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

Explanation

To arrange the words in alphabetical or dictionary order, we compare each letter from left to right. All words begin with the prefix Ma. Comparing the third letter, g (found in words 1, 2, 3, and 4) appears before j (found in word 5), which identifies Majesty (5) as the final word in the sequence.

Next, we look at the fourth letter of the remaining words. The letter i in Magical (4) comes before the letter n in Magnetic (1), Magnify (2), and Magnet (3), establishing Magical (4) as the first word. For the words starting with Magn, we compare the fifth letter. The letter e in Magnetic (1) and Magnet (3) comes before the letter i in Magnify (2), placing Magnify (2) in the fourth position. Finally, comparing Magnet (3) and Magnetic (1), the shorter word Magnet (3) is a complete prefix of the longer word Magnetic (1). In dictionary formatting, a shorter word precedes a longer word that begins with the same letters. Therefore, the sequence is 4, 3, 1, 2, 5.

Explanation

The given sequence follows a pattern where the square of one number subtracted from the square of another results in a third number in the set. Specifically, the relationship x² - y² = z is applied to specific positions in the sequence.

The sequence is: 15, 15, 81, 12, 18, 99, 15, 17, 120, ?

Applying the logic x² - y² = z:

For the first set, using the 1st and 4th numbers to get the 3rd: 15² - 12² = 225 - 144 = 81

For the second set, using the 5th and 2nd numbers to get the 6th: 18² - 15² = 324 - 225 = 99

For the third set, using the 8th and 10th (unknown) numbers to get the 9th: 17² - ?² = 120 289 - ?² = 120 ?² = 289 - 120 ?² = 169 ? = 13

Alternatively, the pattern can be seen as (x + y)(x - y) = z: (17 + 13) × (17 - 13) = 30 × 4 = 120

Explanation

The numerical relationship follows the pattern (n - 3)² where n is the first number in the ratio. In the first pair, subtract 3 from 27 to get 24, and the square of 24 is 24 × 24 = 576. Applying this same logic to the third number, we subtract 3 from 19 to get 16. Squaring this value gives 16 × 16 = 256.

Explanation

Reena refers to the woman as the only daughter of her father-in-law. Reena's father-in-law is the father of Reena's husband. The daughter of Reena's father-in-law is therefore the sister of Reena's husband. In family relationship terms, the sister of one's husband is defined as a sister-in-law.

Explanation

By interchanging the signs ÷ and × in the given equation 72 × 18 ÷ 9 + 19 - 39 = 16, the expression becomes:

72 ÷ 18 × 9 + 19 - 39 = 16

Applying the BODMAS rule (Division, Multiplication, Addition, Subtraction):

First, perform the division: 72 ÷ 18 = 4

The equation now is: 4 × 9 + 19 - 39 = 16

Next, perform the multiplication: 4 × 9 = 36

The equation now is: 36 + 19 - 39 = 16

Perform the addition: 36 + 19 = 55

Finally, perform the subtraction: 55 - 39 = 16

The left hand side equals the right hand side (16 = 16), making the equation correct.

Explanation

By interchanging the signs ÷ and ×, the original equation 28 + 14 × 7 ÷ 5 - 18 = 20 is modified to 28 + 14 ÷ 7 × 5 - 18 = 20. Applying the BODMAS rule, we first perform the division operation 14 ÷ 7 = 2. The equation then becomes 28 + 2 × 5 - 18 = 20. Next, we perform the multiplication 2 × 5 = 10, resulting in 28 + 10 - 18 = 20. Carrying out the addition and subtraction, we get 38 - 18 = 20, which simplifies to 20 = 20. This confirms the equation is balanced.

Explanation

The equation 8 × 3 ÷ 6 + 9 - 7 = 14 is modified by interchanging the signs × and ÷, and replacing the number 7 with 9 and 9 with 7. The resulting expression becomes 8 ÷ 3 × 6 + 7 - 9. Following the BODMAS rule, the operations are performed as follows: first, the division and multiplication are handled from left to right, where 8 ÷ 3 × 6 equals ⁸⁄₃ × 6, which simplifies to 8 × 2 = 16. Then, the addition and subtraction are carried out: 16 + 7 - 9 = 23 - 9 = 14. This confirms that the left hand side equals the right hand side.

