SSC CGL Tier 1 2019 General Intelligence & Reasoning Questions with Solutions

Explanation

Let the amount received by one boy be B, one man be M, and one woman be W. Based on the problem, we have the following relations: M = 1.5B = ³⁄₂B W = M + B = ³⁄₂B + B = ⁵⁄₂B

The total amount of 820 is divided among 6 men, 8 women, and 12 boys. This is expressed as: 6M + 8W + 12B = 820

Substituting the values of M and W in terms of B: 6(³⁄₂B) + 8(⁵⁄₂B) + 12B = 820 9B + 20B + 12B = 820 41B = 820 B = ⁸²⁰⁄₄₁ = 20

The total amount received by 8 women is represented by the term 8W in the equation: 8W = 8 × (⁵⁄₂B) = 20B Substituting B = 20: 20 × 20 = 400

Explanation

The logical sequence follows the chronological stages of book or document production. The process begins with Writing (1), where the author creates the initial manuscript. After the draft is completed, it undergoes Editing (5) to refine the content, correct errors, and improve the quality of the text. Once the manuscript is finalized, the next step is Printing (4), where physical copies of the work are manufactured. After printing, the work moves to Publishing (3), representing the formal release and branding of the book by a publisher. The final stage is Distributing (2), where the published copies are sent to bookstores, libraries, or directly to consumers for final consumption.

Explanation

The coding follows a direct letter-to-digit mapping based on the provided examples. By comparing the letters in POSTER (592314) and DARK (8647), we can extract the corresponding value for each letter: S = 2, T = 3, R = 4, O = 9, K = 7, and E = 1. Note that the digit for R is consistent in both given words as 4. Placing these digits in the sequence required for the word STROKE yields the code 234971.

Explanation

The relationship between the letter-clusters is determined by a specific numerical shift applied to the position of each letter in the English alphabet. For the first pair, JKLM and HLKO, the pattern of changes is -2, +1, -1, and +2. This is calculated as J(10) - 2 = H(8), K(11) + 1 = L(12), L(12) - 1 = K(11), and M(13) + 2 = O(15).

Applying this identical pattern to the third letter-cluster PQRS yields the following results: The first letter P(16) - 2 = N(14). The second letter Q(17) + 1 = R(18). The third letter R(18) - 1 = Q(17). The fourth letter S(19) + 2 = U(21).

Mapping these numerical values back to their alphabetical counterparts results in the cluster NRQU.

Explanation

The numbers in the set (12, 16, 28) follow the logic where the sum of the first and second numbers equals the third number: 12 + 16 = 28. Furthermore, the numbers are in the ratio 3 : 4 : 7, as 12/4 = 3, 16/4 = 4, and 28/4 = 7. The set (18, 24, 42) follows this same pattern precisely. The sum of the first two numbers results in the third number: 18 + 24 = 42. Additionally, dividing each number in this set by their highest common factor, 6, yields the same ratio: 18/6 = 3, 24/6 = 4, and 42/6 = 7.

Explanation

By interchanging the signs - and +, the original equation 12 - 6 ÷ 12 × 6 + 6 = 9 transforms into 12 + 6 ÷ 12 × 6 - 6 = 9. Applying the BODMAS rule, we first perform the division operation: 6 ÷ 12 = 0.5. Substituting this value into the equation, we get 12 + 0.5 × 6 - 6. Next, we perform the multiplication: 0.5 × 6 = 3. This leaves the expression as 12 + 3 - 6. Finally, completing the addition and subtraction results in 15 - 6 = 9. Since the calculated value matches the right-hand side of the equation, the interchange is correct.

Explanation

Conclusion II follows directly from the first statement "Some students are players" by the rule of conversion, which states that if Some A are B, then Some B are A. Regarding conclusions I and III, the statements provide no definite relationship between students and athletes because the middle term players is not distributed in either of the particular affirmative statements. However, conclusion I (Some students are athletes) and conclusion III (No student is an athlete) form a complementary pair of I and E type propositions. Since these two conclusions cover all possible logical possibilities between the sets of students and athletes, one of them must necessarily be true. Therefore, conclusion II follows along with the disjunction of conclusions I or III.

Explanation

166 is the only number in the group that is not divisible by 11. The divisibility rule for 11 states that the difference between the sum of the digits at odd positions and the sum of the digits at even positions must be 0 or a multiple of 11. For the number 166, the sum of the digits at odd positions is 1 + 6 = 7 and the digit at the even position is 6; the difference is 7 - 6 = 1, which is not divisible by 11. The other numbers in the set (132, 341, and 209) all satisfy this rule, leaving 166 as the odd one out.

