Sutton SET Mathematics Mock Paper 6

D

Compare the numbers from left to right. They all begin with 508, so compare the final three digits. Only 640 is greater than 609 and less than 690. The number is 508 640.

Elimination shortcut: 508 096 is too small and 508 906 is too large. The words greater than and less than also rule out the two boundary values, 508 609 and 508 690.

508 096 swaps digits from the lower boundary, while 508 906 swaps the tens and hundreds from a number in the interval. Neither swap preserves the required size.

B

Each team takes 18 + 4 = 22 items. Seven teams take 7 x 22 = 154 items. The store has 250 - 154 = 96 items left.

Elimination shortcut: 7 x 22 ends in 4, so subtracting it from a number ending in 0 must give an answer ending in 6. Only 96 has that last digit and a sensible size.

124 subtracts only the 126 bandages, and 222 subtracts only the 28 cold packs. 404 adds the items taken. 5346 does 250 - 7 first and then multiplies by 22, ignoring the required order.

E

Write 0.35 as 35/100 = 7/20. In sixtieths, 5/12 = 25/60 and 7/20 = 21/60. Paper and glass make 46/60 = 23/30, so metal makes 30/30 - 23/30 = 7/30.

Elimination shortcut: 5/12 is about 42% and glass is 35%, so about 77% is already named. Metal must be about 23%, which fits 7/30.

23/30 is the paper and glass together. 1/15 subtracts their fractions instead of finding what remains. 13/20 ignores the paper, while 7/12 ignores the glass.

A

Convert every length to centimetres: 3.4 m = 340 cm and 1.25 m = 125 cm. Then calculate 340 - 85 - 125 = 130 cm.

1.3 cm has the right number for 1.3 m but the wrong unit, and 130 m also attaches the wrong unit to the correct digits.

255 cm subtracts only the 85 cm piece. 215 cm subtracts only the 125 cm piece, so both answers forget one cut.

C

A square's diagonals are equal, each cuts the other in half, and they meet at right angles. It satisfies all three clues.

Elimination shortcut: an ordinary rectangle has equal diagonals but they do not meet at right angles. An ordinary rhombus has perpendicular diagonals but they need not be equal. Only the square combines both properties.

A kite does not have both diagonals bisecting each other. A general parallelogram has diagonals that bisect each other, but they need not be equal or perpendicular.

A

The difference between 5 parts and 3 parts is 2 parts. That difference is the 8 apples removed, so one part is 8 divided by 2 = 4. There were 8 parts altogether, giving 8 x 4 = 32 pieces of fruit.

Elimination shortcut: the original total must be a multiple of 5 + 3 = 8. Testing 32 gives 20 apples and 12 pears, and 20 - 8 = 12, so it works. Testing 40 does not.

12 is the number of pears and 16 is the size of four parts, not the total. 24 uses only six parts. 40 treats the removed 8 apples as one part instead of the two-part difference.

E

The total mass is (1 x 2) + (2 x 3) + (4 x 1) = 2 + 6 + 4 = 12 kg. Divide by the 6 trips: 12 divided by 6 = 2 kg.

Elimination shortcut: a mean must lie between 1 kg and 4 kg. Because half the trips recorded 2 kg, an answer near 2 kg is sensible. This rules out 7 kg, 12 kg and 4 kg quickly.

2 1/3 kg is the mean of the three listed masses 1, 2 and 4, but it ignores how often each mass occurred. 12 kg is the total rather than the mean.

C

Reflecting in the x-axis changes the sign of the y-coordinate, so (-2, 3) becomes (-2, -3). Moving 5 squares right adds 5 to the x-coordinate: -2 + 5 = 3. The final point is (3, -3).

(3, 3) translates but forgets the reflection. (-7, -3) moves left instead of right, while (7, -3) ignores the starting x-coordinate and uses 2 + 5.

(-3, 2) swaps the coordinates after changing signs, which is not how reflection in the x-axis works.