Explanation

The given number series follows an alternating pattern of division and subtraction using consecutive natural numbers starting from 1. The operations applied to reach each subsequent term are as follows:

The second term is obtained by dividing the first term by 1: 74 ÷ 1 = 74. The third term is obtained by subtracting 2 from the second term: 74 - 2 = 72. The fourth term is obtained by dividing the third term by 3: 72 ÷ 3 = 24. The fifth term, which is the missing number, is obtained by subtracting 4 from the fourth term: 24 - 4 = 20.

To verify the pattern, the sixth term is obtained by dividing the fifth term by 5: 20 ÷ 5 = 4, which matches the final number in the series. Thus, the missing number is 20.

Explanation

By comparing the first phrase 'this is fact' (cuz duz ruz) and the second phrase 'fact is fictional' (guz ruz cuz), the common words are 'is' and 'fact', corresponding to the common codes 'cuz' and 'ruz'. Comparing these with the third phrase 'doubt is clear' (cuz kuz buz), the only common word is 'is', and the only common code is 'cuz'. Therefore, 'is' is coded as 'cuz'.

Since 'is' is 'cuz', it follows from the first two phrases that 'fact' is 'ruz'. In the first phrase, after accounting for 'is' (cuz) and 'fact' (ruz), the remaining word 'this' corresponds to the remaining code 'duz'. In the second phrase, after accounting for 'is' (cuz) and 'fact' (ruz), the remaining word 'fictional' corresponds to the remaining code 'guz'. Thus, the words 'this', 'is', and 'fictional' are represented by 'duz', 'cuz', and 'guz' respectively.

Explanation

The series follows a pattern of alternating operations of multiplication and addition using consecutive even integers starting from 2. Applying the first operation to the first term, we multiply 24 by 2 to get the second term: 24 × 2 = 48.

The validity of this pattern is confirmed by the subsequent terms in the sequence. Adding the next even number, 4, to the second term results in the third term: 48 + 4 = 52. Multiplying the third term by the next even number, 6, results in the fourth term: 52 × 6 = 312. Finally, adding the next even number, 8, to the fourth term results in the fifth term: 312 + 8 = 320. The logic of the series is defined by the sequence of operations × 2, + 4, × 6, + 8.

Explanation

Let the three sets be S for Snooker, T for Tennis, and C for Chess. The number of students playing only two games is the sum of those playing only S ∩ T, only S ∩ C, and only T ∩ C.

Given: Total playing exactly two games = 29 Students playing only S ∩ T = 11 Students playing only S ∩ C = 6 Students playing all three games (S ∩ T ∩ C) = 5 Total Tennis players n(T) = 49

First, calculate the number of students playing only T ∩ C: Only T ∩ C = (Total exactly two games) - (Only S ∩ T) - (Only S ∩ C) Only T ∩ C = 29 - 11 - 6 = 12

The total number of tennis players is the sum of those playing only tennis, those playing only tennis and one other game, and those playing all three games: n(T) = (Only T) + (Only S ∩ T) + (Only T ∩ C) + (S ∩ T ∩ C) 49 = (Only T) + 11 + 12 + 5 49 = (Only T) + 28 Only T = 49 - 28 = 21

We can verify this with the other constraints. For Snooker, n(S) = (Only S) + 11 + 6 + 5 = 42, which gives Only S = 20. Since the problem states the number of students playing only snooker and only chess is equal, Only C = 20. Checking the Chess total: n(C) = 20 (Only C) + 6 (Only S ∩ C) + 12 (Only T ∩ C) + 5 (All) = 43, which perfectly matches the given value.

Explanation

The logic follows a three-step transformation: alphabetical sorting, incrementing, and reversing.

