SSC CGL Tier 1 2022 General Intelligence & Reasoning Questions with Solutions

Explanation

The coding pattern involves taking the positional value of each letter in the English alphabet (A=1, B=2, …, Z=26) and multiplying that value by 2. For the word TOMATO, the positions are T=20, O=15, M=13, A=1, T=20, O=15, which results in 40-30-26-2-40-30. Similarly, for GINGER, the positions are G=7, I=9, N=14, G=7, E=5, R=18, leading to 14-18-28-14-10-36.

Applying this same logic to GARLIC, we first identify the positional values: G=7, A=1, R=18, L=12, I=9, C=3. Multiplying each value by 2 gives 7 × 2 = 14, 1 × 2 = 2, 18 × 2 = 36, 12 × 2 = 24, 9 × 2 = 18, and 3 × 2 = 6. Arranging these results in sequence yields the code 14-2-36-24-18-6.

Explanation

To make the equation 15 + 90 ÷ 9 × 5 - 11 = 28 correct, we interchange the numbers 15 and 9. Substituting 9 in place of 15 and 15 in place of 9, the expression becomes 9 + 90 ÷ 15 × 5 - 11.

Following the BODMAS rule, we first perform the division: 90 ÷ 15 = 6

The equation now reads: 9 + 6 × 5 - 11

Next, we perform the multiplication: 6 × 5 = 30

The equation now reads: 9 + 30 - 11

Finally, we perform addition and subtraction: 39 - 11 = 28

Since the left-hand side equals the right-hand side, the interchange of 15 and 9 satisfies the equation.

Explanation

Mihir's mother's brother-in-law is Mihir's uncle. Since Kaumudi is the daughter of Mihir's uncle, she is Mihir's cousin, and Mihir is also her cousin.

Explanation

Red is worn on Wednesday. The conditions state that Green and Brown cannot be worn on Monday or Friday, which leaves only Tuesday and Thursday for these two colors. Additionally, Green is worn the day after Yellow. If Green were worn on Thursday, Yellow would have to be worn on Wednesday, but Wednesday is already allocated for Red. Therefore, Green must be worn on Tuesday, which implies Yellow is worn on Monday. With Tuesday assigned to Green and Wednesday to Red, the only remaining slot for Brown among the permissible days is Thursday.

Explanation

The coding logic follows the sum of the positional values of the letters in the English alphabet added to the total number of letters in the word. In the English alphabet, the positions are A=1, B=2, ..., Z=26.

For GOLF, the numerical positions are G=7, O=15, L=12, and F=6. The sum of these values is 7 + 15 + 12 + 6 = 40. Since the word consists of 4 letters, adding 4 to the sum yields 40 + 4 = 44.

For BALL, the numerical positions are B=2, A=1, L=12, and L=12. The sum of these values is 2 + 1 + 12 + 12 = 27. Adding the 4 letters in the word results in 27 + 4 = 31.

Applying the same logic to the word PLAY, the numerical positions are P=16, L=12, A=1, and Y=25. Summing these values gives 16 + 12 + 1 + 25 = 54. Adding the number of letters in the word, which is 4, results in 54 + 4 = 58.

Explanation

The given sequence is an alternating series consisting of two distinct patterns. The terms at even positions (2nd, 4th, 6th, 8th, 10th) are consecutive prime numbers: 31, 37, 41, 43, and 47. The terms at odd positions (1st, 3rd, 5th, 7th, 9th, 11th) follow a separate mathematical progression: 2, 4, 10, 28, 82, ?.

The pattern for the odd-positioned terms can be expressed by the formula Tₙ = 3ⁿ⁻¹ + 1, where n represents the position within the sub-series. For n=1, 3⁰ + 1 = 2. For n=2, 3¹ + 1 = 4. For n=3, 3² + 1 = 10. For n=4, 3³ + 1 = 28. For n=5, 3⁴ + 1 = 82. To find the 11th term of the overall series, which is the 6th term of this sub-series (n=6), we calculate 3⁵ + 1 = 243 + 1 = 244.

Alternatively, the logic can be seen through the relationship xₙ = 3xₙ₋₁ - 2. Applying this to the last known term in the sub-series gives 3 × 82 - 2 = 246 - 2 = 244. The differences between these terms also follow a geometric progression of 2, 6, 18, 54, where each difference is multiplied by 3. The next difference is 54 × 3 = 162, and adding this to 82 results in 244.

