15. £3.64: £5.76=12 = 0.48; individually, 0.48 + 0.04 = 0.52, and 0.52 × 7 = £3.64.
16. 70 runs: 10 innings @ 15 per innings = 150 total (average15); 11 innings @ 16 per innings = 176 total (average 16); 11 innings @ 20 per innings = 220 total (average 20); 150 + 70 = 220.
17. 1 part = 500:(2 + 3 + 4); apples 1000, oranges 1500, plums 2000.
18.
19. 15 days: the five men take 21 × 5 = 105 man-days to build the house; seven men therefore build the house in 15 days ().
20. The number of votes the winning candidate received was (972 + 52 + 78 + 102) ÷ 4 = 301; the second received 301 - 52 = 249; the third received 301 -78 = 223, and the fourth received 301 - 102 = 199.
Assessment
Test 2.14 Advanced numerical aptitude test
Answers
1. 26: start at the top number in each group and spiral anti-clockwise, finishing in the centre. The numbers in the first group increase by 2, in the second group by 3, in the third group by 4 and in the fourth group by 5.
2. 97. 5 kg: 100% less 35% = 65%, less 20% = 52%, less 25% = 39%; 39% × 250 = 97.5.
3. 6, 15: there are two interwoven sequences: 10, 9, 8, 7, 6 and 11, 12, 13, 14, 15.
4. 42: (6 × 6) + 6
5. 50%: it is a certainty that at least two coins will fall with the same side up. Thus it is just as likely that these two coins will be tails as it is they will be heads.
6. 2 minutes 12 seconds:
7. 11: [(23 + 15) - 5] ÷ 3
8. 50: add 1, 3, 9, 27, 81, i.e. the amount added is multiplied by 3 each time.
9. 12: 9 × 5 × 12 = 540
10. 18, 68: add the three numbers in each row and column to obtain the fourth number.
11. Seven bags each containing 13 apples: 91 is the product of two prime numbers, 7 and 13.
12. £40.70: train £27.35 + taxi £11.45(27.35 — 15.90) + bus £1.90(11.45 — 9.55) = £40.70.
13. 343: each number is the cube of the number of sides of the figure in which it is contained (7 × 7 × 7 = 343).
14. 46.75 square metres: I have 240 square metres (20 × 4 = 80 sq m × 3 = 240) (6 × 18 = 108) + (15.5 × 5.5 = 85.25) = 193.25; 240 — 193.25 = 46.75.
15. 9:ortook sugar only +ortook milk and sugar +took milk only =the remainder,, took it black;= 9.
Assessment
Test 2.15 Technical aptitude test
Answers
1. Of the nine faces shown (or 18 half-faces), six out of 18 half-faces are shaded. One-third of the total figure visible is therefore shaded.
2.
The value of the circle shown in the middle is 360°. The value of each segment is therefore 45° (360 ÷ 8); the remaining angles, therefore, are equal to 180 - 45 = 135 or 67.5° each (180° being the sum of the internal angles of a triangle); each internal angle is therefore 135°.
3. f) zinc and copper
4. c) heating it
5. d) parallelepiped
6. 6.75 sq units:
7. AB = diameter, CD = radius, EF = chord, GH = secant.
8. Conduction is when heat travels from the warmed end of an object towards the cool end. Radiation is when heat travels through space. Convection is when heat from a hotplate is transferred to water in a pan placed on the hotplate.
9. c) force
10. b) 740 m.p.h.
11. e) 20 hexagons and 12 pentagons
12. 50: 12 at the back, 10 at the sides, 6 underneath, 6 on top, 12 at the front, 4 on the insides.
13. c) Pythagoras’ theorem
14. 224
15. b) Hertz
Assessment
Chapter 3 — Logical reasoning
Test 3.1 Pure logic
Answers
1. tortoise: the name of each creature commences with the letter that come two letters in the alphabet after the last letter of the previous creature. Also the name of each creature contains one more letter than the previous creature.
2. October: jump an extra month each time, i.e. January February (March) April (May June) July (August September October) November (December January February March) April (May June July August September) October.
3. D I S NStarting letters for each square, commencing at the top left-hand corner, are ABCD. Each square jumps an extra letter, rotating clockwise. AbCdEfG, BcdEfgHijK, CdefGhijKlmnO, DefghIjklmNopqrS.
4. 583796: the bottom three rows are the reverse of the top three rows of numbers.
5. 10 and 6: opposite pairs of numbers in the first circle total 11, in the second circle they total 12, and in the third circle 13.
6. 9 4 7 5The numbers reading down the middle are the sum of the top and bottom numbers in another figure; 5821 + 3654 = 9475.
7. 2681749: reverse the first three numbers, then reverse the last four numbers.
8.
3 + 8 = 11, 5 + 9 = 14
1 + 1 = 2, 1 + 4 = 5
9. 16: (33 + 31) ÷ 4 = 16
10. 76: reverse the first number but discard the highest and lowest digits.