For the first term IVORY: Arrange the letters in alphabetical order: I, O, R, V, Y. Increment each letter by one position (+1): J, P, S, W, Z. Reverse the resulting sequence: Z, W, S, P, J. This matches the second term ZWSPJ.

Applying the same logic to the third term CREAM: Arrange the letters in alphabetical order: A, C, E, M, R. Increment each letter by one position (+1): B, D, F, N, S. Reverse the resulting sequence: S, N, F, D, B.

Explanation

The coding logic follows two distinct rules for consonants and vowels. Consonants are replaced by the next letter in the English alphabetical order (position + 1), while vowels are replaced by the next vowel in the standard sequence of A, E, I, O, U.

Applying this to REINCARNATE: The consonant R is followed by S. The vowel E is followed by I in the vowel sequence. The vowel I is followed by O in the vowel sequence. The consonant N is followed by O. The consonant C is followed by D. The vowel A is followed by E in the vowel sequence. The consonant R is followed by S. The consonant N is followed by O. The vowel A is followed by E in the vowel sequence. The consonant T is followed by U. The vowel E is followed by I in the vowel sequence.

Combining these transformations in order, R becomes S, E becomes I, I becomes O, N becomes O, C becomes D, A becomes E, R becomes S, N becomes O, A becomes E, T becomes U, and E becomes I, resulting in the code SIOODESOEUI.

Explanation

The series follows a pattern where each letter of the cluster is transformed by a constant numerical value to derive the next cluster. For the first letter, there is a constant subtraction of 3 such that E(5) - 3 = B(2), B(2) - 3 = Y(25), Y(25) - 3 = V(22), and V(22) - 3 = S(19). For the second letter, there is a constant addition of 4 such that C(3) + 4 = G(7), G(7) + 4 = K(11), K(11) + 4 = O(15), and O(15) + 4 = S(19). For the third letter, there is a constant subtraction of 5 such that D(30) - 5 = Y(25), Y(25) - 5 = T(20), T(20) - 5 = O(15), and O(15) - 5 = J(10). For the fourth letter, there is a constant addition of 5 such that R(18) + 5 = W(23), W(23) + 5 = B(28/2), B(2) + 5 = G(7), and G(7) + 5 = L(12). Combining these values, the missing cluster is SSJL.

Explanation

According to the given conditions, I holds the first rank. The positions of H, K, and L are linked such that L is immediately followed by H, and H is immediately followed by K, creating the sequence L-H-K. Since there are five ranks in total and J is not at the lowest rank, the sequence L-H-K cannot occupy the second, third, and fourth spots because that would leave the fifth and lowest spot for J. Therefore, the L-H-K sequence must occupy the third, fourth, and fifth positions. This placement leaves the second rank for J. Consequently, the final ranking order from top to bottom is I, J, L, H, and finally K at the fifth and lowest position.

Explanation

Pandas are primarily known for feeding on bamboo, and similarly, the primary and characteristic diet of a koala consists of eucalyptus leaves. Therefore, Eucalyptus is the correct term to complete the analogy.

Explanation

Interchanging the numbers 7 and 8 makes the equation correct. By swapping 7 and 8, the expression 7 + 56 ÷ 8 × 2 - 13 becomes:

8 + 56 ÷ 7 × 2 - 13

Applying the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction), we first perform the division: 56 ÷ 7 = 8

The equation now becomes: 8 + 8 × 2 - 13

Next, we perform the multiplication: 8 × 2 = 16

The equation now simplifies to: 8 + 16 - 13

Finally, we perform the addition and subtraction from left to right: 8 + 16 = 24 24 - 13 = 11

As the result matches the value on the right-hand side of the original equation, interchanging 7 and 8 is the correct modification.

