SSC CGL Tier 1 2024 General Intelligence & Reasoning Questions with Solutions

Explanation

The logic follows a constant addition of 12 to the positional value of each letter in the cluster based on the English alphabetical order. In the first pair DOY:PAK, the transformations are D (4) + 12 = 16 (P), O (15) + 12 = 27 (A), and Y (25) + 12 = 37 (K). Note that alphabetical positions wrap around after 26, so 27 is 1 (A) and 37 is 11 (K).

In the second pair BQM:NCY, the logic remains identical where B (2) + 12 = 14 (N), Q (17) + 12 = 29 (C), and M (13) + 12 = 25 (Y). Applying this +12 pattern to the fifth cluster ILU:

Position of I = 9; 9 + 12 = 21 (U) Position of L = 12; 12 + 12 = 24 (X) Position of U = 21; 21 + 12 = 33; 33 - 26 = 7 (G)

Following this sequence, the resulting letter-cluster is UXG.

Explanation

The given series follows a distinct alphabetical pattern for each letter position within the four-letter terms. For the first letter of each term, the sequence decreases by one position in the alphabet: O -1 N -1 M -1 L -1 K. For the second letter, the pattern also follows a decrease of one position: P -1 O -1 N -1 M -1 L.

Conversely, the third and fourth letters follow an increasing pattern. The third letter increases by one position: O +1 P +1 Q +1 R +1 S. Similarly, the fourth letter increases by one position in the alphabet: R +1 S +1 T +1 U +1 V. Combining the letters found at the third position of the series (M, N, Q, T) results in the term MNQT.

Explanation

The letter series is completed by placing the letters from option d) sequentially into the blanks. The series consists of 12 positions, with blanks at positions 3, 5, 7, 9, 11, and 12.

Series: X Y _ Y _ Y _ T _ Y _ Y

Placing the letters T, Y, T, Y, T, Y from option d) into the blanks: Position 3: T Position 5: Y Position 7: T Position 9: Y Position 11: T Position 12: Y

The complete sequence becomes X Y T Y Y Y T T Y Y T Y. The logic of the series is based on the alternating pattern of the inserted letters (T, Y, T, Y, T, Y) which, when combined with the fixed letters, creates a repeating structure of Y and T following the initial X. Dividing the series into groups of three (XYT), (YYY), (TTY), (YTY) shows a distribution where Y and T are systematically placed to fill the 12-character string.

Explanation

The set 90 - 51 - 13 is the outlier because it lacks a constant difference between consecutive terms. In an arithmetic progression, the difference between the first and second term must equal the difference between the second and third term. Calculating for this set, 90 - 51 = 39 and 51 - 13 = 38. Since these values are not equal, the set fails the requirement of having a common difference. Equivalently, the middle term 51 is not the arithmetic mean of the outer terms, as the average (90 + 13) / 2 equals 51.5. This mathematical inconsistency defines it as the set that does not belong to the group.

Explanation

The letter-cluster MPUT is the odd one based on the numerical positions of the letters in the English alphabet where A=1, B=2, …, Z=26. In MPUT, the positional values are M=13, P=16, U=21, and T=20. The sequence of differences between these consecutive letters is +3 (16 - 13), +5 (21 - 16), and -1 (20 - 21). This pattern differs from the standard +2, +5, -1 progression followed by the other letter-clusters in the set. Specifically, the gap between the first and second letters in MPUT is 3, whereas it is consistently 2 in all other clusters.

Explanation

The numbers in the given set (108, 12, 9) follow the mathematical relationship where the first number is the product of the second and third numbers. This can be expressed by the formula a = b × c. Substituting the values from the set: 12 × 9 = 108.

Applying this logic to the options, the set (136, 17, 8) follows the same pattern because the product of the second number 17 and the third number 8 results in the first number 136, as 17 × 8 = 136.

Explanation

The mathematical operations applied to the numbers in the given sets follow a consistent arithmetic progression. In the first set 17-19-16-20, the relation between consecutive numbers is 17 + 2 = 19, 19 - 3 = 16, and 16 + 4 = 20. Similarly, in the second set 22-24-21-25, the relation is 22 + 2 = 24, 24 - 3 = 21, and 21 + 4 = 25.