B

The step is 1.450 - 1.275 = 0.175. The fourth reading is 1.625 + 0.175 = 1.800, and the fifth is 1.800 + 0.175 = 1.975.

Elimination shortcut: the sequence rises by less than 0.2 each time, so the fifth reading must be a little below 2. Only 1.975 fits that rough position.

1.800 stops at the fourth reading and 2.150 goes on to the sixth. 1.790 fails to line up the decimal places when adding. 3.025 adds the first three readings instead of continuing the sequence.

D

Work out 48 x 37 as 48 x 30 + 48 x 7 = 1440 + 336 = 1776. Then subtract 85: 1776 - 85 = 1691.

Elimination shortcut: 48 x 37 must end in 6. Subtracting 85 makes the final digit 1. Only 1861 and 1691 survive that check, and the total must be less than 1776, leaving 1691.

1696 subtracts only 80, 1861 adds 85, and 1776 stops before removing the damaged fruit. 408 subtracts 85 from the sum 48 + 37 instead of from the product.

C

12.5% is 1/8. Together the store uses 1/8 + 3/8 = 4/8 = 1/2 of the original stock. Half of 640 is used, so the other half, 320 masks, remains.

Elimination shortcut: recognising 12.5% as 1/8 makes the two days total exactly one half. You can rule out every option except 320 without finding each day's use separately.

560 is the amount left after Monday only and 400 is the amount left after Tuesday only. 80 is Monday's use, while 240 is Tuesday's use.

A

One dressing has area 12 x 8 = 96 square centimetres. Four have area 4 x 96 = 384 square centimetres. One square centimetre is 100 square millimetres, so 384 x 100 = 38 400 square millimetres.

384 square millimetres keeps the numerical area but forgets to convert. 3840 multiplies by 10, as if converting a length rather than an area.

9600 square millimetres converts only one dressing. 3 840 000 multiplies by 100 twice after the area is already in square centimetres.

D

Two sides of each triangle are sides of the square, so they are equal. They meet at a 90 degree corner. Each triangle is therefore right-angled and isosceles.

Elimination shortcut: the unchanged corner of the square gives a right angle, ruling out equilateral, obtuse and acute descriptions. The two equal square sides then rule out scalene.

Equilateral would require three equal sides and three 60 degree angles. The diagonal is longer than a side, so neither triangle is equilateral.

E

Do the brackets first: 18 + 7 = 25. Then multiply: 6 x 25 = 150. Finally, 240 - 150 + 35 = 125.

Elimination shortcut: the deduction is 150, so the answer must be below 240. The final addition of 35 means it must be greater than 90. Only 125 fits both checks.

65 subtracts the final 35 instead of adding it. 269 ignores the 25 inside the brackets and subtracts only 6. 425 adds the 150-point deduction. 5885 starts with 240 - 6 and then multiplies by 25, ignoring the order of operations.

B

After the morning, 3/5 remains. One third of 3/5 is 1/5, so that is sold in the afternoon. The fraction left is 3/5 - 1/5 = 2/5.

Elimination shortcut: imagine 15 mangoes. Six are sold in the morning, leaving 9. A third of those 9 is 3, so 6 remain. That is 6/15 = 2/5.

3/5 stops after the morning and 1/5 is the afternoon sale, not the amount left. 4/15 subtracts 2/5 and 1/3 as though both were fractions of the original. 2/15 multiplies the two fractions and calls the result the remainder.

E

Try equal parts. If one original part is 4 people, there are 12 adults and 20 cadets. After 4 cadets board, there are 12 adults and 24 cadets, which is 1 : 2. The original total was 12 + 20 = 32.

The original total must be a multiple of 8 because 3 + 5 = 8. Testing the possible multiples shows that 24 gives 9 adults and 19 cadets after boarding, while 40 gives 15 adults and 29 cadets. Neither is 1 : 2.

16 and 24 use parts that are too small to make the new ratio work. 36 is the new total after the four cadets board, not the original total.