Explanation

The logical relationship between the categories is established by the given premises using set theory. The statements All lemons are apricots and All grapes are lemons indicate a nested subset relationship where the set of grapes is entirely contained within the set of lemons, and the set of lemons is entirely contained within the set of apricots (G ⊆ L ⊆ A).

The statement No plum is an apricot defines the set of plums as being completely disjoint from the set of apricots (P ∩ A = ∅). Because the set of lemons and the set of grapes are both subsets of apricots, any element belonging to the category of lemons or grapes is also an apricot. Given that no apricot is a plum, it follows through transitive property that no lemon can be a plum and no grape can be a plum (L ∩ P = ∅ and G ∩ P = ∅). These deductions validate that conclusion II and conclusion III are logically sound.

Explanation

In dictionary order, words are arranged alphabetically based on each letter from left to right. All the given words start with the same first three letters PRO. Therefore, the arrangement is determined by comparing the fourth letter of each word. The fourth letters are D in Product (3), F in Professor (2), J in Projection (1), N in Pronounce (4), and V in Provide (5). Arranging these letters in alphabetical order gives the sequence D, F, J, N, V. Matching these letters to their respective words results in the numerical sequence 3, 2, 1, 4, 5.

Explanation

To find the value of Equation I, substitute 5 for 4 and 4 for 5, and interchange the + and × signs: Original: 4 + 6× 5 - 7÷ 1 New: 5× 6 + 4 - 7÷ 1 Using the BODMAS rule, perform division followed by multiplication, addition, and subtraction: 5× 6 + 4 - 7 = 30 + 4 - 7 = 34 - 7 = 27

To find the value of Equation II, substitute 5 for 4 and 4 for 5, and interchange the × and + signs: Original: 5× 3 - 4 + 8÷ 2 New: 4 + 3 - 5× 8÷ 2 Using the BODMAS rule: 4 + 3 - 5× 4 = 4 + 3 - 20 = 7 - 20 = - 13

The resulting values for equations I and II are 27 and - 13.

Explanation

Applying the sequence of mathematical signs ÷, +, ÷, +, and = to the given numbers results in the expression 99 ÷ 33 + 66 ÷ 22 + 44 = 50. Following the BODMAS rule, the division operations are performed first. Calculating these parts gives 99 ÷ 33 = 3 and 66 ÷ 22 = 3. Substituting these values back into the equation yields 3 + 3 + 44 = 50. Summing the terms on the left side gives 6 + 44 = 50, which simplifies to 50 = 50. The sequence correctly balances the equation.

Explanation

The letter-clusters follow a pattern where the first and second letters are reverse opposites, meaning the sum of their alphabetical positions is 27, and the third letter is determined by subtracting 3 from the positional value of the second letter. In the case of IRP, the positions are I = 9, R = 18, and P = 16. While I and R are opposites (9 + 18 = 27), the third letter P is only 2 positions behind R (18 - 2 = 16), failing to match the subtraction of 3 that defines the rest of the group.

Explanation

To arrange the words in alphabetical order as they appear in an English dictionary, we compare them letter by letter from left to right. All words begin with the prefix Fu. Comparing the third letters, Fundament (6), Funerary (2), and Funicular (4) have n, while the remaining words have s. Since n comes before s in the alphabet, these three appear first. Among them, comparing the fourth letters d, e, and i, the order is Fundament (6), then Funerary (2), and then Funicular (4). Next, for the words starting with Fus, we compare the fourth letters: Fuscous (5) has c, Fuselage (7) has e, Fusion (3) has i, and Fustian (1) has t. Ordering these fourth letters alphabetically gives the sequence 5, 7, 3, 1. Combining both groups results in the final dictionary order 6, 2, 4, 5, 7, 3, 1.

Explanation

Based on the given relationship codes, we decode the expression A+B | C-D+E as follows:

A+B implies A is the father of B.

B | C implies B is the son of C. Since A is already established as B's father, C must be B's mother and the wife of A.

C-D implies C is the mother of D. Since A and C are a couple, D is also the child of A. This makes B and D siblings.

D+E implies D is the father of E.