Explanation

The series follows a triple-difference pattern where the gap between numbers increases at a non-linear rate. First, calculate the differences between consecutive terms: 99 - 61 = 38 152 - 99 = 53 222 - 152 = 70 312 - 222 = 90

Next, find the differences between these values (the second-order differences): 53 - 38 = 15 70 - 53 = 17 90 - 70 = 20

Now, find the differences between these second-order differences (the third-order differences): 17 - 15 = 2 20 - 17 = 3

The third-order differences follow the sequence 2, 3, ..., suggesting the next value is 4. Working backward to find the next term in the series: The next second-order difference is 20 + 4 = 24. The next first-order difference is 90 + 24 = 114. The missing number in the series is 312 + 114 = 426.

Explanation

The given expression is 88 120 42 240 48 * 2. By substituting the signs from option b in the sequential order, the equation becomes 88 = 120 - 42 + 240 ÷ 48 × 2. According to the BODMAS rule, operations must be performed in the order of Division, Multiplication, Addition, and Subtraction.

First, performing the division 240 ÷ 48 gives 5. The equation simplifies to 88 = 120 - 42 + 5 × 2. Next, performing the multiplication 5 × 2 gives 10, resulting in 88 = 120 - 42 + 10. Finally, calculating the addition and subtraction on the right-hand side, 120 - 42 equals 78, and 78 + 10 equals 88. This results in the balanced equation 88 = 88.

Explanation

The pattern follows the logic that the third number in each row is the difference between the squares of the first and second numbers. The formula is a² - b² = c, which can also be expressed as (a + b)(a - b) = c.

In the first row: 15² - 9² = 225 - 81 = 144. In the third row: 22² - 17² = 484 - 289 = 195.

Applying this logic to the second row: 18² - 12² = 324 - 144 = 180.

Alternatively, using the algebraic identity: (18 + 12) × (18 - 12) = 30 × 6 = 180.

Explanation

The relationship between the letter-clusters is determined by a specific arithmetic pattern applied to the positional values of the letters in the English alphabet. In the first pair, RJB is transformed into TGF using the sequence +2, -3, and +4. Specifically, the first letter R (18) + 2 equals T (20), the second letter J (10) - 3 equals G (7), and the third letter B (2) + 4 equals F (6). Applying this same pattern to the third cluster QPG results in the following transformations: Q (17) + 2 equals 19, which is S; P (16) - 3 equals 13, which is M; and G (7) + 4 equals 11, which is K. Combining these letters results in the cluster SMK.

Explanation

The relationship between the numbers follows the logic (n ÷ 4) + 2. In the first pair, dividing 68 by 4 gives 17, and adding 2 to this quotient results in 19. Following the same pattern for the third number, dividing 164 by 4 yields 41. Adding 2 to this value gives 41 + 2 = 43.

Explanation

The series is composed of a repeating 7-letter logical unit with specific internal modifications. By dividing the series into groups of seven, we can identify the following pattern:

Group 1: r h k n b c b Group 2: s h k a b c b Group 3: t n k h b c b

Three distinct patterns govern these groups. First, the initial letter of each group follows an alphabetical sequence: r in Group 1, s in Group 2, and t in Group 3. Second, the final three letters of every group remain constant as b-c-b. Third, the middle letters at positions 2, 3, and 4 undergo transformation: Group 1 uses h-k-n, while Group 3 uses the reverse sequence n-k-h.

By sequentially placing the letters from the correct option (h, b, b, s, k, n, h, n) into the blanks of the provided string r_kn_c__h_abcbt_k_bcb, we fill the positions as follows:

The first three blanks (h, b, b) complete Group 1 as r h k n b c b. The next two blanks (s, k) complete Group 2 as s h k a b c b. The sixth and seventh blanks (n, h) complete Group 3 as t n k h b c b. The eighth letter (n) represents the start of the fourth group.

Explanation

The logical sequence follows the chronological progression of a disease cycle. It begins with the exposure to a Virus (3), which enters the host body and leads to an Infection (5). As the infection progresses, the patient begins to manifest observable physical Symptoms (4). These symptoms necessitate medical intervention in the form of Treatment (1). Once the treatment is administered and the body overcomes the pathogen, the process concludes with the patient's Recovery (2).

