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Logical Reasoning Recap Trainer Handout
Aptitude (10APT21)
Visvesvaraya Technological University
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LOGICAL REASONING RECAP
NUMBER SERIES
- Find the missing term. 1, 2, 3, 6, 11, 20, 37, 68,? a. 125 b. 126 c. 124 d. 105 Answer: a. 125 Solution: Beginning with 6, each term of the series is the sum of the previous 3 terms. Hence, the next term would be 125.
- In the following number series a wrong number is given. Find out the wrong number. 31, 22, 30, – 32, – 89, – 174 a. 22 b. 30 c. - 32 d. - 89 Answer: b. 30 Solution: Obviously 30 is the misplaced number because all other terms are in a reducing series here.
- In the following number series a wrong number is given. Find out the wrong number. 60, 26, 86, 112, 198, 310, 528 a. 112 b. 198 c. 310 d. 528 Answer: d. 528 Solution: The logic of this series is that the sum of two numbers makes the third one in the series. This we can observe by seeing 60+26=86, 86+112=198 and so on. The only number that does not satisfy this logic is 198+310, which should be 528 and not 508. Thus, 528 is the wrong number in the series.
- In the following number series a wrong number is given. Find out the wrong number. 300, 421, 592, 815, 1104, 1465 a. 421 b. 1104 c. 815 d. 592 Answer: c. 815 Solution: The logic of the additions is 121,171, 221, 291, 361 and so on. Thus, the number series should be 300, 421, 592, 813, 1104, 1465. The number 815 is misplaced in the above series.
- Obtain the missing term. 12, 15, 19, ?, 30, 37 a. 35 b. 34 c. 37 d. 24 Answer: d. 24 Solution: The series follows the logic of +3, +4, +5, +6 and +7.
Hence, the missing term would be 19 + 5 = 24.
- Obtain the missing term. 4, 12, 36, 108,?,
- a. 226 b. 324 c. 423 d.
- Answer: b.
- 4 × 3 = Solution: The given number series is based on the following pattern:
- 12 × 3 =
- 36 × 3 =
- 108 × 3 =
- 324 × 3 =
- a. 27 b. 29 c. 31 d. 7. Obtain the missing term. 1, 3, 7, 13, 21,?
- Answer: c.
- 1 + 2 + 0 = Solution: The given number series is based on the following pattern:
- 3 + 2 + 2 =
- 7 + 2 + 4 =
- 13 + 2 + 6 =
- 21 + 2 + 8 =
- Obtain the missing term. 4, 10, 18, ?,
- a. 24 b. 28 c. 32 d.
- Answer: b.
- 4 + 6 = Solution: The given number series is based on the following pattern:
- 10 + 8 =
- 18 + 10 =
- 28 + 12 =
- Calculate the missing term. 120, 170. 70, 120, 20, ?, -
- a. 50 b. 70 c. 60 d.
- Answer: b.
- 120 + 50 = Solution: The series follows the logic of +50, - 100, +50, - 100.
- 170 - 100 =
- 70 + 50 =
- 120 - 100 =
- 20 + 50 =
- 70 - 100 = -
- 8748a. 324 b. 972 c. 2926 d. 10. Find the number which does not belong to the series: 36, 108, 324, 972, 2926.
- Answer: c.
LETTER SERIES
- Find the relevant answer. GFE, NML, SRQ,? , DCB a. PQR b. JAK c. MDN d. XWV Answer: d. XWV Solution: This series consists of letters in a reverse alphabetical order
- Find the relevant answer. J2KL, , JKL4, J5KL, JK6L a. JK3L b. J3KL c. JKL3 d. 3JKL Answer: a. JK3L Solution: Because the letters are the same, concentrate on the number series, which is a simple 2, 3, 4, 5, 6 series, and follows each letter in order.
- Find the relevant answer. DAB, ECD, FEF, , HIJ a. GIH b. GGH c. GHI d. GIJ Answer: b. GGH Solution: There are two alphabetical series here. The first series is with the first letters only: DEFGH. The second series involves the remaining letters: AB, CD, EF, GH, IJ
- Which letter should be the tenth letter to the left of the ninth letter from the right, if the first half of the alphabet of English are reversed? a. D b. F c. E d. I Answer: b. F Solution: We are looking for the 19th letter from the right in the series: MLKJIHGFEDCBA NOPQRSTUVWXYZ. The letter would be F as can be counted from the above series.
- LADAKH : KZCZJG :: SINGAPORE :? a. RHMFZONQD b. HMFRZOQDN c. RMFHNOZQD d. HNOQDZMFR Answer: a. RHMFZONQD Solution: Each letter of the first group moved one step backward to obtain the corresponding letters of the second group.