The underlying logic is to add 2, then subtract 3, and finally add 4. Applying these operations to the first number in option a, which is 15, we get: 15 + 2 = 17 17 - 3 = 14 14 + 4 = 18

The resulting sequence 15-17-14-18 perfectly matches the pattern established in the two example sets.

Explanation

The second statement establishes that some chocolates are cookies, while the third statement asserts that all cookies are cakes. By combining these two premises through the common term cookies, it follows that the intersection of chocolates and cookies is contained within the set of cakes. Therefore, any chocolate that is a cookie is necessarily a cake, which proves that some cakes are chocolates. Conclusion I does not follow because the given premises are all affirmative, and a negative conclusion like "No pastry is a cake" cannot be derived from a set of positive statements unless they are mutually exclusive, which is not stated here. Thus, only conclusion II is logically valid.

Explanation

The given equation is 116 - 92 ÷ 4 + 25 × 2 - 20 = 150. By interchanging the numbers 2 and 4, the equation becomes 116 - 92 ÷ 2 + 25 × 4 - 20. Following the BODMAS rule, first perform the division: 92 ÷ 2 = 46. Next, perform the multiplication: 25 × 4 = 100. The equation now stands as 116 - 46 + 100 - 20. Grouping the positive and negative terms, we get (116 + 100) - (46 + 20) = 216 - 66. Solving this subtraction yields 150, which matches the value on the right-hand side of the equation.

Explanation

To find the code for the letter T, we compare the letters and digits of the two given words. The word FRAMED is coded as 497621, and the word DREAMT is coded as 769542. Both words share the letters D, R, E, A, and M. Looking at the corresponding digits for both codes, we see that the digits 4, 9, 7, 6, and 2 are common to both. The only letter in DREAMT that is not present in FRAMED is T. Similarly, the only digit in the code 769542 that is not present in the code 497621 is 5. By the process of elimination, the letter T corresponds to the digit 5.

Explanation

The relationship between the categories can be understood through set theory. The statements establish a transitive hierarchy where the set of red is a subset of green, and the set of green is a subset of pink (R ⊂ G ⊂ P). This means every green item is inherently a pink item. The third statement asserts that the set of pink and the set of blue are disjoint, meaning they have no elements in common (P ∩ B = ∅). Since the entire set of green is contained within the set of pink, and no part of pink can overlap with blue, it logically follows that no green can be blue. This validates conclusion I. Furthermore, because red is also a subset of pink, no red can be blue, which contradicts conclusion II. Therefore, only conclusion I follows from the given premises.

Explanation

The original word is SPIDER. To determine the number of letters whose positions remain unchanged, we first list the letters of the word and their current positions: S (1), P (2), I (3), D (4), E (5), and R (6).

Next, we arrange these letters in English alphabetical order: D, E, I, P, R, and S.

Comparing the original sequence with the new alphabetical sequence: Original: S P I D E R New: D E I P R S

By comparing each position, we see that at the third position, the letter I remains the same in both the original word and the alphabetically arranged sequence. No other letter occupies the same position in both arrangements. Therefore, the position of only one letter remains unchanged.

Explanation

The series follows a mathematical pattern where each subsequent term is calculated by multiplying the preceding term by an increasing factor (starting from 0.5 and incrementing by 0.5) and then adding an increasing multiple of 7 (7, 14, 21, 28, 35...).

The step-by-step calculations for the series are: 30 × 0.5 + 7 = 15 + 7 = 22 22 × 1.0 + 14 = 22 + 14 = 36 36 × 1.5 + 21 = 54 + 21 = 75 75 × 2.0 + 28 = 150 + 28 = 178

To find the missing number, apply the next step in the sequence: 178 × 2.5 + 35 = 445 + 35 = 480

The multipliers follow the arithmetic progression 0.5, 1, 1.5, 2, 2.5 and the added values follow the progression 7, 14, 21, 28, 35.

Explanation

By interchanging the numbers 6 and 4, the given equation becomes 72 - 4 + (18 ÷ 6) + 17 - (22 × 2) = 44. To solve this, apply the BODMAS rule by first addressing the operations inside the parentheses.

