousandths.

C

If 40% is 18 singers, then 10% is a quarter of that: 18 divided by 4 = 4.5 singers.

The whole choir is 100%, which is ten lots of 10%: 4.5 x 10 = 45 singers. Check it: 40% of 45 is 18.

Rough size narrows the field first. The total must be bigger than 18, so 7.2 goes, and since 40% is nearly half, the total cannot be much more than double 18. That makes 72 and 180 far too big.

72 comes from treating 40% as a quarter and multiplying by 4, 180 from treating the 18 as 10%, and 7.2 is 40% of 18, which answers a question nobody asked.

C

The difference in the ratio is 7 - 2 = 5 parts, and that difference is the 45 extra frogs. So 1 part is 45 divided by 5 = 9 animals.

Newts are 2 parts: 2 x 9 = 18 newts. Frogs are 7 x 9 = 63, and 63 - 18 = 45, so it checks out.

Once you know one part is 9, every possible answer has to be a multiple of 9, which knocks out 10 on the spot.

10 is the answer you get by treating 45 as the total number of animals rather than the difference. 63 is the frogs, 81 is the whole pond population, and 9 is a single part.

A

Regular means all sides equal, so one side of the pentagon is 45 divided by 5 = 9 cm. The triangle's sides are the same length, so its perimeter is 3 x 9 = 27 cm.

The triangle has fewer sides of the same length, so its perimeter simply must be smaller than the pentagon's. 45 cm and 75 cm are gone before you divide anything.

75 cm is the ratio applied backwards, dividing by 3 and multiplying by 5. 15 cm is 45 divided by 3, which treats the 45 cm as though it belonged to the triangle, and 9 cm is one side rather than the perimeter.

C

Find the total first: 18 x 24. Split the 24 into 20 and 4, so 18 x 20 = 360 and 18 x 4 = 72, giving 432 apples.

Then take away the ones sold: 432 - 47 = 385 apples.

The last digit alone identifies the answer. 8 x 4 = 32, so the total ends in 2, and taking away 47 leaves a number ending in 5. Only 385 does.

432 is the number before any were sold, and 479 comes from adding the 47 instead of subtracting. 313 is what you get if you multiply by 20 and forget the 4, and 361 counts only 17 crates.

D

If 45% are juniors, then 100 - 45 = 55% are not. Now find 55% of 200. Since 1% of 200 is 2 members, 55% is 55 x 2 = 110 members.

The quicker route is to notice that more than half the members are not juniors, so the answer must be more than 100. Only 110 and 155 clear that bar, and 155 is 200 - 45, which subtracts the percentage as though it were a number of people.

90 is the number of juniors, 55 is the correct percentage but not the number of members, and 45 is the percentage from the question copied straight down.

D

Every centimetre of model stands for 4 metres of lighthouse, so multiply: 15 x 4 = 60 metres.

Check the unit before you mark anything. 60 cm is the right number in the wrong unit, and a lighthouse 60 cm tall would fit on a desk. The real building has to be measured in metres.

3.75 m comes from dividing by 4 instead of multiplying, and 19 m from adding the 4. 600 m is ten times too big and would make the lighthouse taller than any building in Britain, which is exactly the kind of check worth making.

C

Closest means the smallest gap, so find each gap rather than judging by eye. 4489 is 511 away, 4950 is 50 away, 5049 is 49 away, 5140 is 140 away and 5500 is 500 away.

The smallest gap is 49, so 5049 pounds is closest.

Only two of the five are within 100 pounds of the target, so cross the other three off quickly and spend your time on the pair that matters.

4950 is the trap, and it is a close one. It looks nearer because it is a rounder number, but it is 50 away and 5049 is 49 away, so it loses by a single pound.

E

Records: 3 x 12 = 36 pounds. Books: 5 x 7 = 35 pounds. Together she takes 36 + 35 = 71 pounds.

Profit is what is left after the pitch fee: 71 - 15 = 56 pounds.

A rough estimate points at the answer before you finish. She takes in about 70 pounds and pays out 15, so the profit is somewhere in the mid fifties. Anything near 20 pounds means a whole set of boxes has been left out.

71 pounds is the money taken rather than the profit, and 86 pounds adds the pitch fee instead of subtracting it. 20 pounds forgets the records and 21 pounds forgets the books.

A

A quarter of a half means splitting the half into 4 equal pieces. A half split into 4 gives eighths, and you want one of them, so the answer is 1/8.

In numbers that is 1/4 of 1/2, which is 1/4 x 1/2 = 1/8.

Size tells you a lot for free. The Sunday group is only part of the weekend group, which is only half of everyone, so the answer must be smaller than 1/4. Only 1/8 and 1/6 are, and 1/6 comes from adding the 2 and the 4 to make sixths.

1/4 is the trap of reading the quarter as a quarter of everybody, and 3/8 is the weekend volunteers who do not work on Sundays.

B

Share the mass between the bricks: 15.6 divided by 6. Split it up as 12 divided by 6 = 2, and 3.6 divided by 6 = 0.6, so the answer is 2.6 kg.

Check it forwards: 6 x 2.6 = 15.6 kg.

Rough size does the work of the division. Six bricks weigh about 15 kg, so one brick is about two and a half kilograms. That makes 26 kg and 93.6 kg impossible, and 9.6 kg far too heavy.

93.6 kg comes from multiplying instead of dividing, 9.6 kg from subtracting the 6, and 26 kg has the right digits with the decimal point in the wrong place.

B

Turn the mean back into a total: five seedlings with a mean of 12 cm have a total height of 5 x 12 = 60 cm.

Adding the sixth gives 60 + 18 = 78 cm across 6 seedlings, so the new mean is 78 divided by 6 = 13 cm.

You can predict the answer before dividing. The new seedling is taller than the old mean, so the mean must rise, but one seedling out of six cannot drag it far. Anything from 15 cm upwards is the wrong size.

15 cm is the mean of 12 and 18, which treats the five seedlings as though they were one. 15.6 cm divides the new total by 5 instead of 6, and 78 cm is the total height, not a mean.

B

The 84 daffodils are the 4 parts of the ratio, so one part is 84 divided by 4 = 21 bulbs.

Tulips are 3 parts: 3 x 21 = 63 bulbs.

Elimination is quicker than any of that. Tulips have the smaller share, so there must be fewer of them than the 84 daffodils. Three of the five options are bigger than 84 and can go without a moment's thought.

112 is the ratio used backwards, dividing by 3 and multiplying by 4. 147 is the total number of bulbs, 252 multiplies by 3 without dividing by 4, and 21 is a single part.