Explanation

The coding language follows a pattern where the letters of the word are shifted in pairs. The first and third pairs of letters are shifted backward by one position in the alphabet (-1), while the second and fourth pairs are shifted forward by one position (+1).

For the word TEACHING: Pair 1 (TE): T - 1 = S, E - 1 = D Pair 2 (AC): A + 1 = B, C + 1 = D Pair 3 (HI): H - 1 = G, I - 1 = H Pair 4 (NG): N + 1 = O, G + 1 = H Concatenating these results in SDBDGHOH.

Applying the same logic to the word BOOKWORM: Pair 1 (BO): B - 1 = A, O - 1 = N Pair 2 (OK): O + 1 = P, K + 1 = L Pair 3 (WO): W - 1 = V, O - 1 = N Pair 4 (RM): The letters are shifted by +1. R + 1 = S and M + 1 = N. In the code sequence for option d, these resulting letters are presented as N and S.

This pattern generates the sequence ANPLVNNS, making d the correct choice.

Explanation

The given sequence follows a logic where the difference between consecutive terms increases by a constant value of 4, forming a series of multiples of 4.

The difference between the first and second terms is 11 - 7 = 4. The difference between the second and third terms is 19 - 11 = 8. The difference between the third and fourth terms is 31 - 19 = 12.

The differences follow the pattern 4 × 1, 4 × 2, 4 × 3, …. Therefore, the next difference in the sequence must be 4 × 4 = 16. Adding this difference to the fourth term gives 31 + 16 = 47.

To verify the pattern, the next difference should be 4 × 5 = 20. Adding 20 to the calculated term results in 47 + 20 = 67, which matches the final term provided in the series.

Explanation

The pair Garden: Lade is the odd one out because it presents a mismatch between a location and its typical functional object. A ladle (often appearing as lade in these contexts) is a kitchen utensil characterized by a long handle and a deep bowl used for serving liquids such as soup or sauce. It is not an item or fixture naturally associated with or used in a garden. The classification logic in the other pairs relies on a consistent relationship where the second term is a standard object or fixture found within the specific room or area mentioned in the first term. This pair fails to maintain that relationship by placing a kitchen tool in an unrelated outdoor setting.

Explanation

The numbers in the set (6, 9, 18) follow the ratio 2 : 3 : 6. This is obtained by dividing each term by their greatest common divisor, 3, resulting in 6/3 = 2, 9/3 = 3, and 18/3 = 6. Alternatively, the second number is 1.5 times the first number (6 × 1.5 = 9) and the third number is 3 times the first number (6 × 3 = 18).

The set (14, 21, 42) follows this same mathematical pattern. Dividing each term by the common factor of 7 yields the same ratio: 14/7 = 2, 21/7 = 3, and 42/7 = 6. The multiplicative relationship also holds as 14 × 1.5 = 21 and 14 × 3 = 42.

Explanation

Intermission refers to a temporary pause or a short interval between the parts of a performance, movie, or event. It signifies a transition within an ongoing activity that is intended to resume, rather than a permanent conclusion. This word is the odd one out because it describes a mid-event break, whereas the other words in the set all share the common theme of finality, completion, or the definitive end of a process.

Explanation

The sequence follows the natural and meteorological progression of a weather event leading to a disaster. It begins with Low Pressure (5), which is the primary atmospheric condition required for air to rise and cool. This cooling leads to the formation of a Cloud (1). As the moisture in the clouds condenses further, it results in Rain (4). During or immediately following the rain, the interaction of sunlight with water droplets in the air produces a Rainbow (2). If the rainfall is extremely heavy or prolonged, it leads to a Flood (6). The final consequence of such a massive overflow of water is Devastation (3). This chronological and causal order logically connects the atmospheric cause to the eventual environmental impact.

Explanation

The logic followed in the letter-clusters is based on the concept of opposite letters in the English alphabet. Two letters are considered opposites if the sum of their positional values is equal to 27.

In the first pair C DAF : XWZU, the transformation is as follows: C (3) corresponds to X (24) since 3 + 24 = 27. D (4) corresponds to W (23) since 4 + 23 = 27. A (1) corresponds to Z (26) since 1 + 26 = 27. F (6) corresponds to U (21) since 6 + 21 = 27.

Applying the same logic to the third letter-cluster DEFC: D (4) corresponds to W (23). E (5) corresponds to V (22). F (6) corresponds to U (21). C (3) corresponds to X (24).