- HERO : GIDFQSNP :: HEROINE :? a. JMODFGIDFQSNPH b. GIDFQSNPHJMODF c. GDIFSQPHNODJMF d. GIDSFQHONDMFJP Answer: b. GIDFQSNPHJMODF Solution: Each letter of the first group is replaced by the two letters one come after it and one that comes before it in the second group.
- GSWT : WTSG :: AKLS :? a. LSAK b. AKLS c. LSKA d. SALK Answer: c. LSKA Solution: The 1st, 2nd, 3rd, 4th letters of the second group are respectively the 3rd, 4th, 2nd and 1st letters of the 1st group.
- Study the following information carefully to answer the questions given below:
S Q A 5 N % T 7 B 4 # J E $ 2 T D * 1 8 H 3 U @ 9 F W © K
How many such consonants are there in the above arrangement, each of which is either immediately precededby a vowel or immediately followed by a symbol but not both? a. None b. One c. Two d. Three Answer: b. One Solution: 5N% is the only instance of a consonant either followed by a symbol or preceded by a vowel but not both. 9. Which of the following will come in place of the question mark (?) in the following sequence? 16D7, 18G10, 21KI4, 25P19,? a. 30V20 b. 30V25 c. 30V24 d. 29V Answer: b. 30V Solution: There are three series in the sequence. The numbers to the left of the letter — 16, 18, 21, 25 are increasing continuously by 1 more than the previous increase, i., the series of increases in these numbers are + 2, +3, +4 and the next number should be +5; thus 25 +5 = 30. The letters DGKP form a series where 2, 3 and 4 letters are skipped every time. Hence, the next letter would be V. Similarly, 7, 10, 14, 19 would give 25 as the next term. Thus, the correct answer would be 30V25. 10. MAIN : NOBCJKOP :: NOPE : a. PPOQFGQR b. POPQFGQR c. OPPQQRFG d. GOPPRFQQ Answer: c. OPPQQRFG Solution: Each letter of the first group is replaced by the two letters which comes after the main letter. For example: M--NO A--BC I--JK N--OP
- In a classroom, there are 5 rows, and 5 children P, Q, R, S and T are seated one behind the other in 5 separate rows as follows: P is sitting behind R, but in front of Q. R is sitting behind T. S is sitting in front of T. The order in which they are sitting from the first row to the last is a. STRPQ b. QPRTS c. PRQST d. PQTSR Answer: a. STRPQ Solution: 1st Row = S 2nd Row = T 3rd Row = R 4th Row = P 5th Row = Q
- Peter, Quro, Russel, Starc and Tuco are sitting in a straight line facing North. Peter sits next to Starc but not to Tuco. Quro is sitting next to Russel who sits on the extreme left corner. Who sits to the left of Starc if Tuco does not sit next to Quro? a. Peter b. Quro c. Russel d. Tuco Answer: a. Peter Solution:
- In a circular arrangement of 3 boys (B1, B2 and B3) and 3 girls (G1, G2 and G3) sitting for a dinner successively, what will be the position of G3 and B3, if no two girls sit together? a. 4 th and 5 th b. 5 th and 6 th c. 3 rd and 4 th d. 3 rd and 6 th Answer: b. 5th and 6th Solution:
Directions for 8 - 10: Study the following information carefully and answer the questions given below: M, N, P, R, T, W, F and H are sitting around a circle facing the centre. P is third to the left of M and second to the right of T. N is second to the right of P. R is second to the right of W, who is second to the right of M. F is not an immediate neighbour of P. 8. Who is to the immediate right of P? a. H b. F c. R d. Data Inadequate Answer: a. H 9. Who is to the immediate left of R? a. P b. H c. W d. T Answer: d. T 10. In which of the following is the first person sitting in between the second and the third person? a. NHM b. PHN c. TRP d. TWF Answer: a. NHM
Solution: Just subtracting 2 for all the letters. HKUJ = F(H-2) I(K-2) S(U-2) H(J-2) EAT= C(E-2) Y(A-2) R(T-2) 6. In a certain code FORGET is written as DPPHCU, DOCTOR is written as BPAUMS. How can TEACHER be written in that code? a. RFYDFFP b. FFFRDYP c. RYFPFFD d. DFFRYFP Answer: a. RFYDFFP Solution: The pattern is as follows: - 2, + Odd places: - 2 Even places: + 7. If EARTHQUAKE is coded as EKAUQHTRAE then ELECTRONICS will be coded as: a. ESCINOTCELR b. TCELERSCINO c. SCINORTCELE d. ELESCINORTC Answer: c. SCINORTCELE Solution: EARTHQUAKE = EKAUQHTRAE Reverse order of letters. Therefore, ELECTRONICS = SCINORTCELE 8. If ‘A’ = 26, SUN = 27, then LIE=? a. 52 b. 55 c. 58 d. 60 Answer: b. 55 Solution: Position of A from backward counting is 26. When you count from Z - Z= Y becomes 2. So, SUN = 8+6+13= LIE = 15+18+22 = 55 9. In a certain coded language, ‘hit ka tom’ is written as ‘tie the shoes’, ‘ka lo fod’ is written as ‘shoes of leather’ and ‘lo tin hit’ is written as ‘leather and tie’. How is ‘the’ written in this code language? a. hit b. tom c. tom or ka d. ka Answer: b. tom Solution: Shoes are common in two statements - > ka tie is common - > hit Hence, the means tom 10. In a certain code language, ‘Biscuits are nice’ is written as ‘lo pur tan’, ‘Movies are good’ is written as ‘tan fu