B

Tuesday has 12, which is twice Monday's 6. Thursday has 15, which is at least twice Wednesday's 7 because twice 7 is 14. Friday has 30, exactly twice Thursday's 15.

Elimination shortcut: Tuesday and Friday are exact doubles, so every valid option must include both. Thursday must also be included because 15 is greater than 14. This leaves Tuesday, Thursday and Friday.

Option A misses Thursday by treating at least twice as exactly twice. Option C overlooks Tuesday's exact double. Options D and E wrongly include Wednesday, even though 7 is not at least twice 12.

A

The factors of 28 are 1, 2, 4, 7, 14 and 28. There are exactly six.

Elimination shortcut: 29 is prime, so it has only two factors. The factors of 25 are 1, 5 and 25, and the factors of 27 are 1, 3, 9 and 27. Those three options go quickly.

24 has the factors 1, 2, 3, 4, 6, 8, 12 and 24, which is eight factors rather than six.

C

Angles around a point total 360 degrees. The two flags use 90 + 60 = 150 degrees, leaving 360 - 150 = 210 degrees. This is a reflex angle because it is greater than 180 degrees.

Elimination shortcut: the answer must be reflex, so 30, 120 and 150 degrees are impossible. A square alone would leave 270 degrees, but the triangle uses another 60 degrees, leaving 210 degrees.

30 degrees is the difference between the two corner angles. 150 degrees is their sum, and 120 degrees doubles the triangle angle instead of finding the space around the point.

D

There are 12 x 48 = 576 dressings. After 175 are used, 401 remain. Put 2 in reserve to leave 399, then calculate 399 divided by 7 = 57 for each ward.

Elimination shortcut: the answer should be a little below 400 divided by 7, so it should be a little below 60. Also, 7 x 57 = 399. This singles out 57.

82 divides the original 576 between 7 and ignores the later changes. 401 is the amount before sharing. 55 rounds too early, while 5.7 misplaces the decimal point when dividing.

B

Convert 7/10 to 70%. The difference from the 62.5% target is 70 - 62.5 = 7.5 percentage points.

Elimination shortcut: 70% and 62.5% are less than 10 percentage points apart, but clearly more than 1 point apart. Only 7.5 percentage points has the right size.

0.75 and 0.075 move the decimal point too far left. 75 treats the decimal difference 0.075 as 75%. 17.5 subtracts 52.5 from 70 instead of using the stated target.

D

Convert 0.8 m to 80 cm. The volume is 80 x 35 x 20 = 56 000 cubic centimetres.

560 cubic centimetres uses 0.8 in the multiplication without converting metres to centimetres. 5600 converts 0.8 m incorrectly to 8 cm.

2800 multiplies only the length and width, forgetting the height. 560 000 converts 0.8 m to 800 cm, adding an extra zero.

A

Each large triangle is 1/4 of the square. Each small triangle is one third of 1/4, which is 1/12. The shaded fraction is 1/4 + 2/12 = 3/12 + 2/12 = 5/12.

Elimination shortcut: one whole quarter is shaded, plus some more, but less than another whole quarter. The answer must be between 1/4 and 1/2, which leaves 5/12.

1/2 counts the six visible pieces as though they were equal. 1/4 ignores the two small shaded triangles. 3/4 treats each small triangle as a whole quarter, while 1/6 counts only the two small triangles and forgets the large one.

E

In 45 minutes, one volunteer sorts 18 divided by 3 = 6 bags. In 90 minutes, one volunteer sorts 12 bags. Five volunteers sort 5 x 12 = 60 bags.

Elimination shortcut: changing from 3 volunteers to 5 would raise 18 bags to 30 in 45 minutes. Doubling the time then doubles 30 to 60.

30 adjusts the number of volunteers but forgets to double the time. 36 doubles the time but keeps only three volunteers. 50 adds the changes instead of scaling them, and 120 doubles the correct result once too often.