Following the lineage, A is the father of D, and D is the father of E. Therefore, A is the father of E's father, which makes A the paternal grandfather of E.

Explanation

The pattern follows the arrangement of the letters of the word in alphabetical order. In the first pair, the letters of the word PRACTISE are rearranged alphabetically to form ACEIPRST. Similarly, for the word TECHNOLOGY, the letters T, E, C, H, N, O, L, O, G, and Y are rearranged in ascending alphabetical sequence: C, E, G, H, L, N, O, O, T, and Y. This alphabetical sorting results in the term CEGHLNOOTY.

Explanation

The coding logic is based on the position of each letter in the English alphabet (A=1, B=2, ..., Z=26), where the numerical value is multiplied by 3 to obtain the code. For the word BHOPAL, the positions are B=2, H=8, O=15, P=16, A=1, L=12. Multiplying these by 3 results in 2 × 3 = 6, 8 × 3 = 24, 15 × 3 = 45, 16 × 3 = 48, 1 × 3 = 3, and 12 × 3 = 36. For the word IMPHAL, the positions are I=9, M=13, P=16, H=8, A=1, L=12, which result in 27-39-48-24-3-36. Applying the same logic to the word KOHIMA, the alphabetical positions are K=11, O=15, H=8, I=9, M=13, A=1. Multiplying each by 3, we get 11 × 3 = 33, 15 × 3 = 45, 8 × 3 = 24, 9 × 3 = 27, 13 × 3 = 39, and 1 × 3 = 3. This generates the sequence 33-45-24-27-39-3.

Explanation

The relationship established in the pair Hansini : Swan is based on gender, specifically the feminine and masculine forms of a species. Hansini is the term for a female swan, while Hans, commonly translated as Swan, denotes the masculine form. In a similar manner, a Sorceress is a woman who practices magic, serving as the feminine counterpart to the male practitioner, the Magician. Both pairs represent the female and male equivalents of the same biological or professional entity.

Explanation

The series is completed by placing the letters from option a) into the blanks. By dividing the series into logical segments, we can observe a repeating pattern of the constituent letters a, b, c, d, h, and q.

Filling the blanks sequentially with hacabdab: d(h)a(a)b(c)qd(a)h(b)a(d)cq(a)h(b)acq

The series can be broken down into three main blocks based on the position of q and the repetition of the letter sets: Block 1: dha + abcq (7 letters) Block 2: dah + badcq (8 letters) Block 3: ah + bacq (6 letters)

In this pattern: The first part of each block (dha, dah, ah) undergoes a permutation: the h and a are swapped in the second block, and the d is removed in the third. The second part of each block (abcq, badcq, bacq) also undergoes a permutation: the a and b are swapped, and a d is temporarily inserted in the second block before being removed in the third.

Substituting the letters from option a) maintains this consistent structural transformation throughout the series.

Explanation

Substitute the letters with their respective mathematical operators: A = +, B = ×, C = -, and D = ÷. The given expression 441 D 7 A 21 B 6 C (189 D 7) A (46 C 12) is rewritten as:

(441 ÷ 7) + (21 × 6) - (189 ÷ 7) + (46 - 12)

Applying the BODMAS rule, first solve the operations inside the brackets and the divisions: 441 ÷ 7 = 63 189 ÷ 7 = 27 46 - 12 = 34

The expression now becomes: 63 + (21 × 6) - 27 + 34

Next, perform the multiplication: 21 × 6 = 126

Now, substitute this value back into the expression and solve the addition and subtraction: 63 + 126 - 27 + 34 = 189 - 27 + 34 = 162 + 34 = 196

Explanation

The coding follows a specific two-step logic. First, the letters of the given word are arranged in alphabetical order. Second, an alternating shift of +4 and -4 is applied to each letter in this sorted sequence to generate the final code.

For the word TEDIOUS, the letters in alphabetical order are D, E, I, O, S, T, and U. Applying the alternating shift: D (4) + 4 = 8 (H) E (5) - 4 = 1 (A) I (9) + 4 = 13 (M) O (15) - 4 = 11 (K) S (19) + 4 = 23 (W) T (20) - 4 = 16 (P) U (21) + 4 = 25 (Y) The resulting code is HAMKWPY.

