Abstract Reasoning Young Einstein Learning Center College Entrance Test Review Simulated Exam
COMPLETING THE SERIES
1 A B C D E The first square has 25 black squares, the second has 16, the third 9, the fourth 4 and so the 5 th will have one square (reducing sequence of the square numbers 25, 16, 9, 4, 1) Also squares are removed from the right and from the bottom, so the final square will be in the top left corner. ANSWER: D
2 A B C D E The first box has two lines, the second 3, the third 4, the fourth 5 and so the fifth box will have six lines, so the answer is. . ANSWER: C
3 A B C D E The first box has 5 short lines and no long lines, the second box: 4 short & 1 long, the third box: 3 short & 2 long, the fourth box 2 short and 3 long. So each time there is one more long line and one less short line, so in the fifth box there will be 1 short and 4 long lines. ANSWER: A
4 A B C D E Each box contains 8 straight lines and a circle. Only answer C contains 8 straight lines and a circle. ANSWER: C
5 A B C D E The first box has 7 straight lines, the second 11, the third 15, the fourth 19 and so the fifth box will have 23 lines, so the answer is C ANSWER: D
6 A B C D E Triangle pattern: Triangle None Triangle… The next one should have a Triangle. All images have V. ANSWER: D
7 2 3 4 1 A B C D E Number of black circles: 1, 2, 3, 4… so the next one in the pattern should have 5. ANSWER: A
8 A B C D E Shapes are rotating COUNTERCLOCKWISE Answer should have a square at the upper right corner to continue the counterclockwise movement. ANSWER: B
9 A B C D E Number of squares: 3, 4, 5, 6… the next one should have 7. The set of 3 squares should be on top, and the other set should be at the bottom. ANSWER: A
10 4 3 8 A 2 6 B 1 4 C D 2 E Number of black circles are decreasing: 4, 3, 2, 1. Next one should have 0. Gray circles are decreasing by 2: 8, 6, 4, 2. Next one should have 0. ANSWER: B
11 f g e h A. A C. J E. L d i c ? B. B D. K 2 interspersed sequences: First pattern F E D C: decreasing by one Second pattern: G H I: increasing by one answer should follow this pattern, so. . ANSWER: C
12 y e A. S C. R E. L w g u i ? B. T D. K 2 interspersed sequences again. First one decrementing by 2, second incrementing by 2. Answer should follow first pattern. ANSWER: A
13 g ? d i j d k l d A. F C. C B. E D. H E. D Take out the d's and you get a simple alphabetical sequence! ANSWER: D
14 b c e g k ? q s A. L C. N B. M D. O E. P Prime numbers: B=2, C=3, E=5, G=7, K=11, ___, Q=17, S=19 Next one should be 13. Answer is… ANSWER: B
15 1 2 8 7 1 2 A. 5 B. 6 8 8 Alternating numbers are added. 1/8 + ½ = ___ (answer) 2/7 + 13/35 = 23/35 13 ? 35 C. 4 35 D. 11 35 ANSWER: A
16 -5 3 -2 1 10 A. 3 C. 4 B. -3 D. -4 -5 x -2 = 10 3 x 1 = __ ANSWER: A
17 1 3 A. 223 C. 243 9 27 B. 253 D. 213 81 Each number is multiplied by 3 every time to get the next number in the pattern, starts with number 1: 1 x 3 = 3 3 x 3= 9 9 x 3= 27 27 x 3= 81 81 x 3= ______ ANSWER: C
18 1 5 A. 465 C. 365 17 53 B. 485 D. 385 161 Each number is multiplied by 3 then 2 is added every time to get the next number in the pattern, starts with number 1: 1 x 3 +2 = 5 5 x 3 +2 = 17 17 x 3 +2 = 53 53 x 3 +2 = 161 x 3 = 483+2= ____ ANSWER: B
19 1 5 A. 105 C. 81 14 30 B. 95 D. 91 55 Perfect squares are added to each number to get the next one: 1+4 = 5 5+9 = 14 14+16 = 30 30+25 = 55 55+ (next perfect square is 36)= ____ ANSWER: D
SPATIAL PROBLEMS
20 Use the map to answer the question: Officer Mc. Kay starts from location ‘O’ and proceeds as follows: left onto plaza way - heading North, second left heading west, second left - heading south, first left - heading east. She proceeds for one block. What is her location? A. M B. N C. R D. P ANSWER: B
21 If you continue folding along the dotted line, which image would result? A B C D E ANSWER: E
22 Identify the figure when folded: A B C D ANSWER: A
23 Find the number of triangles in the given figure: A. 8 B. 10 C. 12 D. 14 ANSWER: D
24 Find the minimum number of straight lines required to make the given figure: A. 13 B. 15 C. 17 D. 19 ANSWER: A