The resulting letter-cluster is WVUX.

Explanation

The relationship in the given pair is that of a creator and its creation. An author is a person who creates or produces a book through their work. Similarly, a spider is a living creature that creates or produces a web as a result of its natural labor. In both pairs, the first word represents the agent and the second word represents the specific product generated by that agent.

Explanation

The relationship is based on a specific positional rearrangement of the letters within the word. In the first pair, the letters of LAMP are rearranged to form PALM according to the pattern where the fourth letter moves to the first position, the second letter remains in the second position, the first letter moves to the third position, and the third letter moves to the fourth position. By applying this same transformation to the word MALE, the fourth letter E moves to the first position, the second letter A remains in the second position, the first letter M moves to the third position, and the third letter L moves to the fourth position. This process results in the word EAML.

Explanation

The letter-cluster DGKL consists of letters at the 4th, 7th, 11th, and 12th positions of the English alphabet. The numerical gaps between these consecutive letters are +3 (7 - 4), +4 (11 - 7), and +1 (12 - 11). This sequence of differences deviates from the consistent pattern of +4, +7, +4 established by the other clusters in the set. To follow the common logic, the first letter should be shifted forward by 4 places, the second by 7 places, and the third by 4 places. Since DGKL follows a +3, +4, +1 progression instead, it is the odd one out.

Explanation

The relationship between the two terms is based on their physical structure, where the second term represents the upper interior surface or roof of the first term. In a room, the ceiling is the top internal boundary. Similarly, in the human mouth, the palate (specifically the hard and soft palate) constitutes the roof or the upper interior surface.

Explanation

Based on the provided operator substitutions, the expression 72 × 9 - 3 ÷ 8 + 2 is rewritten by replacing × with ÷, - with ×, ÷ with +, and + with -.

The new expression is: 72 ÷ 9 × 3 + 8 - 2

Following the BODMAS rule for the order of operations: The division 72 ÷ 9 equals 8. The product 8 × 3 equals 24. The sum 24 + 8 equals 32. The difference 32 - 2 equals 30.

Explanation

The logic followed in the given number pair 35:6 is that the first number is obtained by squaring the second number and then subtracting 1. The mathematical relation is x = y² - 1, where y is the second number and x is the first number. Substituting the values from the given pair, we get 6² - 1 = 36 - 1 = 35.

Applying this same logic to the selected pair 120:11, we use y = 11. Calculating 11² - 1 gives 121 - 1 = 120, which matches the first number in the pair.

Explanation

The series consists of 18 characters which can be divided into six groups of three letters each. By substituting the letters b, d, c, b, and a into the respective blanks, the sequence follows a clear alternating pattern of two distinct triplets: abc and adb. The resulting sequence is abc adb abc adb abc adb. This pattern of periodicity ensures that every odd-numbered group is abc and every even-numbered group is adb, maintaining logical consistency throughout the entire series. Specifically, the first blank completes the first group abc, the second completes adb, the third completes abc, the fourth completes adb, and the final blank completes the last adb group.

Explanation

The first statement establishes that every pond is a pool, effectively making the set of ponds a subset of the set of pools. The second statement confirms that an intersection exists between the set of wells and the set of ponds. Since any item belonging to the pond category is automatically part of the pool category, any item that is both a well and a pond must also be a pool. This logical link confirms that at least some wells are pools. This derivation validates conclusion II. No other conclusion can be drawn with certainty because the premises do not provide information regarding the total number of pools in relation to wells, nor do they guarantee that any ponds exist outside the category of wells.

Explanation

The coding logic is based on rearranging the positions of the letters in the word. First, assign numerical positions to the letters in the word SEDATIVE: S(1), E(2), D(3), A(4), T(5), I(6), V(7), and E(8). The code ATDESEVI is obtained by rearranging these positions in the sequence 4, 5, 3, 2, 1, 8, 7, 6.

Applying this same positional mapping to the word PERSONAL: 1:P, 2:E, 3:R, 4:S, 5:O, 6:N, 7:A, 8:L

Following the sequence 4-5-3-2-1-8-7-6: 4th letter: S 5th letter: O 3rd letter: R 2nd letter: E 1st letter: P 8th letter: L 7th letter: A 6th letter: N

Combining these letters in the specified order results in the code SOREPLAN.