Explanation

The numerical value of each word is calculated by summing the positional values of its letters in the English alphabet (A=1, B=2, …, Z=26) and then multiplying the total sum by 3.

For ONION: O(15) + N(14) + I(9) + O(15) + N(14) = 67. The code is 67 × 3 = 201.

For POTATO: P(16) + O(15) + T(20) + A(1) + T(20) + O(15) = 87. The code is 87 × 3 = 261.

Following the same logic for MANGO: Sum of positional values = M(13) + A(1) + N(14) + G(7) + O(15) = 50 Code = 50 × 3 = 150

Explanation

The series follows a pattern where the difference between consecutive terms consists of squares of decreasing odd numbers.

The first difference is 298 - 217 = 81, which is 9². The second difference is 217 - 168 = 49, which is 7². The third difference is 168 - 143 = 25, which is 5².

The sequence of numbers being squared is 9, 7, 5, which are consecutive odd numbers in descending order. The next odd number in this descending sequence is 3. Therefore, the next difference should be 3² = 9.

To find the missing number, subtract 9 from the last given term: 143 - 9 = 134.

Explanation

The statement all pencils are colours establishes that the set of pencils is entirely contained within the set of colours. Consequently, any element belonging to the pencil set must also belong to the colour set, which validates the conclusion that some colours are pencils. Similarly, the statement all pens are papers defines pens as a subset of papers. Following the rule of conversion for universal affirmative propositions, if every pen is a paper, then it is inherently true that some papers are pens, thereby confirming conclusion III.

Explanation

Mahesh is the father of Aakash, and Aakash is the husband of Maya (as they are the parents of Vansh and Ritu). Therefore, Maya is the daughter-in-law of Mahesh.

Explanation

Let the ages of Tarun and Saurabh five years ago be 4x and x respectively. Consequently, their present ages are 4x + 5 and x + 5. Five years from now, their ages will be (4x + 5) + 5 = 4x + 10 and (x + 5) + 5 = x + 10.

According to the given condition, the ratio of their ages after five years will be 2:1. Setting up the equation:

(4x + 10)/(x + 10) = ²⁄₁

By cross-multiplying, we get 4x + 10 = 2(x + 10), which simplifies to 4x + 10 = 2x + 20. Rearranging the terms to solve for x results in 4x - 2x = 20 - 10, which gives 2x = 10, or x = 5.

Saurabh's present age is x + 5. Substituting the value of x, we find his present age to be 5 + 5 = 10 years.

Explanation

The code is generated by shifting each letter of the word forward in the alphabet by an increasing sequence of integers starting from 3. For the word FLASK, the shifts are F + 3 = I, L + 4 = P, A + 5 = F, S + 6 = Y, and K + 7 = R.

Following this pattern for TOURS: The first letter T (20) shifts by +3 to become W (23). The second letter O (15) shifts by +4 to become S (19). The third letter U (21) shifts by +5 to become Z (26). The fourth letter R (18) shifts by +6 to become X (24). The fifth letter S (19) shifts by +7 to become Z (26).

The word TOURS is thus encoded as WSZXZ.

Explanation

The logic followed in the given analogy is x : x(x + 1) or x : x² + x. For the first pair, the relationship is 7 : 7 × (7 + 1), which simplifies to 7 : 7 × 8 = 56. Applying the same logic to the third number, we calculate 11 × (11 + 1), which is 11 × 12 = 132. Alternatively, using the square method, 11² + 11 = 121 + 11 = 132.

Explanation

The letter-cluster CNDV is the odd one out because the numerical difference between the first and second letters is not equal to the numerical difference between the third and fourth letters. For CNDV, the difference between the positions of C (3) and N (14) is 14 - 3 = 11, while the difference between the positions of D (4) and V (22) is 22 - 4 = 18. This inconsistency in the letter gaps distinguishes it from the pattern where these differences are identical.