25 Find out the alternative figure which contains figure (X) as its part. X 1 2 3 4 A. 1 B. 2 C. 3 D. 4 ANSWER: D
26 Find out the alternative figure which contains figure (X) as its part. X 1 2 3 4 A. 1 B. 2 C. 3 D. 4 ANSWER: A
27 Find out the alternative figure which contains figure (X) as its part. A. 1 B. 2 C. 3 D. 4 ANSWER: A
28 Find out the alternative figure which contains figure (X) as its part. A. 1 B. 2 C. 3 D. 4 ANSWER: C
29 Select the alternative which represents three out of the five alternative figures which when fitted into each other would form a complete square. A. 1, 4, 5 C. 2, 4, 5 B. 1, 2, 3 D. 2, 3, 4 ANSWER: C
30 Select the alternative which represents three out of the five alternative figures which when fitted into each other would form a complete square. A. 1, 2, 3 C. 1, 3, 5 B. 1, 3, 4 D. 3, 4, 5 ANSWER: C
31 Choose the alternative which closely resembles the water-image of the given combination. ANSWER: D
32 Choose the alternative which closely resembles the water-image of the given combination. ANSWER: B
33 Find out from the four alternatives how the pattern (X) would appear when the transparent sheet is folded at the dotted line. (X) A B C D ANSWER: D
34 Find out from the four alternatives how the pattern (X) would appear when the transparent sheet is folded at the dotted line. (X) A B C D ANSWER: B
35 -38 For the next four numbers, you will see fictitious constellations of stars. Some stars are light; others are dark. All stars are the same size. So, when some stars appear to be large, they are in the foreground of the constellation; when others appear to be small, they are in the background. Note that further stars might be hidden behind those that you see. Look at the example below. The perspective from which you see the constellation on the left is assumed to be the view from the FRONT. If the constellation would rotate in space or if you were in a spaceship orbiting it, you could see it from other perspectives, relative to the front view. For instance, you might see it from the LEFT or from the RIGHT as indicated here:
35 A. Left View C. Right View B. Top View D. Bottom View ANSWER: A
36 A. Left View C. Right View B. Top View D. Bottom View ANSWER: B
37 A. Left View C. Right View B. Top View D. Bottom View ANSWER: C
38 A. Left View C. Right View B. Top View D. Bottom View ANSWER: D
LOGICAL REASONING
39 Based on the 2 previous statements (statement i and ii), shade the letter of the only CORRECT conclusion. I. All hamburgers are meals II. Some cows are hamburgers Conclusion: A. All meals are cows B. At least some meals are cows C. No cows are meals D. None of the meals are cows M H C ANSWER: B
40 Based on the 2 previous statements (statement i and ii), shade the letter of the only INCORRECT conclusion. I. All cities have houses II. All countries have cities Conclusion: A. All houses have countries B. All countries have houses C. Not all houses have countries D. No valid conclusion is possible H Ci C ANSWER: A
41 Based on the 2 previous statements (statement i and ii), shade the letter of the only CORRECT conclusion. I. Some cars are four wheelers II. All cars are three wheelers Conclusion: A. No three wheelers are four wheelers B. All four wheelers are three wheelers C. At least some three wheelers are four wheelers D. No valid conclusion is possible 4 C 3 ANSWER: C
42 In a horse race: Hill Royal came in ahead of Trigger. Hill Royal finished after Black Beauty. Copenhagen beat Black Beauty but finished after Bucephalus. Where did Copenhagen finish? A. B. C. D. E. First Second Third Fourth Fifth Bucephalus Copenhagen Black Beauty Hill Royal Trigger ANSWER: B
43 You take seven children to a toy shop to buy each a soft toy. The toy shop only has one of each type so you ask the children their preferences. You decide to give each child one of their preferred toys. Which animal will you give Jezebel? NAME: James Josh Jezebel Jamelia Janine Jasbeet Jason A. B. C. D. E. TOY PREFERENCES: Wombat Panda Gorilla Panda Donkey Dog Panda Donkey Kitten Panda Donkey Dog Wombat Gorilla Donkey Panda Dog Wombat Gorilla Dog Panda Donkey Wombat Dog Kitten Rat Kitten The trick here is to realize that you can ignore the children with more than four choices. Josh, Jamelia and Jasbeet all have only two or three choices and all want a panda, donkey or dog, so they must each get one of these. Jezebel also wants a panda, donkey or dog, but she would also accept a kitten, so she must be given this, if each child is to be allowed a preferred animal. ANSWER: E