C

The middle of five consecutive numbers is their mean. Calculate 285 divided by 5 = 57. The five odd numbers are 53, 55, 57, 59 and 61, so the largest is 61.

Elimination shortcut: 57 is the middle number, so the answer must be two odd-number steps above it: 57 + 2 + 2 = 61.

57 reports the mean and 53 reports the smallest number. 59 uses consecutive whole numbers rather than consecutive odd numbers. 63 takes three odd-number steps above the mean instead of two.

D

Write 3/4 as 0.75 and 15% as 0.15. The amount after the trip is 0.75 - 0.28 = 0.47. Adding fuel gives 0.47 + 0.15 = 0.62.

0.32 subtracts the added 0.15 instead of adding it. 0.90 adds the fuel but forgets what was used. 0.47 stops before the fuel is added.

0.68 subtracts 0.15 and adds 0.28, reversing both changes.

C

64 = 8 x 8, so it is a square number. It is also 4 x 4 x 4, so it is a cube number.

Elimination shortcut: 36 and 81 are familiar squares but are not cubes. 27 and 125 are familiar cubes but are not squares. This leaves 64.

Choosing 36 or 81 checks only the square condition. Choosing 27 or 125 checks only the cube condition, but the number must satisfy both.

B

One complete turn is 360 degrees. Equal turns of 60 degrees fit into 360 degrees exactly 360 divided by 60 = 6 times, so the polygon has 6 sides.

Elimination shortcut: six 60 degree turns make 360 degrees. Three turns make only 180 degrees, and five make only 300 degrees, so neither closes the route facing the starting direction.

8 would be the answer for 45 degree turns. 60 copies the angle as the number of sides instead of dividing the full turn by it.

A

Convert to millimetres: 4.5 m = 4500 mm, 85 cm = 850 mm, and 1.65 m = 1650 mm. Then 4500 - 850 - 1200 - 1650 = 800 mm.

80 mm converts centimetres to millimetres in the wrong direction. 800 cm has the right digits but gives the answer in the wrong unit.

1650 mm reports the final piece used rather than the remainder. 2000 mm forgets to subtract the 1200 mm piece.

E

The first team collects 17 x 36 = 612 bottles. The second collects 24 x 25 = 600 bottles. The difference is 612 - 600 = 12.

Elimination shortcut: 24 x 25 is exactly 600. Also, 17 x 36 is just over 600, so the difference must be small. Only 12 has a sensible size.

1212 adds the two totals. 612 and 600 report one team's total instead of the difference. 36 subtracts the numbers of containers, 24 from 17, incorrectly and then uses a bottle count from the question.

A

5/8 = 0.625. Also, 19/30 = 0.6333... because 19 divided by 30 is a little more than 0.63. This is greater than 0.625 and less than 0.64.

Elimination shortcut: 3/5 = 0.6 and 31/50 = 0.62, so both are too small. 13/20 = 0.65 and 2/3 is about 0.667, so both are too large.

13/20 is tempting if you round 0.64 up before comparing, but 0.65 is outside the interval. The word strictly also means neither boundary itself would be allowed.

C

The times are already in order, so the median is the middle value, 12 minutes. The unusually high 55 does not change which value is in the middle, making the median the best choice here.

The mean is 20 minutes, but it is pulled upwards by 55 and is not close to four of the five times. The range measures spread, not a typical value.

There is no mode because no time repeats, so 55 cannot be the mode. The midpoint of the extremes is not the median and is also pulled upwards by the unusual value.

E

There are 7 equal parts, so one part is 630 divided by 7 = 90 g. Dates weigh 5 x 90 = 450 g and figs weigh 2 x 90 = 180 g. After 90 g of dates are removed, dates weigh 360 g. The ratio 360 : 180 simplifies to 2 : 1.

Elimination shortcut: removing exactly one 90 g part changes 5 : 2 to 4 : 2. Simplifying 4 : 2 gives 2 : 1.

5 : 2 is the original ratio and 4 : 2 is correct before simplifying. 1 : 2 reverses the simplified ratio. 3 : 2 removes two date parts instead of one.