For the word PROFUSE, the letters in alphabetical order are E, F, O, P, R, S, and U. Applying the same alternating shift pattern: E (5) + 4 = 9 (I) F (6) - 4 = 2 (B) O (15) + 4 = 19 (S) P (16) - 4 = 12 (L) R (18) + 4 = 22 (V) S (19) - 4 = 15 (O) U (21) + 4 = 25 (Y) The resulting code is IBSLVOY.

Explanation

Taruni is married to Dilip, and they have only one son, Raghu. Since Taruni is the mother-in-law of Hema, and Hema is the mother of Manoj, Raghu must be the husband of Hema and the father of Manoj. This establishes that Dilip is Manoj's paternal grandfather. Jahnavi's sister is Taruni. Given that Taruni and Dilip are a married couple, Taruni is the wife of Dilip, who is Manoj's paternal grandfather.

Explanation

The pattern followed in the letter-clusters involves dividing the seven-letter word into three segments of lengths 3, 2, and 2. The first segment (positions 1-3) is reversed, the second segment (positions 4-5) remains unchanged, and the third segment (positions 6-7) is reversed.

Applying this to CONTROL: 1-3: CON becomes NOC 4-5: TR remains TR 6-7: OL becomes LO Result: NOCTRLO

Applying this to MISTAKE: 1-3: MIS becomes SIM 4-5: TA remains TA 6-7: KE becomes EK Result: SIMTAEK

Applying this to JOURNAL: 1-3: JOU becomes UOJ 4-5: RN remains RN 6-7: AL becomes LA Result: UOJRNLA

Explanation

The numbers in the given sets follow the logic that the difference between the first and second numbers, when further reduced by 2, results in the third number. The pattern can be expressed by the formula:

(First Number - Second Number) - 2 = Third Number

Applying this to the provided sets: For (15, 9, 4): (15 - 9) - 2 = 6 - 2 = 4 For (7, 2, 3): (7 - 2) - 2 = 5 - 2 = 3

Similarly, in the set (19, 13, 4): (19 - 13) - 2 = 6 - 2 = 4

The arithmetic operation remains consistent with the logic observed in the initial sets.

Explanation

The groups follow a pattern where the second number is ten times the first, and the third number is ten less than the second number. This can be represented by the operations n₂ = n₁ × 10 and n₃ = n₂ - 10. In the group (7- 70- 68), the first operation holds as 7 × 10 = 70, but the second operation fails because 70 - 10 results in 60 rather than 68. This deviation from the required difference of ten between the second and third values makes this group the outlier.

Explanation

In syllogistic logic, the combination of two particular affirmative statements (I-type: Some A are B) does not lead to a definite conclusion between the non-adjacent terms. This is because the middle term is not distributed in either premise, meaning it is possible for the subsets mentioned to be entirely distinct from one another within the larger sets.

The statement Some grasses are trees and Some trees are branches does not guarantee an intersection between grasses and branches; therefore, Conclusions I and IV do not follow. Similarly, the statements Some trees are branches and Some branches are dogs provide no logical necessity for an overlap between trees and dogs, meaning Conclusion II does not follow. Finally, since there is no established link between grasses and branches, and no link between trees and dogs, there is no basis for Conclusion III regarding grasses and dogs. Since no definite logical connection is established between any of the terms across the premises, none of the conclusions follow.

Explanation

To verify the equation in option a, we interchange the signs × and + and the numbers 9 and 6.

The original equation is 7 × 6 ÷ 3 + 9 - 8 = 17.

Applying the interchanges to the left-hand side (LHS): LHS = 7 + 9 ÷ 3 × 6 - 8

Following the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction):

Perform Division: 9 ÷ 3 = 3 LHS = 7 + 3 × 6 - 8

Perform Multiplication: 3 × 6 = 18 LHS = 7 + 18 - 8

Perform Addition: 7 + 18 = 25 LHS = 25 - 8

Perform Subtraction: 25 - 8 = 17

Since the calculated LHS is 17, it matches the right-hand side (RHS) of the equation.