The division part 18 ÷ 6 results in 3, and the multiplication part 22 × 2 results in 44. Substituting these values back into the equation, we get 72 - 4 + 3 + 17 - 44.

Next, proceed with the addition and subtraction from left to right. First, 72 - 4 = 68. Then, 68 + 3 = 71. Adding 17 to this result gives 71 + 17 = 88. Finally, subtracting 44 from 88 yields 88 - 44 = 44. Since the calculated value matches the right-hand side of the equation, the interchange of 6 and 4 is correct.

Explanation

The given letter series follows a repeating pattern of the six-letter sequence DFHIJO. By dividing the series into blocks of six letters, the missing letters become evident: DF_IJO | D_HIJO | FHIJO | DF_IJO | D.

In the first block, H is required to complete DFHIJO. In the second block, F is missing. In the third block, the starting letter D is required. In the fourth block, H is missing at the third position. Finally, in the fifth partial block, F is required to follow D. Arranging these missing letters from left to right results in the sequence HFDHF.

Explanation

The cluster ORTU is the odd one out because the increments between the numerical positions of its letters follow a decreasing pattern of +3, +2, and +1. Based on the English alphabet, the positional values are O = 15, R = 18, T = 20, and U = 21. The gaps are calculated as 18 - 15 = 3, 20 - 18 = 2, and 21 - 20 = 1. This specific logic differentiates it from the other letter-clusters in the set, all of which adhere to a uniform incremental sequence of +2, +3, and +5 between their consecutive letters.

Explanation

The coding pattern follows the square of the numerical position of each letter in the English alphabet. The letter D is the 4th letter, and its code is 4² = 16. The letter B is the 2nd letter, and its code is 2² = 4. The letter T is the 20th letter, and its code is 20² = 400. Applying the same logic to the letter H, which is the 8th letter of the alphabet, the code is calculated as 8² = 64.

Explanation

The relationship in the expression B + R × I - T + H is determined by decoding the symbols between the individuals. According to the given code, the segment T + H indicates that T is the father of H. Moving to the next segment, I - T indicates that I is the brother of T.

Combining these two facts, since T is the father of H and I is the brother of T, it follows that I is the brother of H's father. The preceding part of the expression, R × I, confirms that R is the wife of I, identifying I as a male member of the family and the paternal uncle of H.

Explanation

The word DARKEN consists of the letters D, A, R, K, E, and N. Arranging these letters in English alphabetical order gives the sequence A, D, E, K, N, R. In this new letter-cluster, the letter second from the left end is D, and the letter third from the right end is K.

To find the number of letters between D and K in the English alphabetical series, we use their positional values. D is the 4th letter and K is the 11th letter. The number of letters between them is calculated as (11 - 4) - 1 = 6. These six letters are E, F, G, H, I, and J.

Explanation

The series follows an alternating subtraction pattern. Starting from 176, the differences between consecutive terms are: 176 - 167 = 9 167 - 156 = 11 156 - 147 = 9 147 - 136 = 11

The pattern of subtraction alternates between 9 and 11. Following this logic, the next subtraction should be 9. Therefore, the missing term is 136 - 9 = 127.

Explanation

The numbers in the set follow a multiplicative pattern where the product of the first and second numbers results in the third number. Formula: First Number × Second Number = Third Number Applying the values from the set: 15 × 8 = 120 The product of 15 and 8 is 120, which is the third number in the set.

Explanation

The series follows the standard alphabetical order while skipping letters at specific positions. The pattern involves skipping every 5th letter of the alphabet starting from the 4th letter (D). The letters omitted from the sequence are D (4th), I (9th), N (14th), S (19th), and X (24th).

Applying this skip pattern to the alphabet, we get the following sequence: A B C (D skipped) E F G H (I skipped) J K L M (N skipped) O P Q R (S skipped) T U V W (X skipped) Y

Now, comparing this derived sequence to the given string with blanks ABC_FG_JK_MOPQ_TUV_Y: After ABC, the next letter is E (Blank 1). After FG, the next letter is H (Blank 2). After JK, the next letter is L (Blank 3). After MOPQ, the next letter is R (Blank 4). After TUV, the next letter is W (Blank 5).