Explanation

The letter cluster GHTV is the odd one out because it fails to follow the alphabetical position pattern of +1, +13, +1. In the English alphabet, the numerical positions for the letters in this cluster are G(7), H(8), T(20), and V(22). The progression in this cluster consists of an initial increase of 1 (7 to 8), followed by an increase of 12 (8 to 20), and finally an increase of 2 (20 to 22). This sequence deviates from the uniform pattern where the first and second letters are consecutive, the second and third letters have a gap of 13, and the third and fourth letters are consecutive.

Explanation

The coding logic follows a simple alphabetical shift where each letter is replaced by the character immediately preceding it in the English alphabet (n - 1).

For the word VERY: V - 1 = U E - 1 = D R - 1 = Q Y - 1 = X

Applying the same logic to each letter of the word URGENT: U - 1 = T R - 1 = Q G - 1 = F E - 1 = D N - 1 = M T - 1 = S

By performing this -1 shift on the letters of the word, the resulting sequence of characters is TQFDMS.

Explanation

According to the first statement, the entire set of knives is contained within the set of instruments (K ⊆ I). The second statement asserts that there is an intersection between the set of cutters and the set of knives (C ∩ K ≠ ∅). Because every knife is also an instrument, any object that is both a cutter and a knife is guaranteed to be an instrument as well. This logical link ensures that there is at least one element common to both cutters and instruments, which validates conclusion I. Conclusion II cannot be definitively concluded because the statements only provide information about some cutters being knives, not the reverse. Conclusion III is false because it contradicts the premise that all knives are instruments.

Explanation

The series follows a pattern where the difference between consecutive terms increases according to the formula n² + 1, starting from n = 1.

The difference between the first two terms is 5 - 3 = 2, which is 1² + 1. The difference between the second and third terms is 10 - 5 = 5, which is 2² + 1. The difference between the third and fourth terms is 20 - 10 = 10, which is 3² + 1. The difference between the fourth and fifth terms is 37 - 20 = 17, which is 4² + 1.

Following this logic, the difference between the fifth and the next term must be 5² + 1 = 26. Adding this difference to the last known term gives 37 + 26 = 63.

Explanation

The words camouflage, conceal, and mask are synonyms that all relate to the act of hiding, disguising, or obscuring something from view. In contrast, a horde refers to a large group of people or a nomadic tribe, describing a collective quantity or mass rather than an action or method of concealment. Therefore, horde is the odd word out as it does not share the common theme of hiding or disguise present in the other terms.

Explanation

The relationship between the words in the given pair is that of a distressing condition and its corresponding remedy or source of relief. Grief is a state of intense sorrow or mental distress, and consolation is the comfort or solace provided to alleviate that grief. Similarly, pain is a state of physical suffering or discomfort, and a sedative is a substance administered to reduce or mitigate that pain. In both instances, the second word represents something used to soothe or treat the condition described by the first word.

Explanation

In this direct letter-to-digit coding system, each letter in the given words corresponds to a specific number based on its position. From the word SMOKE coded as 81643, we find that S corresponds to 8, M to 1, O to 6, K to 4, and E to 3. From the word PRANK coded as 72954, we find that P corresponds to 7, R to 2, A to 9, N to 5, and K to 4. To determine the code for the word ROSE, we extract the digits assigned to its individual letters: R corresponds to 2, O corresponds to 6, S corresponds to 8, and E corresponds to 3. Arranging these digits in the sequence of the letters in ROSE yields 2683.

Explanation

The given relationship follows the pattern of an activity and its resulting acquisition. Study is the process or effort one engages in to acquire Knowledge. Similarly, Work is the activity through which an individual gains Experience. Just as Knowledge is the internal intellectual outcome of studying, Experience is the practical skill and wisdom accumulated through the process of working.

Explanation

The logic followed in the given analogy is a repetitive pattern of +2 and -2 applied to the positional values of the letters in the English alphabet. In the first pair FKPV to HIRT, the transformation is: F (6) + 2 = H (8) K (11) - 2 = I (9) P (16) + 2 = R (18) V (22) - 2 = T (20)

Applying this same pattern (+2, -2, +2, -2) to the letters of BHMR: B (2) + 2 = D (4) H (8) - 2 = F (6) M (13) + 2 = O (15) R (18) - 2 = P (16)

The resulting letter-cluster is DFOP.

Explanation

Options B, C, and D all follow a consistent arithmetic progression in their letter positions with constant increasing gaps of +2, +3, and +1 respectively. Option A is the odd one out because it follows a decreasing order and has an inconsistent gap (-1, -1, -2).