Explanation

The series follows a pattern where each term is increased by an increment that grows by one in each step. Calculating the differences between consecutive terms reveals a sequence of consecutive integers:

356 - 345 = 11 368 - 356 = 12 381 - 368 = 13 395 - 381 = 14

Since the differences follow the pattern 11, 12, 13, 14, the next increment in the series must be 15. Adding this value to the last term provides the missing number:

395 + 15 = 410

Explanation

The given sequence follows an arithmetic progression where each subsequent term is obtained by adding a constant value to the preceding term. By calculating the difference between consecutive terms, we find:

178 - 115 = 63 241 - 178 = 63 304 - 241 = 63

Since the common difference is 63, the next number in the series is determined by adding 63 to the last given term:

304 + 63 = 367

Explanation

Hatchel is a primary root word that refers to a specific tool for combing flax or hemp and is not a derivative or compound of the word hatch. It is the only cluster where the sequence h-a-t-c-h does not function as an independent base word associated with an opening or the emergence of young from an egg. While the other letter-clusters are formed by appending standard suffixes or secondary words to a common root to modify its meaning, hatchel is an uncompounded term with a distinct etymological origin.

Explanation

To evaluate the logical validity of the conclusions, we examine the relationships between the sets described in the statements. The premise "All calculators are markers" establishes that the set of calculators is a subset of the markers. The second premise, "Some markers are pencils," indicates an overlap between markers and pencils, but it does not require that any pencils overlap with the specific subset of markers that are calculators. Consequently, Conclusion II, which suggests an intersection between pencils and calculators, is not necessarily true based on the provided information.

Furthermore, the third premise, "Some pencils are erasers," establishes an overlap between pencils and erasers. However, the information provided does not create any link between erasers and markers. The intersection of pencils and erasers could exist entirely outside the set of markers. Therefore, Conclusion I, which claims an intersection between erasers and markers, does not logically follow. Since neither conclusion is a necessary consequence of the statements, neither conclusion I nor II follows.

Explanation

The series follows a specific arithmetic pattern for each corresponding letter in the clusters based on their alphabetical positions.

First letter: The sequence is S(19), O(15), K(11), G(7). The pattern is a subtraction of 4 in each step. The next letter is 7 - 4 = 3, which corresponds to C.

Second letter: The sequence is K(11), O(15), S(19), W(23). The pattern is an addition of 4 in each step. The next letter is 23 + 4 = 27. In a circular alphabet (A-Z), 27 corresponds to A.

Third letter: The sequence is H(8), D(4), Z(26), V(22). The pattern is a subtraction of 4 in each step. The next letter is 22 - 4 = 18, which corresponds to R.

Fourth letter: The sequence is M(13), Q(17), U(21), Y(25). The pattern is an addition of 4 in each step. The next letter is 25 + 4 = 29. In a circular alphabet, 29 corresponds to C (29 - 26 = 3).

Combining these results, the next cluster in the series is CARC.

Explanation

The series follows a consistent arithmetic progression for the position of each letter in the alphabet.

For the first letter in each set, the positions are D (4), J (10), P (16), and V (22). The sequence increases by 6 at each step. Following this pattern, 22 + 6 = 28. In the alphabetical cycle of 26 letters, 28 - 26 = 2, which corresponds to the letter B.

For the second letter in each set, the positions are M (13), O (15), Q (17), and S (19). The sequence increases by 2 at each step. Following this pattern, 19 + 2 = 21, which corresponds to the letter U.

For the third letter in each set, the positions are T (20), B (2), J (10), and R (18). The sequence increases by 8 at each step. Note that 20 + 8 = 28, and 28 - 26 = 2 (B). Following this pattern, 18 + 8 = 26, which corresponds to the letter Z.

The missing term generated by combining these characters is BUZ.

Explanation

The relationship follows the mathematical series y = x³ + x² + x + 3 for the third number x = 7.

For x = 7: y = 7³ + 7² + 7 + 3 y = 343 + 49 + 7 + 3 y = 402

In the first and third pairs, the relation is y = 4x + 7: For x = 5: y = 4(5) + 7 = 27 For x = 8: y = 4(8) + 7 = 39

Applying the cubic transformation specifically to the middle term 7 results in 402.

Explanation

To find the shortest distance between G and C, we analyze the relevant parts of the expression C12mSS5m*G.

According to the given code, PSQ means P is to the north of Q. Therefore, C12mSS indicates that C is 12 m to the north of S.

The code PQ means Q is to the west of P. Thus, S5mG implies that G is 5 m to the west of S, which conversely means S is 5 m to the east of G.