Assessment
Test 3.2 Progressive matrices test
Answers
1. B: the diamond is shown pointing north, south, east and west.
2. E: the lines within the large square are drawn top, bottom, middle left and middle bottom.
3. A: looking down, the large circle disappears, and looking across, the smaller middle circle disappears.
4. F: each line across and down contains one triangle upside down, one circle, and one set of vertical lines.
5. B: looking across and down only, lines (and the circle) which appear in the same position twice in the first two squares are carried forward to the final square.
6. E: looking across and down, any lines that appear in the same position twice in the first two squares are cancelled out in the final square.
7. G: only dots of the same colour which appear in the same position twice in the first two squares are carried forward to the final square; however, they then change from black to white and vice versa.
8. C: so that each vertical and horizontal line contains one each of the four different circle combinations.
9. F: so that the first and third lines are the same as are the second and fourth lines.
10. B: looking across and down, alternate circle combinations are repeated with the addition of an extra circle.
Assessment Each correct answer scores one point
Test 3.3 Advanced logic test
Answers
1. 74: the numbers 1 37 4 9 32 5 68 1 appear in the same order, reading clockwise around the outer and inner sections of the heptagon.
2. 129: 53 — 44; 3 × 4 = 12 and 5 + 4 = 9
3. 8492: The numbers in the bottom rectangle are formed by taking digits from opposite pairs of numbers in the top rectangle, e.g. the digits 3829 and 4873, produce the numbers 7338 and 8492 in the bottom rectangle.
4. humane: the words have alternate consonant=vowel arrangement, starting with a consonant.
5. It was Ernie. If the statements are set out as in the table below, it is seen that only Ernie has three ticks against his name, which means that if it was Ernie, just three statements, those of Ben, Dave and Ernie, are correct.
6. 60587
7.
The grid contains 1 × 1, 2 × 2, 3 × 3, 4 × 4, 5 × 5, 6 × 6, 7 × 7 and 8 × 8. All numbers are placed in the grid so that the same two numbers are never in adjacent squares, either horizontally, vertically or diagonally.
8. C: A is the same figure as E and B is the same figure as D.
9. You have drunk exactly the same amount of coffee as you have drunk milk. The cup originally contained coffee only; you have poured in one-third + one-half + one-sixth, which adds up to 1. You have therefore poured into the cup exactly the same amount of milk as the coffee and have, in effect, drunk one full cup of coffee and one full cup of milk.
10. Take one ball from bag 1, two balls from bag 2, three balls from bag 3, four balls from bag 4 and five balls from bag 5. Place all 15 balls on the scale
. The scale would register 150 × 20 = 3000 grams if all balls weighed 20 grams. If the scale registers 2998 grams, then the balls in bag 1 are light; if the scale registers 2996, the balls in bag 2 are light; if the scale registers 2994, it is the balls in bag 3; if the scale registers 2992, it is the balls in bag 4; and if the scale registers 2990, it is the balls in bag 5 that are light.
Assessment
Chapter 4 — Creativity
Test 4.0 Creativity personality test
Assessment
Total score 90 - 125
This score indicates a high degree of creativity and means that the right, creative, side of your brain appears to be extremely active.
People who are creative in nature are likely to have tried out many different pursuits during their lifetime and will continue to do so in the coming years, as they are never afraid of trying out something new. It is even possible that you have already achieved some degree of success and fulfilment within a creative environment, e.g. as a writer or designer.
It is suggested that people who have achieved a high score on this test, but who have not yet experimented with creative pursuits such as painting, garden or interior design or music, should follow their intuition and do so now, whatever their age, since they appear to have the necessary qualities, which possibly have been lying dormant, to achieve success and fulfilment in some sort of creative pursuit.
While it is difficult to be too creative, people who have scored highly on this test should not overlook the importance of developing their analytical and intellectual skills, as well as their creative talents.
Total score 65 - 89
This score indicates an average degree of creativity.
Although you may exhibit creative tendencies, a score at the lower end of this group suggests it is possible you may have neither the time nor the confidence to try out new creative pursuits. In order to become more creative it may be necessary to develop more confidence and be more relaxed about taking intellectual risks, such as sitting down and doing some drawing or painting, or making a start on writing the novel you always felt was inside you.
A score within the higher range of this group suggests that you may have already achieved some degree of creative success, but that you may also have major undeveloped talents waiting to surface and be cultivated.
Generally, however, any score within this group does suggest you are in the fortunate position of being able to balance your creative tendencies with logical and analytically formed judgements in order to turn many of your ideas into a single, realistic and workable concept.
Total score less than 65
Although this score indicates a lower than average degree of creative talents there may be many reasons for this, e.g. while you may possess a rich storehouse of ideas, it may be that you feel more comfortable when guided by set principles and traditional conventions.
Although each one of us has the potential to be creative in some way or other, it may be that, like many other people, you have not yet explored your creative talents.
It is quite likely that your skill outlets have been channelled into one particular area in order to develop a career, and as such you are a specialist who has little time to explore other avenues.
Creativity and intellect are two quite separate brain functions and it is thus entirely possible to be highly intellectual in some fields but not creative, and vice versa. It is, however, possible to train yourself to bring out latent creative talents if you have the time and inclination to do so. By exploring new avenues and learning experiences it is possible to broaden your horizons considerably, and possibly surprise yourself by discovering you possess creative talents and aptitudes of which you were previously unaware.