B

The large rectangle has area 8 x 6 = 48 square metres. The missing rectangle has area 3 x 2 = 6 square metres. The L-shape has area 48 - 6 = 42 square metres.

48 square metres ignores the removed corner, while 6 square metres is only the removed area.

18 square metres subtracts the side lengths first and multiplies 8 - 3 by 6 - 2 incorrectly. 22 square metres is the perimeter of the full 8 m by 6 m rectangle, not an area.

D

Use multiplication to check: 28 x 70 = 1960, leaving 56. Another 2 groups of 28 use the 56, so 2016 divided by 28 = 72.

7.2 and 720 place the decimal point or zero incorrectly. 62 is one group of 280 too small because 28 x 62 = 1736.

82 is one group of 280 too large because 28 x 82 = 2296. Checking by multiplication confirms that only 72 gives exactly 2016.

E

A multiple of 5 must end in 0 or 5. Check 360: its digit sum is 9, so it is a multiple of 9, and 360 divided by 8 = 45. No smaller listed number passes all three tests, so 360 is the answer.

Elimination shortcut: 72 fails the last-digit test for 5. The digit sum of 120 is 3, so it fails the test for 9. Although 180 is a multiple of 9 and 5, its last three digits are not divisible by 8.

3600 is a multiple of all three numbers, but it is not the smallest. It adds an unnecessary zero to 360.

B

First find 5/8 of 240: 240 divided by 8 is 30, and 30 x 5 = 150. Then find 80% of 150: 10% is 15, so 80% is 120.

There is also a quick fraction link: 80% is 4/5. Taking 4/5 of 5/8 cancels the fives and gives 4/8 = 1/2. Half of 240 is 120.

150 counts everyone who passes the practical test, while 192 finds 80% of all 240 people. 75 halves 150, and 30 counts the 20% of practical-test passers who do not pass theory.

D

A small cube has exactly two painted faces when it lies in the middle of an edge of the large cube. A cube has 12 edges, and a 3 by 3 by 3 cube has one such middle cube on each edge. Therefore there are 12.

8 counts the corner cubes, but each corner cube has three painted faces. 6 counts the centre cube on each face, and those have one painted face.

1 is the unpainted cube at the very centre. 20 counts the 12 edge-middle cubes and the 8 corner cubes together, even though the corners have three painted faces.

C

Distance from the y-axis is shown by the size of the x-coordinate. B has x = 2 and D has x = -2, so both are 2 units from the y-axis on opposite sides.

A and C have x-coordinates with different sizes, 3 and 4. C and D are 4 and 2 units from the y-axis.

E lies on the y-axis because its x-coordinate is 0, so it cannot be on the opposite side from B or A. Comparing y-coordinates instead of x-coordinates leads to the wrong pairs.

A

If every box were full, there would be 125 x 48 = 6000 cans. The shortfall is 7 x 6 = 42 cans. Therefore there are 6000 - 42 = 5958 cans.

Elimination shortcut: the full total is 6000 and the shortfall ends in 2, so the answer must be just below 6000 and end in 8. Only 5958 fits.

6000 ignores the shortfall. 5664 counts only the 118 full boxes. 6042 adds the missing cans instead of subtracting them, and 42 is only the shortfall.

C

Convert to metres: 1 km 450 m = 1450 m and 0.8 km = 800 m. Add 1450 + 800 + 675 = 2925 m, which is 2.925 km.

2.125 km omits the 0.8 km stage. 2925 km keeps the metres number but labels it as kilometres, while 29.25 km moves the decimal point only two places.

3.725 km adds the 0.8 km stage twice. Converting the final 2925 m by dividing by 1000 gives the correct unit and value.

D

Convert 3/8 to a decimal: 3 divided by 8 = 0.375. The total sold is 0.375 + 0.375 = 0.75 kg. The amount left is 1.2 - 0.75 = 0.45 kg.