These positions form a right-angled triangle GSC, where the distance GS is the base and SC is the perpendicular height. Point S serves as the vertex of the right angle because SC is a vertical line (north) and GS is a horizontal line (east-west).

Base GS = 5 m Perpendicular SC = 12 m

Using the Pythagoras theorem, the shortest distance GC (the hypotenuse) is calculated as: GC = √(GS² + SC²) GC = √(5² + 12²) GC = √(25 + 144) GC = √(169) GC = 13 m

Explanation

The coding logic follows a specific pattern: the sum of the reverse positional values of the letters (where A = 26, B = 25, ..., Z = 1) is multiplied by the number of vowels present in the word.

For the word GLOVE: The reverse positional values are G = 20, L = 15, O = 12, V = 5, and E = 22. The sum of these values is 20 + 15 + 12 + 5 + 22 = 74. The word GLOVE contains 2 vowels (O and E). The final code is 74 × 2 = 148.

For the word OBDURATE: The reverse positional values are O = 12, B = 25, D = 23, U = 6, R = 9, A = 26, T = 7, and E = 22. The sum of these values is 12 + 25 + 23 + 6 + 9 + 26 + 7 + 22 = 130. The word OBDURATE contains 4 vowels (O, U, A, and E). The final code is 130 × 4 = 520.

Explanation

The logic follows the rearrangement of the letters of the given word in ascending alphabetical order. In the first pair, the word FASTER is composed of the letters F, A, S, T, E, and R. When these letters are arranged according to their position in the English alphabet, they form AEFRST (A-E-F-R-S-T). Applying the same logic to the word KINGDOM, we identify the constituent letters as K, I, N, G, D, O, and M. Arranging these seven letters in alphabetical order yields D, G, I, K, M, N, and O, resulting in the term DGIKMNO.

Explanation

The sequence is formed by the repeated pattern of the four-letter block GANG. By inserting the letters G, N, N, and G into the blanks of the given series A_GGA_GGAN, the complete string becomes GANGGANGGANG. This pattern consists of the unit GANG repeating three times consecutively. Placing G in the first blank, N in the second, N in the third, and G in the fourth satisfies the logic of a consistent repeating sequence.

Explanation

To make the equation correct, the numbers 119 and 153 are interchanged. Replacing 119 with 153 and 153 with 119 in the expression 119 + 11 × 5 - 153 ÷ 17 = 201 results in:

153 + 11 × 5 - 119 ÷ 17 = 201

Applying the BODMAS rule, perform the operations in the following order:

First, perform the division: 119 ÷ 17 = 7

Next, perform the multiplication: 11 × 5 = 55

Now, the equation is: 153 + 55 - 7 = 201

Perform the addition: 153 + 55 = 208

Finally, perform the subtraction: 208 - 7 = 201

Since the left-hand side equals the right-hand side (201 = 201), the interchange of 119 and 153 makes the equation correct.

Explanation

To determine the seating arrangement, we place the eight individuals in positions 1 to 8 around the circular table in a counter-clockwise direction. Starting with Piyush at position 1, Sundar sits second to his right at position 3. Since only two persons sit between Sundar and Krunal, Krunal must be at position 6 (moving counter-clockwise) or position 8 (moving clockwise).

Nilima is an immediate neighbour of both Krunal and Bindu, which means she sits between them. If Krunal is at position 6, Nilima must be at position 5 and Bindu at position 4. This satisfies the condition that Bindu is not an immediate neighbour of Piyush (1) or Krunal (6). Manoj sits third to the right of Bindu, placing him at position 7 (4 + 3 = 7). Omkar sits opposite Bindu, placing him at position 8. The only remaining spot, position 2, is occupied by Renu.

In this configuration, the seating order is 1-Piyush, 2-Renu, 3-Sundar, 4-Bindu, 5-Nilima, 6-Krunal, 7-Manoj, and 8-Omkar. Facing the centre, the immediate left of Renu at position 2 is Piyush at position 1. In a group of eight, the person opposite position 1 is position 5. Since Nilima is at position 5, she sits opposite the person who is to the immediate left of Renu.