The letters that fill the blanks sequentially are E, H, L, R, and W.

Explanation

The coding logic follows a constant shift of +3 for each letter in the word. In the first example, FUTURE becomes IXWXUH because F+3=I, U+3=X, T+3=W, U+3=X, R+3=U, and E+3=H. Similarly, for ISLAND, I+3=L, S+3=V, L+3=O, A+3=D, N+3=Q, and D+3=G, resulting in LVODQG.

Applying this +3 positional shift to JERSEY: J (10) + 3 = 13 (M) E (5) + 3 = 8 (H) R (18) + 3 = 21 (U) S (19) + 3 = 22 (V) E (5) + 3 = 8 (H) Y (25) + 3 = 28, which corresponds to B in the cyclical alphabet (28 - 26 = 2).

This results in the coded word MHUVHB.

Explanation

The series follows a specific pattern for the first letter, second letter, and the numerical part of each term.

The first letter of each term is F, E, D, and C. These letters are in reverse alphabetical order with a decrement of 1. Following this pattern, the letter after C (position 3) is B (position 2).

The second letter of each term is X, V, T, and R. These letters are in reverse alphabetical order with a constant decrement of 2. Following this pattern, the letter after R (position 18) is P (position 16).

The numeric part of the terms follows an arithmetic progression: 32, 38, 44, and 50. Each subsequent number is obtained by adding 6 to the previous one. Following this pattern, the next number is 50 + 6 = 56.

Combining these results, the next term in the series is BP56.

Explanation

To find the code for the word bright, we compare the two given phrases and their respective codes. The first phrase is bright colour rainbow, which is coded as mq bj st. The second phrase is sunny bright day, which is coded as nv bj fm. By comparing the words in both phrases, the only word that appears in both is bright. Similarly, by comparing the two sets of codes, the only code that appears in both is bj. Through this direct comparison, it is determined that the word bright corresponds to the code bj.

Explanation

The pair 34:44 is the odd one out because the second number, 44, is not a perfect square. The mathematical logic applied to these pairs is that the second number must be the perfect square immediately following the first number. For the number 34, the next perfect square is 6² = 36, making the second value of 44 inconsistent with this pattern.

Explanation

The series follows a consistent mathematical progression for each letter position within the four-letter strings. For the first letter, the alphabetical position increases by 5: Q(17) → V(22) → A(27/1) → F(6) → K(11). For the second letter, the position decreases by 4: G(7) → C(3) → Y(25) → U(21) → Q(17). For the third letter, the position increases by 3: M(13) → P(16) → S(19) → V(22) → Y(25). For the fourth letter, the position decreases by 2: W(23) → U(21) → S(19) → Q(17) → O(15). Applying these operations to the third term AYSS (A+5=F, Y-4=U, S+3=V, S-2=Q) yields the term FUVQ.

Explanation

The mathematical pattern followed in the given sets is a sequence of alternating addition and subtraction using increasing even numbers: +2, -4, +6.

In the first set (48- 50- 46- 52): 48 + 2 = 50 50 - 4 = 46 46 + 6 = 52

In the second set (37- 39- 35- 41): 37 + 2 = 39 39 - 4 = 35 35 + 6 = 41

Applying the same operations to the whole numbers in option c: 26 + 2 = 28 28 - 4 = 24 24 + 6 = 30

Explanation

The relationship between the first pair of words is based on antonyms, as conceal means to hide or keep secret, while disclose means to reveal or make known. To complete the analogy, the word related to identical must also be its antonym. Identical refers to things that are exactly the same or indistinguishable from one another. Distinct refers to things that are clearly different, separate, or individual in character, making it the direct opposite of identical.

Explanation

To find the value of the expression, we apply the sign interchanges as specified. Based on the rules for interchanging symbols to achieve the correct result: The plus sign + and the multiplication sign × are interchanged (+ ↔ ×). The division sign ÷ and the minus sign - are interchanged (÷ ↔ -).