44 Debbie, Kimi and Michael have Ferraris. Michael also has a Reliant Robin. Jensen has a Mercedes and a Model T. Rubens also has a Mercedes. Debbie also has a Bugatti Veyron. Rubens has just bought a Toyota Prius. Who has the fewest cars? Ferrari A. B. C. D. E. R. Robin Mercedes Model T. Bugatti Debbie Kimi Michael Jensen Rubens ANSWER: B Prius
45 Jensen, Lewis and Mika need to be able to run 100 m in under 12. 5 seconds to qualify for a championship. Lewis and Mika run faster than Jensen's best time for the 100 m is 13. 1 seconds. Which of the following MUST be true? A. B. C. D. E. Only Jensen qualify Jensen doesn’t qualify L ewis and Mika both qualify Jensen qualifies No one qualifies ANSWER: B
46 An old treasure map has the following instructions: Stand next to the black rock and face West. Walk 20 yards and then turn 90 degrees clockwise. Walk another 10 yards and then turn 45 degrees anticlockwise. Walk another 15 yards, reverse your direction and walk 5 yards back. Turn 135 degrees clockwise and walk another 10 yards. In which direction are you now facing? A. B. C. D. E. North South East West South East Ignore the distances (these are red herrings) , the direction you face is all that matters! W, N, NW, SE, W ANSWER: D
47 Athos, Porthos and Aramis live in three adjoining houses. Aramis has a black cat called d'Artagnan, Porthos has a white dog whereas Athos has a red herring. Porthos has a neighbor with a red door. The owner of a four legged animal has a blue door. Either a feline or fish owner has a green door. Aramis and Porthos are not neighbors. Whose door is red? A. B. C. D. E. Athos Porthos Aramis D’Artagnan None of the above Porthos, white dog, blue door Athos, red herring, red door Aramis, black cat, green door ANSWER: A
48 Mrs Krashem, a driving instructor, has to arrange bookings for some of her pupils. She has 8 new pupils who wish to book either a morning or afternoon of a particular day. These are 2 hour introductory lessons, so she only sees one pupil each morning or afternoon. Ms Banger is only available Tuesday AM but Mr Bumpem can make any time on a Wednesday. Mrs Exhaust is free on Tuesdays all day but Mr Hilstart is only free Wednesday afternoons. Ms Boot is only available Friday AM whereas Miss Bonnet can only make Saturday PM. Mrs Speed is available all day Fridays whereas Mr Parker can make any time on a Saturday. Which of the following must both have MORNING appointments? A. B. C. D. E. Mr Bumpen and Mrs Exhaust and Mr Parker and Mrs Speed and Mrs Exhaust Mr Bumpen and Mr Parker ANSWER: E
49 How many degrees are there between the two hands of a clock at 6. 30 am? A. B. C. D. E. O degrees 5 degrees 10 degrees 15 degrees 30 degrees Minute hand is at 180 degrees Hour hand is at 180 + 360/24 degrees as it has moved half an hour further = 180 +15 degrees. Therefore difference in angle = 15 degrees ANSWER: D
50 It is 4. 30 am and your alarm goes off. You crawl sleepily out of bed. You have a job interview to go to that day and you must leave by 5 am to catch the train as the interview is being held 150 miles away. Suddenly all the lights go off. There has been a power failure. It is still pitch dark outside and you have no other light available. You have 6 brown socks and 6 pink socks in your drawer, all mixed up and identical in all but color. How many socks must you take from the drawer to be sure of taking a matching pair of the same color? A. B. C. D. E. 2 3 4 5 6 Once you have taken two socks from the drawer (the possible combinations are BB, PP or BP), the third sock you remove must give you a pair of either brown or pink. By the way, you didn't get the job. ANSWER: B
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