Explanation

In a circular arrangement of five people facing the centre, we can fix Kavya's position to determine the others. Vishnu is seated to the immediate right of Kavya. Moving clockwise to find the positions to the left, the third position from Kavya is occupied by Chirag. This leaves two vacant spots between Kavya and Chirag: the first seat to the left and the second seat to the left of Kavya. Since Surbhi is not adjacent to Chirag, she cannot occupy the seat that is second to the left of Kavya because that seat is right next to Chirag. Therefore, Surbhi must sit in the first seat to the left of Kavya. The only remaining person, Raina, must then occupy the seat that is second to the left of Kavya.

Explanation

The series follows a logical progression where each subsequent term is obtained by multiplying the previous term by a factor that increases by 0.5 at each step. The multipliers in the sequence are 0.5, 1.0, 1.5, 2.0, and 2.5. Starting from the first term, 240 × 0.5 = 120. Following the pattern, the second term is multiplied by 1.0 to find the missing value, resulting in 120 × 1.0 = 120. This logic is confirmed by the remaining terms: 120 × 1.5 = 180, 180 × 2.0 = 360, and 360 × 2.5 = 900.

Explanation

The coding logic follows a rule where each consonant is replaced by its succeeding letter (+1) and each vowel is replaced by its preceding letter (-1) in the English alphabetical order.

In MANIA, the consonants M and N become N and O respectively, while the vowels A, I, and A become Z, H, and Z. Similarly, in PROUD, the consonants P, R, and D become Q, S, and E, while the vowels O and U become N and T.

Applying this logic to DONKEY: D (consonant) + 1 = E O (vowel) - 1 = N N (consonant) + 1 = O K (consonant) + 1 = L E (vowel) - 1 = D Y (consonant) + 1 = Z

The resulting code is ENOLDZ.

Explanation

The series follows a pattern of alternating operations. The first operation involves multiplying the current term by 2 and subtracting 3 to get the next term. The second operation involves adding a number that increments by 1 with each occurrence.

The steps are calculated as follows: 7 × 2 - 3 = 11 11 + 3 = 14 14 × 2 - 3 = 25 25 + 4 = 29 29 × 2 - 3 = 55

Following this pattern, the next operation after adding 4 is to add 5. 55 + 5 = 60

Explanation

The series follows a pattern where the five-letter cluster QKTRS is repeated three times. By dividing the 15-character sequence into three equal groups, the structure becomes:

Q _ T _ S | _ K _ R _ | _ K _ R S

Substituting the letters from option d (K, R, Q, T, S, Q, T) into the blanks sequentially completes the pattern:

Q (K) T (R) S | (Q) K (T) R (S) | (Q) K (T) R S

This results in the uniform repetition of QKTRS | QKTRS | QKTRS.

Explanation

The coding language follows a pattern based on the alphabetical positions (A=1, B=2, ..., Z=26) of the letters, with specific transformations applied to each position within the word.

For the first letter: The code is calculated as the ceiling of the alphabetical rank divided by 6 (⌈ Rank / 6 ⌉). L (12): 12 / 6 = 2 → 2 B (2): 2 / 6 = 0.33 → 1 H (8): 8 / 6 = 1.33 → 2

For the second letter: The transformation for vowels follows a decreasing pattern where A (1) and E (5) are coded as 4, and O (15) is coded as 3. Applying this to HELP: E (5) → 4

For the third letter: Subtract 11 from the alphabetical rank if it is even, and 12 if it is odd. O (15, odd): 15 - 12 = 3 L (12, even): 12 - 11 = 1 L (12, even): 12 - 11 = 1

For the fourth letter: Subtract 9 from the alphabetical rank if it is even, and 11 if it is odd. K (11, odd): 11 - 11 = 0 L (12, even): 12 - 9 = 3 P (16, even): 16 - 9 = 7

Combining these transformations for HELP (H=8, E=5, L=12, P=16): H: 2 E: 4 L: 1 P: 7

This results in the code 2417.

Explanation

The equation is balanced by replacing the asterisks with the mathematical signs in the sequence provided in option c, which corresponds to the operations ÷, -, +, × followed by =.