0.825 kg subtracts only the morning sale. 1.95 kg adds the amount sold instead of subtracting it.

0.075 kg treats 3/8 as 0.75 before subtracting it from 0.825. 0.375 kg reports one amount sold rather than the remainder.

A

The teams record 10 + 15 = 25 metal items and 12 + 8 = 20 glass items. The difference is 25 - 20 = 5.

4 is the difference between the two glass counts, not between the combined material totals. 20 is the combined glass total and 25 is the combined metal total.

45 adds the combined metal and glass totals instead of finding how many more metal items there are.

B

The food provides 18 x 14 = 252 person-days. For 21 people, it lasts 252 divided by 21 = 12 days.

16 1/3 days scales in the wrong direction: more people must make the food last for fewer days. 14 days assumes the number of people makes no difference.

10 1/2 days subtracts one quarter of 14 because there are 3 extra people, but 3 is one sixth of 18, not one quarter. 252 days is the number of person-days, not the time for 21 people.

E

Numbers from 445 to 454 round to 450. For a multiple of 9, the digit sum must be a multiple of 9. The digits of 450 total 9, so 450 satisfies both clues.

Elimination shortcut: 441 and 459 have digit sums of 9 and 18, but they round to 440 and 460. The remaining boundary choices 445 and 454 have digit sums of 13, so they are not multiples of 9.

445 and 454 satisfy only the rounding clue. 441 and 459 satisfy only the multiple-of-9 clue. You must check both conditions.

B

Add back the 17 passengers missing from boat C. This gives 180 passengers split into five equal parts: one part for A, two for B and two for the adjusted C. One part is 180 divided by 5 = 36, so boat B carries 2 x 36 = 72 passengers.

36 is boat A's number and 55 is boat C's number, 72 - 17. Both are intermediate results rather than the requested boat.

32.6 divides 163 by five without first restoring the missing 17, and it also gives part of a passenger. 90 restores 17 but divides the five parts into only two.

E

From 08:55 to 17:20 is 8 hours 25 minutes, which is 8 x 60 + 25 = 505 minutes. Breaks total 60 + 35 = 95 minutes. The team is on duty for 505 - 95 = 410 minutes.

505 minutes is the full opening time and ignores all breaks. 470 subtracts only the 35 minutes, while 445 subtracts only the one hour.

370 treats 1 hour 35 minutes as 135 minutes. Clock time uses 60 minutes in an hour, so the break is 95 minutes, not 135.

C

55% of 80 is 44, and 3/8 of 80 is 30. Adding gives 74, but the 12 scouts with both items have been counted twice. Subtract one copy: 74 - 12 = 62.

74 forgets to correct the double count. 50 subtracts the 12 shared scouts twice, once from each group.

12 counts only the scouts with both items. 86 adds the shared group again instead of subtracting its extra count.

D

Treat each equal angle as one part. The fourth angle is two parts, so there are 1 + 1 + 1 + 2 = 5 parts in 360 degrees. One part is 360 divided by 5 = 72 degrees, and the largest angle is 2 x 72 = 144 degrees.

72 degrees is one of the three equal smaller angles. 90 degrees assumes all four angles are equal, as in a rectangle.

120 degrees divides 360 by the three equal angles and forgets the fourth. 216 degrees subtracts the correct largest angle from 360 and reports the other three angles together.

A

There are 28 x 36 = 1008 bottles. One ninth are rejected: 1008 divided by 9 = 112. That leaves 1008 - 112 = 896 accepted bottles. Finally, 896 divided by 16 = 56 full boxes.

A quicker calculation is to notice that 36 divided by 9 = 4 rejected bottles per tray. Each tray therefore supplies 32 accepted bottles, which is exactly 2 boxes. Twenty-eight trays make 28 x 2 = 56 boxes.

63 divides all 1008 bottles into boxes before rejecting any. 7 packs only the 112 rejected bottles. 112 is the rejected bottle count, while 896 is the accepted bottle count before packing.