Explanation

The given letter series consists of 17 characters which can be divided into groups of six to identify the underlying pattern. By substituting the letters from the correct option (c, b, a, c, e) into the blanks, the series is completed as follows:

(b a c d b c) (b a c d b c) (b a e d b)

The first two groups of six letters are identical, following the pattern b-a-c-d-b-c. The third group begins the same sequence (b-a-...) but replaces the character in the third position (c) with 'e'. This indicates a repeating periodic pattern where the first twelve letters consist of two identical cycles, followed by a slight variation in the third cycle as shown by the inclusion of 'e' in the final blank.

Explanation

Based on the provided information, P and R are siblings. R is married to M, and P is married to T. Since R's nephew is the son of P and has sister V, it follows that V is the daughter of P and T. As M is the spouse of V's paternal uncle R, V is the niece of M. This completes the family structure of eight persons consisting of Q in the first generation; P, T, R, and M in the second generation; and S, V, and P's son in the third generation.

Explanation

The coding logic follows two steps: first, the letters of the word are written in reverse order, and second, each letter is replaced by its succeeding letter in the English alphabet (+1 shift).

For the word STROKE: The reverse order is EKORTS. Incrementing each letter by 1: E + 1 = F K + 1 = L O + 1 = P R + 1 = S T + 1 = U S + 1 = T The resulting code is FLPSUT.

Applying the same logic to the word BRIGHT: The reverse order is THGIRB. Incrementing each letter by 1: T + 1 = U H + 1 = I G + 1 = H I + 1 = J R + 1 = S B + 1 = C The resulting code is UIHJSC.

Explanation

The relationship within the set (4, 12, 16) is defined by the sum of the first two numbers equaling the third number, which can be expressed by the formula a + b = c. Substituting the values from the set, we get 4 + 12 = 16. This same arithmetic property is present in the set (64, 36, 100), where 64 + 36 = 100. Additionally, the elements involved in these sets are perfect squares: in the first set, 4 = 2² and 16 = 4², while in the matching set, 64 = 8², 36 = 6², and 100 = 10². The consistent application of the addition rule a + b = c characterizes the similarity between the two sets.

Explanation

In the number set (3, 20, 7), the relationship between the numbers follows a mathematical pattern where the middle number is exactly twice the sum of the first and the third numbers.

Formula: Middle Number = 2 × (First Number + Third Number)

Applying the values from the set: First Number = 3 Third Number = 7 Sum = 3 + 7 = 10 Calculation = 10 × 2 = 20

The result matches the middle number of the set, confirming the logic.

Explanation

The logic followed in the given set (8, 28, 6) is that the middle number is twice the sum of the first and the third numbers. The relationship can be expressed by the formula b = 2 × (a + c). Substituting the values from the given set, we get 2 × (8 + 6) = 2 × 14 = 28.

Applying this same logic to the set (3, 20, 7), the sum of the first and third numbers is 3 + 7 = 10. Multiplying this sum by 2 results in 10 × 2 = 20, which is the middle number. This confirms that the set (3, 20, 7) follows the exact same pattern as the original set.

Explanation

The logical order follows the chronological progression of a career path within an organization. The process begins with the identification of a Job (3) opportunity or the act of applying for one. This is followed by an Interview (4) to assess the candidate's suitability for the role. Once the interview is successful, the candidate receives Confirmation (5) of their appointment or selection. After joining the organization, the employee serves a period of Probation (1), which acts as a trial phase to evaluate their performance and conduct. Upon the successful completion of the probation period and subsequent years of service, the employee earns a Promotion (2) to a higher position.

Explanation

The series follows a pattern where each term is calculated by multiplying the preceding term by 2 and then adding 2. This can be expressed by the recurrence relation aₙ = (aₙ₋₁ × 2) + 2.

Following this logic: 5 × 2 + 2 = 12 12 × 2 + 2 = 26 26 × 2 + 2 = 54 54 × 2 + 2 = 110

Alternatively, the difference between consecutive terms doubles at each step. The difference between 5 and 12 is 7; between 12 and 26 is 14; and between 26 and 54 is 28. Since the differences are 7, 14, and 28, the next difference in the sequence must be 28 × 2 = 56. Adding this to the last term gives 54 + 56 = 110.

Explanation

Let the present age of Mitali be 4x and the present age of Shabnam be 7x based on the given ratio 4:7. According to the problem, the difference between the present age of Shabnam and Mitali's age after 5 years is 13 years. This can be expressed as:

7x - (4x + 5) = 13

Solving for x: 3x - 5 = 13 3x = 18 x = 6

The sum of their present ages is 4x + 7x = 11x. Substituting the value of x: Sum = 11 × 6 = 66 years.