Substituting the signs into the equation: 34 ÷ 17 - 54 + 18 × 6 = 56

Following the BODMAS/VBODMAS rule, operations are performed in the order of Division, Multiplication, Addition, and then Subtraction:

First, perform the division: 34 ÷ 17 = 2 The equation becomes: 2 - 54 + 108 = 56

Next, perform the multiplication: 18 × 6 = 108 The equation becomes: 2 - 54 + 108 = 56

Now, perform the addition and subtraction: 2 + 108 - 54 = 56 110 - 54 = 56 56 = 56

The left-hand side (LHS) is equal to the right-hand side (RHS), confirming that the combination balances the equation.

Explanation

The given words describe the chronological stages of creating and presenting a piece of artwork. The process begins with making a scratch (2), which refers to creating the initial rough sketch or outline. Once the drawing is prepared, the next logical step is filling colour (3) to complete the visual details of the painting. After the artwork is finished, it is secured and prepared for presentation by doing frame (4). Finally, once the piece is framed and ready, the last stage is to display (1) it for viewing. This sequence follows the natural progression from the inception of an art project to its final exhibition.

Explanation

Let n be the number of matches played by Mithali before the national series. The total runs scored by her before the series was 45n. In the national series, she played 10 matches and scored 500 runs, making the total runs scored till date 45n + 500. The total number of matches played till date is n + 10.

The new average is given as 47.5. Using the formula for average: Average = (Total Runs)/(Total Matches) 47.5 = (45n + 500)/(n + 10)

Multiplying both sides by n + 10: 47.5(n + 10) = 45n + 500 47.5n + 475 = 45n + 500

Rearranging the terms to solve for n: 47.5n - 45n = 500 - 475 2.5n = 25 n = (25)/(2.5) = 10

The number of matches played before the series was 10. Therefore, the total number of matches played till date is n + 10 = 10 + 10 = 20.

Explanation

In the given equation 63÷ 15 + 21× 5 - 4 = 74, interchanging the numbers 15 and 21 results in the modified expression 63÷ 21 + 15× 5 - 4. Following the BODMAS rule, the division is performed first, giving 63÷ 21 = 3. Then the multiplication is carried out, yielding 15× 5 = 75. The expression now simplifies to 3 + 75 - 4. Adding 3 and 75 gives 78, and subtracting 4 results in 74. Since the left-hand side equals the right-hand side, the equation is correctly balanced.

Explanation

The series follows a specific pattern for each corresponding letter in the clusters based on their numerical positions in the English alphabet (A=1, B=2, ..., Z=26):

First letter: D(4), H(8), L(12), P(16). The pattern is +4. The next letter is 16 + 4 = 20, which is T.

Second letter: J(10), D(4), X(24), R(18). The pattern is -6. Note that 4 - 6 = -2, and in a circular alphabet, -2 ≡ 24 (X). The next letter is 18 - 6 = 12, which is L.

Third letter: R(18), Z(26), H(8), P(16). The pattern is +8. Note that 26 + 8 = 34, and 34 ≡ 8 (H). The next letter is 16 + 8 = 24, which is X.

Fourth letter: Z(26), P(16), F(6), V(22). The pattern is -10. Note that 6 - 10 = -4, and -4 ≡ 22 (V). The next letter is 22 - 10 = 12, which is L.

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

Explanation

The relationship between the categories can be understood through set theory. The statement All engineers are doctors implies that the set of engineers is a subset of the set of doctors (E ⊆ D). The statement No police officer is a doctor means that the set of police officers and the set of doctors are disjoint (P ∩ D = ∅). Since all engineers are contained within the set of doctors, and no doctor is a police officer, it logically follows that no engineer can be a police officer (E ∩ P = ∅). This validates conclusion II.

Regarding conclusion III, the statement All engineers are doctors establishes that every member of the engineer group is also a member of the doctor group. In logical deduction, if the set of engineers is not empty, the existence of engineers within the doctor category ensures that some doctors are indeed engineers. This validates conclusion III. Since conclusion II is a universal negative statement that has been proven true, conclusion I, which is its contradictory particular affirmative, cannot follow.