Explanation

To make the equation correct, the digits 3 and 4 are interchanged. Following this rule, the number 37 becomes 47 and the number 47 becomes 37. Substituting these values into the given equation:

47 + 1152 × 8 ÷ 768 - 37 = 22

According to BODMAS rules, we first perform the multiplication and division operations: 1152 × 8 ÷ 768 = (1152 × 8)/(768) = ⁹²¹⁶⁄₇₆₈ = 12

The expression now simplifies to: 47 + 12 - 37

Next, perform addition and subtraction from left to right: 59 - 37 = 22

Since the calculated result matches the value on the right-hand side, the interchange of digits 3 and 4 makes the equation correct.

Explanation

The coding pattern follows a simple subtraction of 1 from the positional value of each letter in the English alphabetical series (Letter - 1).

Applying this logic to the given words: In DENTIST: D (4) - 1 = C (3) E (5) - 1 = D (4) N (14) - 1 = M (13) T (20) - 1 = S (19) I (9) - 1 = H (8) S (19) - 1 = R (18) T (20) - 1 = S (19) Result: CDMSHRS

In TOOTH: T (20) - 1 = S (19) O (15) - 1 = N (14) O (15) - 1 = N (14) T (20) - 1 = S (19) H (8) - 1 = G (7) Result: SNNSG

Applying the same pattern to HEALING: H (8) - 1 = G (7) E (5) - 1 = D (4) A (1) - 1 = Z (26) L (12) - 1 = K (11) I (9) - 1 = H (8) N (14) - 1 = M (13) G (7) - 1 = F (6)

The resulting sequence is GDZKHMF. The sequence GDZKHM corresponds to the letters obtained through this -1 shift.

Explanation

The coding logic is based on whether a letter is a vowel or a consonant. Vowels are shifted forward by 5 positions in the English alphabetical sequence, while consonants are shifted backward by 6 positions. In a cyclic alphabet, if a subtraction result is less than 1, we continue counting backward from 26 (Z).

In the word BUILDER: B is a consonant: 2 - 6 = 22 (V) U is a vowel: 21 + 5 = 26 (Z) I is a vowel: 9 + 5 = 14 (N) L is a consonant: 12 - 6 = 6 (F) D is a consonant: 4 - 6 = 24 (X) E is a vowel: 5 + 5 = 10 (J) R is a consonant: 18 - 6 = 12 (L) This results in the code VZNFXJL.

Applying the same logic to the word PARKING: P is a consonant: 16 - 6 = 10 (J) A is a vowel: 1 + 5 = 6 (F) R is a consonant: 18 - 6 = 12 (L) K is a consonant: 11 - 6 = 5 (E) I is a vowel: 9 + 5 = 14 (N) N is a consonant: 14 - 6 = 8 (H) G is a consonant: 7 - 6 = 1 (A) Assembling these letters in sequence gives the code JFLENHA.

Explanation

The pattern in the given grid is based on the sum of the digits of all the numbers in each row. First, organize the numbers into a grid of five rows and three columns:

Row 1: 28, 54, 32 Row 2: 56, 8, 7 Row 3: 65, 8, 18 Row 4: 84, ?, 8 Row 5: 14, 13, 12

Now, calculate the sum of the digits for the first three rows: Row 3: 6 + 5 + 8 + 1 + 8 = 28 Row 2: 5 + 6 + 8 + 7 = 26 Row 1: 2 + 8 + 5 + 4 + 3 + 2 = 24

The sums follow a decreasing arithmetic progression: 28, 26, 24. Following this logic, the sum of the digits for the numbers in Row 4 should be 22.

Calculation for Row 4: Sum = (8 + 4) + (sum of digits of ?) + 8 = 22 12 + (sum of digits of ?) + 8 = 22 20 + (sum of digits of ?) = 22 Sum of digits of ? = 22 - 20 = 2

Comparing this with the given options: a) 9: Sum = 9 b) 11: Sum = 1 + 1 = 2 c) 8: Sum = 8 d) 10: Sum = 1 + 0 = 1

The number 11 is the only option where the sum of the digits is 2. Substituting 11 into the row completes the sequence 28, 26, 24, 22. While Row 5 (1+4+1+3+1+2=12) does not continue this specific progression, the pattern for the other four rows is consistent and directly identifies the missing value.

Explanation

To find the code for Sohan, we compare the two given sentences to identify common words and their corresponding codes.