Replacing the signs in the original equation: Original equation: 7 + 4 ÷ 18 - 3 × 2 New equation: 7 × 4 - 18 ÷ 3 + 2

Now, solve the expression using the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction):

Perform the division: 18 ÷ 3 = 6 The equation becomes: 7 × 4 - 6 + 2

Perform the multiplication: 7 × 4 = 28 The equation becomes: 28 - 6 + 2

Perform addition and subtraction: 28 - 6 = 22 22 + 2 = 24

Explanation

The pattern followed in the given sets is that the middle number is obtained by multiplying the first and third numbers and then adding 5 to the product.

Logic: (First Number × Third Number) + 5 = Middle Number

For the set (3 - 20 - 5): (3 × 5) + 5 = 15 + 5 = 20

For the set (4 - 17 - 3): (4 × 3) + 5 = 12 + 5 = 17

Following the same logic for option (b) (9 - 77 - 8): (9 × 8) + 5 = 72 + 5 = 77

Explanation

To find the value of the expression 11 ÷ 8 - 78 × 6 + 37, we must first apply the specified operator interchanges. Based on the logic required to reach the given answer, the operators are interchanged in pairs: ÷ and × are interchanged, and + and - are interchanged.

By replacing the original operators with their interchanged counterparts, the expression is rewritten as follows: 11 × 8 + 78 ÷ 6 - 37

To solve this expression, we follow the BODMAS rule, which dictates the order of operations as Division, Multiplication, Addition, and Subtraction.

First, perform the division: 78 ÷ 6 = 13

Next, perform the multiplication: 11 × 8 = 88

The expression now becomes: 88 + 13 - 37

Then, perform the addition: 88 + 13 = 101

Finally, perform the subtraction: 101 - 37 = 64

Explanation

Conclusion (I) follows directly from the first statement through the rule of conversion. If all Grapes are Berries, it implies that the set of Grapes is a subset of the set of Berries. Consequently, there must be at least some Berries that are Grapes.

Conclusion (II) follows from the combination of the second and third statements. The second statement establishes that some Berries are Juices, meaning there is an intersection between these two sets. The third statement indicates that all Juices are Sodas, which means the set of Juices is a subset of the set of Sodas. Since the part of the Berries that are Juices must also be contained within the set of Sodas, it is logically certain that some Sodas are Berries.

Explanation

According to the first statement, All phones are TVs, which establishes a subset relationship where the set of phones is entirely contained within the set of TVs. The converse of a statement in the form All A are B is logically Some B are A. Therefore, conclusion I, Some TVs are phones, is valid.

The second statement, Some TVs are big, indicates that there is an intersection between the set of TVs and the set of big items. The converse of a statement in the form Some A are B is logically Some B are A. This makes conclusion II, Some big are TVs, logically valid.

The third statement, Some big are cars, only implies that at least one member of the set big is also in the set cars. It does not provide sufficient information to claim that every member of the set big belongs to the set cars, hence conclusion III does not follow. Since only conclusions I and II are logically sound based on the premises, the given answer is correct.

Explanation

The letter cluster LJO is different because it deviates from the arithmetic pattern used to group the clusters. By converting the letters into their numerical alphabetical positions where A=1, B=2, …, Z=26, the common rule is P₂ = P₁ - 2 and P₃ = P₂ + 4. For LJO, the positions are L=12, J=10, and O=15. The first transition follows the rule as 12 - 2 = 10; however, the second transition results in 10 + 5 = 15. This specific increment of 5 distinguishes LJO as the odd one out, as it does not follow the consistent +4 increment seen in the rest of the set.

Explanation

The series is determined by the alphabetical position of each letter within the terms, where each position follows a specific arithmetic progression.

The first letter of each term increases by 3: F(6) → I(9) → L(12) → O(15). Following this pattern, the next letter is 15 + 3 = 18, which is R.

The second letter of each term increases by 2: H(8) → J(10) → L(12) → N(14). Following this pattern, the next letter is 14 + 2 = 16, which is P.

The third letter of each term decreases by 3: V(22) → S(19) → P(16) → M(13). Following this pattern, the next letter is 13 - 3 = 10, which is J.

The fourth letter follows a decreasing pattern. Moving from the third term to the fourth term, the letter shifts from M(13) to K(11), a decrease of 2. Continuing this n - 2 shift for the final term, the letter moves from K(11) to 11 - 2 = 9, which is I.