gil’ and ‘Biscuits contain sugar’ is written as ‘pur st mo’. What is the code for ‘contain’ in that code language? a. tan b. st c. mo d. st or mo Answer: d. st or mo Solution: Biscuits are written twice - Code common between two statements are "pur."Are written twice - Code common between two statements are "Tan" Hence contain can be either st or mo
DATA SUFFICIENCY
Directions to Solve: In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and Give answer
- If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
- (B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
- (C) If the data either in statement I alone or in statement II alone are sufficient to answer the question
- (D) If the data given in both statements I and II together are not sufficient to answer the question and
- (E) If the data in both statements I and II together are necessary to answer the question.
- Question 1 How many children are there in the row of children facing North? Statements: I who is fifth from the left end is eighth to the left of Ashish who is twelfth from the right end. II is fifth to the left of Nisha who is seventh from the right end and eighteenth from the left end. A alone is sufficient while II alone is not sufficient B alone is sufficient while I alone is not sufficient C. Either I or II is sufficient D I nor II is sufficient E. Both I and II are sufficient Solution: Option C
Solution: Option E From I, we know that the serials were screened on 23rd, 24th, 25th and 26th. Clearly, D was screened second i. on 24th, Wednesday. From II, we know that one serial was screened between A and B. So, A and B were screened first and third, i. on 23rd and 25th. But, A was not screened on 25th. So, A was screened on 23rd and B on 25th. Thus, C was screened on 26th, Friday. 4. Question 4 How many speeches were delivered in the two days' programme? Statements: I. 18 speakers were invited to give at least one speech (maximum of two speech), out of which one-sixth of the speakers could not come. II. One-third of the speakers gave two speeches each. A. I alone is sufficient while II alone is not sufficient B. II alone is sufficient while I alone is not sufficient C. Either I or II is sufficient D. Neither I nor II is sufficient E. Both I and II are sufficient Solution: Option E From I, we find that number of speakers who attended programme =18-(1/6) of 18 = 15. From II, we find that one-third of 15 i. 5 speakers gave 2 speeches each, while each of the remaining 10 speakers delivered only one speech. So, total number of speeches delivered = (5 x 2 + 10 x 1) = 20. 5. Question 5 Among M, N, D, P and K, who earns more than only the least earner among them? Statements: I. N earns more than M and P but less than only D. II. M earns more than P who earns less than K. A. I alone is sufficient while II alone is not sufficient B. II alone is sufficient while I alone is not sufficient C. Either I or II is sufficient D. Neither I nor II is sufficient
E. Both I and II are sufficient Solution: Option D From I, we have: N > M, N > P, D > N. Thus, we have: D > N > M > P or D>N> P>M. But, from II, M earns more than P i. D > N > M > P. Also, since P earns less than K and N earns less than only D, so we have: D>N>K>M>P or D>N>M> K > P. Hence, either K or M earns more than only the least earner i. P. 6. Question 6 The chairman of a big company visits one department on Monday of every week except for the Monday of third week of every month. When did he visit the purchase department? Statements: I. He visited Accounts department in the second week of September after having visited purchase department on the earlier occasion. II. He has visited purchase department immediately after visiting stores department but before visiting Account department. A. a B. b C. c D. d E. e Solution: Option A From statement I we can conclude that the chairman visited purchase department on Monday of the first week of September. So I alone is sufficient. 7. Question 7 A,B,C,D and E are sitting in a row. B is between A and E. Who among them is in the middle? Statements: I. A is left of B and right of D II. C is at the right end A. a B. b C. c D. d E. e Solution: Option E Clearly we have the order : A,B,C From I we have the order D,A,B,E From II we get the complete sequence as D,A,B,E,C. clearly B is in middle. So both I and II are required
(2) x cannot be divided evenly by an odd number other than 1. This statement implies that x is some power of 2: 2, 4, 8, 16, ... Not sufficient. (1)+(2) Still not sufficient. 10. Question 10 What are the speeds two trains travels with 80 yards and 85 yards long respectively? (Assume that former is faster than later) Statements: I take 75 seconds to pass each other in opposite direction. II. they take 5 seconds to pass each other in same direction A. a B. b C. c D. d E. e Solution: Option E let the speeds be x and y when moves in same direction the relative speed, x-y = 85 - 80/37 = 0 ..... (l) when moves in opposite direction the relative speed, x+y = 165/75 = 2.. (ll) now, equation l + equation ll gives, 2x = 0+2 = 2 => x=1. from equation l, x-y=0 => y = 1.165-0 = 1. therefore the speeds are 1 yards/sec and 1 yards/sec.