Explanation

P and Q are siblings as P is the sister of Q. S is the wife of Q, and since S is the daughter-in-law of W, it follows that Q is the son of W. The statement that W has only two children implies those children are P and Q. M is the brother of V and is described as the nephew of P; for M to be the nephew of P in this immediate family, he must be the son of P's brother, Q. Because M and V are siblings, they are both the children of Q. Therefore, Q is the father of V.

Explanation

The relationship between the words is that of an outward physical expression or gesture and the underlying emotion it represents. A kick is a physical action that serves as a direct manifestation or expression of the feeling of hostility. In this analogy, the first word describes a specific visible act, while the second word identifies the internal state or sentiment associated with that behavior.

Explanation

The coding pattern follows the numerical positions of the letters in the English alphabet (A=1, B=2, …, Z=26) written in reverse order from the last letter of the word to the first. For CLEAN, the positions are C=3, L=12, E=5, A=1, and N=14; reversing these values gives 14, 1, 5, 12, 3, which results in the code 1415123. Similarly, for BLOW, the positions are B=2, L=12, O=15, and W=23; reversing these gives 23, 15, 12, 2, resulting in 2315122.

Applying this logic to JOKE: J = 10 O = 15 K = 11 E = 5

Arranging these numerical values in reverse order (from the last letter to the first) gives 5, 11, 15, 10. Concatenating these numbers yields the final code 5111510.

Explanation

The relationship between the first and second letter-clusters is based on the concept of opposite letters in the English alphabet. Two letters are considered opposites if the sum of their numerical positions is 27 (i.e., their positions are the same whether counting from the beginning or the end of the alphabet).

In the first pair, DFIM : WURN: D (4th) and W (23rd): 4 + 23 = 27 F (6th) and U (21st): 6 + 21 = 27 I (9th) and R (18th): 9 + 18 = 27 M (13th) and N (14th): 13 + 14 = 27

Applying this logic to the third cluster GENP to find the fourth cluster: G (7th) corresponds to T (20th): 7 + 20 = 27 N (14th) corresponds to M (13th): 14 + 13 = 27 P (16th) corresponds to K (11th): 16 + 11 = 27

While the second letter E (5th) would ideally correspond to V (22nd) to maintain the sum of 27, TPMK is the only option that correctly identifies the opposite letters for the first, third, and fourth positions (G-T, N-M, P-K). Additionally, the internal structure of the result clusters shows a consistent decreasing gap pattern: WURN follows a -2, -3, -4 letter gap sequence, and TPMK follows a -4, -3, -2 letter gap sequence.

Explanation

The logic followed in the given number-pair 12:42 is that the second number is 3.5 times the first number. This can be expressed by the relation y = x × 3.5, where x is the first term and y is the second term. For the given pair: 12 × 3.5 = 42

Applying the same mathematical operation to the pair 8:28, we get: 8 × 3.5 = 28

Alternatively, the pattern can be seen as y = (x × 3) + ˣ⁄₂. For the number 8, the calculation is (8 × 3) + ⁸⁄₂ = 24 + 4 = 28.

Explanation

The relationship between the numbers in the set (3, 16, 5) follows the pattern where the second number is equal to twice the sum of the first and third numbers. This can be expressed using the formula n₂ = 2 × (n₁ + n₃). Applying this to the given set, we get 2 × (3 + 5) = 2 × 8 = 16.

In the set (7, 32, 9), the same logic applies. Calculating the sum of the first and third numbers gives 7 + 9 = 16. Multiplying this sum by 2 results in 16 × 2 = 32, which is the middle number.

Explanation

The given statements follow the I + I pattern, where both premises are particular affirmative. In syllogism, no definite conclusion can be drawn between the subject of the first statement (roads) and the predicate of the second statement (lanes) because the middle term (streets) is not distributed in either premise.

When no definite relationship exists between two terms, we look for a complementary pair in the conclusions. Conclusion I (No road is a lane) is a universal negative (E-type), and Conclusion III (Some lanes are roads) is a particular affirmative (I-type). Since both conclusions involve the same terms (roads and lanes) and cover all possible logical relationships between them—either they have no intersection or they have at least some intersection—one of them must necessarily be true. This triggers the either-or condition. Conclusion II does not follow because the statement only confirms that some streets are lanes, which does not imply that all streets are lanes.