Test 4.1 Imaginative shapes
Assessment
You can mark this test yourself; however, it is best marked by a friend or family member. Award one mark for each recognisable sketch, provided that it is not similar to any of the other sketches. For example, if you draw a face, a second face scores no points as each sketch must have an original theme. You thus obtain marks for variety. If you are creative, you will tend to try to draw something different for each sketch.
There is no one correct answer to any of the eight sketches as for each there is any number of ideas.
Repeat the exercise as many times as you wish. Try other geometric objects or lines as a starting point.
Test 4.3 Creative logic
Answers
1. C: the rest are the same figure rotated.
2. D: so that the dot appears in the diamond and two circles.
3. B: the black dots increase by 1 each time and alternate top=bottom. The white dots decrease by 1 each time and alternate bottom=top.
4. B: every alternate circle contains a dot, every fourth circle contains lines middle of top and bottom; starting at the second circle, every alternate circle contains a right bottom line and starting at the third circle every fourth circle contains a right top line.
5. F: looking at rows and columns, in each horizontal and vertical line of dots, just one in each line of three dots appears black in each row and column.
6. B: Only lines that appear in the same position just twice in the four surrounding circles are transferred to the centre circle.
7. D: A is the same as F with black=white dot reversal. Similarly, B is the same as E and C is the same as G.
8. E: the rest are the same figure rotated.
9. E: the box with the black border is the combination of the remaining three boxes in the same row, except where lines appear in the same position in any of these three boxes, in which case they are cancelled out.
10. D: the rest are the same figure rotated.
Assessment
Test 4.4 The bucket test
Assessment
You can self-evaluate this test; however, it is best marked by a friend or family member.
The following scores should be awarded:• 2 points for any good, original, or useful answer.
• 1 point for not-so-good answers that nevertheless constitute a good attempt.
• 0 points for completely impractical answers.
• 0 points for anti-social answers, such as hitting someone over the head with the bucket.
Test 4.5 Lateral thinking test
Answers
1. E T ARead up each column in turn in each square to spell out the words ‘carpentry’, ‘redevelop’ and ‘candidate’.
2. prisoners: the letters ‘one’ appear in the sequence one * * * * * *, *one*****, **one****, *** one ***, **** one **.
3. 922: 107 + 236 = 343, 236 + 343 = 579, 343 + 579 = 922.
4. J: Each group is a set of alternate letters of the alphabet, FgHiJkL.
5. 9: the totals of the columns decrease; 9, 8, 7, 6, 5.
6. Just one: the one in the middle. No other circles appear, just arcs.
7. L: to spell BAGEL. Take the first letter on the top row with the last letter on the bottom row, etc., which plus the AGE in the middle spell out BAGEL, PAGER, LAGER, CAGEY, WAGED, EAGER and RAGES.
8. 85: reverse the numbers at the top and add 1 to the digit originally on the left.
9. G: so that the letters inside the triangle can be rearranged to spell the word ‘triangle’.
10. 9: it is the number of straight lines in each word.
Assessment
Test 4.6 Lateral thinking exercises
Answers
1.
Many people have difficulty with this type of question because they do not think of using the space outside the boundary of the dots.
2. HTSI: eigHT; SIx
3.
Look at the white squares only and the numbers 2 4 6 8 will appear.
4. The word: wholesome
5. 2: every other set is a mirror image of its adjacent set, to the left, right, above or below.
6.
7.
The numbers 4, 9 and 49 are all squares.
8. He falls off the edge inwards onto
the top of the roof, rather than onto the road below.
9.
Turn the page onto its side and look at the figures from the right-hand side. The letters K L M N will appear. The next in sequence is therefore O.
10. insatiable: the abbreviated letters of the week appear in the words: sunflower, among, statuette, Sweden, enthusiasm, befriend and insatiable
Test 4.7 Problem-solving exercises
Answers
1. Weigh yourself. Then pick up the puppy and weigh yourself again, but this time holding the puppy. The difference between the two weighings is the weight of the puppy.
2. You ask to die of old age and natural causes.
3.
4. Amy was born just before midnight on February 28 and Matthew was born just after midnight on March 1. The year in question is a leap year, so that February 29 falls in between their birthdays.
5.
Number the segments 1 — 5. Triangles are formed by the following segments or combinations:1, 2, 3, 4, 5, 1 — 2, 1 — 3, 2 — 5, 3 — 4, 2 — 5 — 4, 3 — 4 — 5, 1 — 2 — 3 — 4 — 5.
So, in total there are 12 triangles.
6.
7.
8.
9. The gladiator quickly swallows the piece of paper he picks and offers the other to the emperor, saying, ‘Show this paper to the crowd and tell me what I picked and what will be my fate’. Since the eaten one says ‘death’, in order to save face with the crowd, the emperor has to concede that the paper chosen by the gladiator says ‘freedom’.
The Complete Book of Intelligence Tests Page 10