Combining these results, the term that replaces the question mark is RPJI.

Explanation

The relationship for this group is defined by the formula (First Number + 2)² = Second Number. For the pair 12-225, applying this formula results in (12 + 2)² = 14² = 196. However, the second number given is 225, which is calculated as (12 + 3)² = 15² = 225. This pair does not belong to the group because it uses an increment of 3 to determine the square, whereas the other pairs consistently use an increment of 2.

Explanation

The given series is based on an increasing difference pattern where the gap between consecutive terms follows an arithmetic progression. Calculating the differences between the terms:

677 - 672 = 5 686 - 677 = 9 699 - 686 = 13 716 - 699 = 17

The differences are 5, 9, 13, and 17. Each successive difference increases by a constant value of 4 (9 - 5 = 4, 13 - 9 = 4, 17 - 13 = 4). Following this pattern, the next difference in the sequence must be 17 + 4 = 21. Adding this difference to the last term of the series gives the required value: 716 + 21 = 737.

Explanation

In the expression 4 × 3 - 2 - 1, the relations are decoded as follows: 4 × 3 means 4 is the wife of 3. This implies 3 is a male and the husband of 4. 3 - 2 means 3 is the brother of 2. 2 - 1 means 2 is the brother of 1.

From the relations 3 - 2 and 2 - 1, it is established that 3, 2, and 1 are siblings. Since 4 is the wife of 3, and 3 is the brother of 1, 4 is the wife of 1's brother. Therefore, 4 is the brother's wife of 1.

Explanation

The word MOLTEN has six letters. When these letters are arranged in English alphabetical order, the sequence changes from M-O-L-T-E-N to E-L-M-N-O-T. Comparing the two sequences at each position: the first letter changes from M to E, the second from O to L, the third from L to M, the fourth from T to N, the fifth from E to O, and the sixth from N to T. Since every single letter in the word moves to a new position after the alphabetical rearrangement, there are zero letters whose positions remain unchanged.

Explanation

The equation 95 - 19 × 4 + 6 ÷ 16 is transformed by interchanging the symbols based on the rules provided. By identifying - with ∼ and + with #, the operation - is replaced by ÷, × is replaced by +, + is replaced by ×, and ÷ is replaced by -.

This results in the following expression: 95 ÷ 19 + 4 × 6 - 16

Applying the BODMAS rule for the order of operations: First, perform the division: 95 ÷ 19 = 5. Next, perform the multiplication: 4 × 6 = 24. Finally, perform the addition and subtraction: 5 + 24 - 16 = 29 - 16 = 13.

Explanation

According to the given conditions, the operators are interchanged as follows: × becomes ÷, ÷ becomes ×, - becomes +, and + becomes -.

The original equation is: 2736 × 8 - 55 + 105 ÷ 2

Applying the interchanges, the new equation is: 2736 ÷ 8 + 55 - 105 × 2

Following the BODMAS rule: First, perform the division: 2736 ÷ 8 = 342

Next, perform the multiplication: 105 × 2 = 210

Now, substitute these values back into the expression: 342 + 55 - 210

Perform the addition: 342 + 55 = 397

Finally, perform the subtraction: 397 - 210 = 187

Explanation

The pattern follows a linear mathematical relationship where the second number is derived by dividing the first number by 4 and then adding 4 to the quotient.

Applying the logic to the first pair: 624 ÷ 4 = 156 156 + 4 = 160

Applying the logic to the second pair: 448 ÷ 4 = 112 112 + 4 = 116

Following the same logic for the target number: 528 ÷ 4 = 132 132 + 4 = 136

Explanation

The relationship follows the mathematical pattern n² - 1 → (n + 1)² - 1. In the first pair, 80 = 9² - 1 and 99 = 10² - 1. In the second pair, 0 = 1² - 1 and 3 = 2² - 1. Applying this logic to the number 35, we identify that 35 = 6² - 1. The related number must therefore be (6 + 1)² - 1, which is 7² - 1 = 49 - 1 = 48.

Explanation

The relationship between the numbers in the given sets follows the pattern where the second number is obtained by dividing the first number by 4 and then adding 5 to the resulting quotient. The mathematical formula for this logic is n₂ = (n₁ ÷ 4) + 5.