Explanation

The relationship between the letter-clusters follows a specific mathematical pattern based on the alphabetical positions of the letters. For the first letter in the cluster, the rule is Position - 4. For the second and third letters, the rule is to find the opposite letter in the alphabet, which is determined by the formula 27 - Position.

In the first pair KCH to GXS: The first letter K (11) transforms to 11 - 4 = 7, which is G. The second letter C (3) transforms to its opposite 27 - 3 = 24, which is X. The third letter H (8) transforms to its opposite 27 - 8 = 19, which is S.

Applying this logic to TJD: The first letter T (20) transforms to 20 - 4 = 16, which is P. The second letter J (10) transforms to its opposite 27 - 10 = 17, which is Q. The third letter D (4) transforms to its opposite 27 - 4 = 23, which is W.

This sequence of operations results in the letter-cluster PQW.

Explanation

To find the code for lost drinks, we identify the codes for lost and drinks individually by comparing the given phrases.

To find drinks, compare cool drinks available here (bhu man juk lop) and available drinks desert search (but juk der lop). The common words are available and drinks, and the common codes are juk and lop. Now, observe available lost objects here (gan bhu nut juk). It contains the word available and the code juk, but does not contain drinks or lop. Thus, available is juk and drinks is lop.

To find lost, look at available lost objects here (gan bhu nut juk). We already know available is juk. Comparing this phrase with cool drinks available here (bhu man juk lop) shows the word here is common, corresponding to the code bhu. Comparing available lost objects here with be cool search objects (vax der man nut) shows the word objects is common, corresponding to the code nut. With available (juk), here (bhu), and objects (nut) identified, the remaining word in the second phrase is lost and the remaining code is gan.

Combining these results, lost is gan and drinks is lop, making the code gan lop.

Explanation

To determine the relationship, simplify the description of Arpita starting from the end. Pritam's wife's mother is his mother-in-law, and her husband is Pritam's father-in-law. Arpita is the only daughter of Pritam's father-in-law. Since Pritam is married to a daughter of this man and Arpita is the only daughter, Arpita must be Pritam's wife. Therefore, Arpita is the mother of Pritam's son.

Explanation

The letter-cluster BYXW is the odd one out because it does not follow a continuous sequence of letters in reverse alphabetical order. In a consistent reverse alphabetical pattern, each letter is the immediate predecessor of the one before it, which corresponds to a constant difference of -1 in their alphabetical positions. While the letters Y, X, and W are consecutive in descending order, the transition from the first letter B to the second letter Y involves a numerical shift of three positions (B → A → Z → Y). This break in the step-wise progression distinguishes it from a uniform linear sequence.

Explanation

All five words share the common prefix Overw. To determine their dictionary order, we compare the letters following this prefix. The sixth letters for the given words are e in Overweening and Overweight, h in Overwhelming, o in Overwork, and r in Overwrought. Alphabetically, e appears before h, o, and r. This means the two words starting with Overwe must occupy the first and second positions. Specifically, Overweening ranks first and Overweight ranks second because the seventh letter e in Overweening precedes the i in Overweight. Following the words starting with e, the next letter in alphabetical sequence is h. Therefore, Overwhelming, which is the only word with h at the sixth position, follows the two Overwe words and occupies the third position in the dictionary order.

Explanation

The logical validity of the conclusions can be determined by analyzing the relationships between the sets. Since all balls are contained within the set of rods and no rod is a door, it follows by the transitive property of disjoint sets that no ball can be a door, which validates Conclusion II. For Conclusion I, we know that some pencils are rods and all balls are rods. Because there is no statement explicitly separating pencils from balls, it is entirely possible for these two sets to overlap within the larger set of rods, making the possibility valid. Conclusion III is not necessarily true because the statement all balls are rods does not imply that all rods are balls. Conclusion IV does not follow because while rod-pencils cannot be doors, the pencils that are not rods have no specified restriction regarding doors. Thus, only Conclusions I and II are supported.