SYLLOGISMS
DIRECTIONS for question 1 - 4: Two statements are given followed by two conclusions I and II. You have to consider the two statements to be true even if they seem to be at variance from commonly known facts. You have to decide which one of the given conclusions are definitely drawn from the givenstatements:
Statements: Some peons are poor. X is poor. Conclusions: I. X is a peon. II. X has a large family. a. Only I follows b. Only II follows c. Both I & II follow d. Neither I nor II follows Answer: d. Neither I nor II follows Solution: The first premise is particular Affirmative (I-type). The second premise is Universal affirmative (A-Type). We can align the premises by converting the first premises by converting the first premise and changing their order. Thus, we know that, A + I = No conclusion
Statements: All basketball players are tall men. All basketball players are athletes. Conclusions: I. All tall men are basketball players. II. All athletes are basketball players. a. I alone can be drawn b. Both can be drawn c. Both cannot be drawn d. II alone can be drawn Answer: c. Both cannot be drawn
Statement: Population is the greatest pollutant. Assumptions: I. Increased population is the greatest resource. II. Illiterate mass leads to dirt and degradation. a. Only I is implicit b. Only II is implicit c. Both I and II are implicit d. Neither I nor II is implicit Answer: d. Neither I nor II is implicit Solution: Neither assumption I nor II is implicit in the statement. Any resource is exploited by human itself. Therefore, population is the greatest pollution.
Statement: Many people feel nervous when giving a talk before a group. Conclusions: I. Many people can talk confidently before a group. II. Very few people can talk confidently before a group. a. Only I follows b. Only II follows c. Neither I nor II follows d. Both I and II follow Answer: d. Both I and II follow Solution: Obviously, both the conclusions follow. If many people can talk confidently before a group then very few people can also talk confidently before a group.
No monkey can sing but some monkeys can talk. If this statement is correct, then which of the following is correct? a. Some monkeys may sing b. All monkeys can’t sing c. All monkeys can’t talk d. All monkeys can talk Answer: b. All monkeys can’t sing Solution: Clearly, all monkeys cannot sing.
A conclusion followed by statements I, II and III is given. Which one of the four alternatives is correct? Conclusion: Many drug addicts were arrested Statements: I. Taking drugs is a crime. II. One who commits a crime can be arrested. III. Many people take drugs regularly. a. All the 3 statements taken together brings to the conclusion. b. Only I and II statements bring to the conclusion. c. Only II and III bring to the conclusion d. Data is insufficient to draw the conclusion. Answer: a. All the 3 statements taken together brings to the conclusion. Solution: We are arriving at the conclusion by combining three pieces of information given in the three statements.
A statement is given followed by four alternative arguments. Select the alternative which is most appropriate. Statement: Is it necessary that education should be job oriented? Arguments: I. Yes, the aim of education is to prepare persons for earning. II. Yes, educated person should stand on his own feet after completion of education. III. No, education should be for sake of knowledge only. IV. No, one may take up agriculture where education is not necessary. a. Only I and II arguments are strong b. Only III and IV arguments are strong c. Only I argument is strong d. Only I and III arguments are strong Answer: a. Only I and II arguments are strong Solution: Only I and II arguments are strong. Education is meant for both knowledge and securing a job. Any skill is acquired to use it purposefully.
Logical Reasoning Recap Trainer Handout
Course: Aptitude (10APT21)
University: Visvesvaraya Technological University
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