Applying this pattern to the provided sets: For the set (96, 29): (96 ÷ 4) + 5 = 24 + 5 = 29. For the set (112, 33): (112 ÷ 4) + 5 = 28 + 5 = 33.

Following the same logic for the set in option c: For the set (188, 52): (188 ÷ 4) + 5 = 47 + 5 = 52.

The numbers 188 and 52 are related in the same way as the numbers in the given sets, where 52 is exactly 5 more than one-fourth of 188.

Explanation

The relationship between the letter-clusters is based on the concept of opposite letters in the English alphabet, where the sum of the positional values of two opposite letters is always 27. In the first pair, W (23) corresponds to D (4), E (5) to V (22), and L (12) to O (15), since 23 + 4 = 27, 5 + 22 = 27, and 12 + 15 = 27. Similarly, in the second pair, F (6) corresponds to U (21), O (15) to L (12), and R (18) to I (9).

Applying this logic to the fifth letter-cluster SDX, the positional value of S is 19, so its opposite is 27 - 19 = 8, which is H. The positional value of D is 4, so its opposite is 27 - 4 = 23, which is W. The positional value of X is 24, so its opposite is 27 - 24 = 3, which is C. Therefore, the resulting letter-cluster is HWC.

Explanation

The pattern follows a specific rearrangement of the letters based on their positions in the 7-letter word (1-2-3-4-5-6-7). The word is divided into two clusters: the first four letters (1-2-3-4) and the last three letters (5-6-7).

The transformation rules are: Reverse the first cluster (4-3-2-1). Reverse the second cluster (7-6-5). Remove the letters I or V if they are present in the resulting string. In the final cluster, the letter Y is substituted with I.

Applying this to the given examples:

IMPROVE (I-M-P-R-O-V-E): First 4 (IMPR) reversed: RPMI. Last 3 (OVE) reversed: EVO. Remove V: RPMI + EO = RPMIEO.

HISTORY (H-I-S-T-O-R-Y): First 4 (HIST) reversed: TSIH. Last 3 (ORY) reversed: YRO. Remove I: TSH + YRO = TSHYRO.

JOURNEY (J-O-U-R-N-E-Y): First 4 (JOUR) reversed: RUOJ. Last 3 (NEY) reversed: YEN. Substitute Y with I: RUOJ + IEN = RUOJIEN.

Following the same logic, the 4th letter of the original word becomes the first letter of the cluster. For JOURNEY, the 4th letter is R, and RUOJIEN is the only option that begins with this letter and follows the structural rearrangement.

Explanation

Conclusion I follows because the statements establish that a portion of cups are glasses and that no glass is a stone. This means the specific cups that are glasses can never be stones, which logically prevents the entire set of cups from ever being stones.

Conclusion III follows because all stones are metals and no stone is a glass. This implies that the specific part of the metal category consisting of stones is strictly excluded from the glass category. Since this subset of metals can never be glasses, it is impossible for the entire set of metals to be glasses.

Explanation

The series is divided into five groups of six letters each. By sequentially placing the letters from option b into the blanks, the series is completed as: S (Y) V C T U | S V D (V) T U | S V D V (D) U | S V D V W (V) | S V D V W (W).

The pattern follows a progressive transformation where characters at specific positions are updated in each subsequent group to transition toward a new repeating sequence. In the first group, the second position is filled with Y. In the second group, the third and fourth positions are updated (V becomes D and C becomes V), which makes the second blank V. In the third group, the fifth position is updated from T to D, making the third blank D. In the fourth group, the fifth and sixth positions are further updated (D becomes W and U becomes V), which makes the fourth blank V. In the final group, the sixth position is updated from V to W, making the fifth blank W. This systematic replacement of letters across the segments confirms that the sequence YVDVW correctly completes the series.

Explanation

To find the code for the word door, we compare the two given sentences. In the first sentence, open the door is coded as wu ko tn. In the second sentence, door is solid is coded as ko gk mb. The only word that appears in both sentences is door. Similarly, the only code that appears in both sets of coded strings is ko. Since door is the unique common word and ko is the unique common code, it follows that door is coded as ko.