Sentence 1: Min Fin Dig = Sohan is Engineer Sentence 2: Sic Ric Min Dic Fin = Profession of Engineer is tough

The words is and Engineer appear in both English sentences. Similarly, the codes Min and Fin appear in both coded sentences. This means the set {Min, Fin} represents the set {is, Engineer}.

By eliminating the common elements from the first sentence, we are left with the word Sohan and the code Dig. Since Dig is the only code in the first sentence not shared with the second sentence, it must represent the word Sohan.

Explanation

In the expression W % O - B ? C ? D, the relationship W % O indicates that W is the son-in-law of O. The relationship O - B indicates that B is the wife of O. Consequently, O and B are the parents-in-law of W. For D to be the wife of W, D must be the daughter of O and B.

By substituting the symbols + and # into the expression, we get W % O - B + C # D. The term B + C means C is the son of B. The term C # D means D is the only sister of C. Since C is the son of B and D is the sister of C, D is the daughter of B. As W is the son-in-law of the couple O and B and D is their daughter, D is the wife of W.

Explanation

Conclusion I follows because Statement II establishes that No B is A, which is logically equivalent to the statement No A is B. In formal logic, if a universal negative statement No A is B is true, then the particular negative statement Some A are not B must also be true.

Conclusion II does not follow because the premises do not define the total relationship between B and H. Statement I indicates that the entire set A is contained within set H, and Statement II indicates that set B and set A are disjoint. While B cannot overlap with the part of H that contains A, it is entirely possible for B to overlap with the part of H that does not contain A. Since the statements do not rule out an intersection between B and H, the conclusion No B is H is not necessarily true. Therefore, only conclusion I is logically certain.

Explanation

In the expression P ÷ Q × R, the symbol ÷ indicates that the first person is the father of the second. Thus, P ÷ Q means P is the father of Q. The symbol × indicates that the first person is the mother of the second. Thus, Q × R means Q is the mother of R. Since Q is a mother, it is established that Q is female. Because P is the father of Q and Q is female, Q is the daughter of P.

Explanation

The numerical pairs follow the pattern (n + 7) × 7, where n is the first term of each pair.

For the first pair, 21:196: (21 + 7) × 7 = 28 × 7 = 196

For the third pair, 38:315: (38 + 7) × 7 = 45 × 7 = 315

Applying the same logic to the middle term, 29: (29 + 7) × 7 = 36 × 7 = 252

Explanation

The relationship between the terms is established by reversing the letters of the word and then shifting each letter forward by two positions in the alphabetical sequence (+2 shift). For the first term QUICKER, reversing the order of its letters results in REKCIUQ. Applying the +2 shift to this reversed string gives: R +2 T, E +2 G, K +2 M, C +2 E, I +2 K, U +2 W, and Q +2 S. Combining these letters forms the second term, TGMEKWS.

Applying the same logic to the third term REPORTS, the word is first written in reverse order as STROPER. Then, each letter is shifted forward by two positions: S +2 U, T +2 V, R +2 T, O +2 Q, P +2 R, E +2 G, and R +2 T. This sequence of letters forms the word UVTQRGT.

Explanation

Substituting the signs from the sequence in option d into the expression 22 66 33 11 44 * 0, where T represents addition (+), M represents division (÷), G represents multiplication (×), I represents subtraction (-), and B represents equality (=), the equation becomes:

22 + 66 ÷ 33 × 11 - 44 = 0

According to the BODMAS rule, the operations are performed in a specific hierarchy. First, the division operation is performed: 66 ÷ 33 = 2, reducing the expression to 22 + 2 × 11 - 44. Next, the multiplication operation is carried out: 2 × 11 = 22, which leads to 22 + 22 - 44. Following this, the addition operation is performed: 22 + 22 = 44. Finally, the subtraction operation 44 - 44 results in 0. This confirms that 0 = 0, balancing the equation perfectly. The sixth letter A in the sequence is extraneous to the five required mathematical signs.

Explanation

The coding logic involves arranging the letters of the given word in descending alphabetical order. In the word FIXED, the letters sorted from Z to A are X, I, F, E, and D. For the word MOUSE, the letters in alphabetical order are E, M, O, S, and U, and arranging them in descending order results in USOME. Following the same pattern for the word GAMBIT, the letters are A, B, G, I, M, and T. Arranging these letters from the highest alphabetical rank to the lowest results in the sequence T, M, I, G, B, A.