SSC CGL Tier 1 2020 General Intelligence & Reasoning Questions with Solutions

Explanation

To make the equation correct, we interchange the numbers 7 and 4. The original equation is 9 + 7× 5 - 18÷ 2 = 3× 4 - 10 + 45÷ 5.

After interchanging 7 and 4, the Left Hand Side (LHS) becomes: 9 + 4 × 5 - 18 ÷ 2 According to the BODMAS rule, we perform division and multiplication first: 9 + 20 - 9 29 - 9 = 20

The Right Hand Side (RHS) becomes: 3 × 7 - 10 + 45 ÷ 5 Performing division and multiplication: 21 - 10 + 9 11 + 9 = 20

Since LHS = RHS = 20, the interchange of 7 and 4 balances the equation.

Explanation

In an English dictionary, words are arranged alphabetically by comparing letters from left to right. All five words begin with the same three letters Rig. Comparing the fourth letter, Rightly (1), Righteous (3), and Rights (5) have h, while Rigidly (2) has i and Rigour (4) has o. Since h precedes i and i precedes o in the alphabet, the words starting with Righ must appear first.

Among Righteous (3), Rightly (1), and Rights (5), the fifth letter is t for all three. Moving to the sixth letter, e in Righteous (3) comes before l in Rightly (1), and l comes before s in Rights (5). This determines the first part of the sequence as 3, 1, 5.

For the remaining two words, Rigidly (2) and Rigour (4), the fourth letter i in Rigidly comes before the fourth letter o in Rigour. Therefore, 2 appears before 4. Combining these groups, the complete alphabetical order is 3, 1, 5, 2, 4.

Explanation

Let the present ages of Asha and Lata be 5x and 6x respectively. The problem states that the difference between their ages is 6 years, which gives the equation 6x - 5x = 6, hence x = 6. Substituting this value back into the expression for Lata's present age, we find that she is currently 6 × 6 = 36 years old. To determine her age after 5 years, we add 5 to her present age: 36 + 5 = 41 years.

Explanation

The numbers in the set (269, 278, 296) follow a pattern where the difference between the first and second number is 9, and the difference between the second and third number is 18. Mathematically, 269 + 9 = 278 and 278 + 18 = 296. The set in option a follows the exact same logic: the second number is the first number plus 9 (313 + 9 = 322), and the third number is the second number plus 18 (322 + 18 = 340). Additionally, both sets maintain a constant sum of digits for all three numbers within the set. In the original set, the sum of digits for each number is 2+6+9 = 17, 2+7+8 = 17, and 2+9+6 = 17. Similarly, in the correct option, the sum of digits for each number is 3+1+3 = 7, 3+2+2 = 7, and 3+4+0 = 7.

Explanation

The cluster FVKO is the odd one out because it does not adhere to the pattern of comprising two pairs of opposite letters. In the English alphabet, opposite letters are defined as pairs whose positional values sum to 27. In this cluster, the first pair F (6) and V (22) results in a sum of 28, and the second pair K (11) and O (15) results in a sum of 26. To follow the logic of opposite pairs, F should be paired with U (21) and K should be paired with P (16).

Explanation

The family relationship can be traced by connecting the generations. Sonia is the daughter of Satish's father, which means Sonia and Satish are siblings. Amit is the brother of Sonia, so Amit, Sonia, and Satish are all siblings from the same parents. Since Jyoti is the mother of Amit, she is also the mother of Satish. Jyoti is the sister of Nikita, and Nikita is the daughter of Kavinder, which implies that Jyoti is also the daughter of Kavinder. Consequently, Satish is the son of Kavinder's daughter Jyoti, making Satish the grandson of Kavinder.

Explanation

A submarine is specifically designed to operate and travel while fully submerged underwater. In contrast, ferries, yachts, and ships are surface vessels that remain afloat on the water's surface during their entire operation. This fundamental difference in buoyancy control and operational environment makes the submarine the odd word in the group.

Explanation

The coding logic follows an alternating pattern of addition and subtraction using consecutive integers starting from 2. In the word WARDROBE, the pattern is applied as follows: W+2=Y, A-3=X, R+4=V, D-5=Y, R+6=X, O-7=H, B+8=J, and E-9=V.

Applying this same sequence +2, -3, +4, -5, +6, -7, +8, -9 to the word ACCURATE: A (1) + 2 = 3 → C C (3) - 3 = 0 → Z C (3) + 4 = 7 → G U (21) - 5 = 16 → P R (18) + 6 = 24 → X A (1) - 7 = -6, which corresponds to 26 - 6 = 20 → T T (20) + 8 = 28, which corresponds to 28 - 26 = 2 → B E (5) - 9 = -4, which corresponds to 26 - 4 = 22 → V

The resulting code is CZGPXTBV.

Explanation

The series follows a pattern where the difference between consecutive terms is the square of consecutive natural numbers starting from 2. Calculating the differences between the given terms:

21 - 17 = 4 = 2² 30 - 21 = 9 = 3² 46 - 30 = 16 = 4² 71 - 46 = 25 = 5²

The differences are 2², 3², 4², 5². Following this sequence, the next difference must be 6² = 36. Adding this to the last term of the series:

71 + 36 = 107

Explanation

The statements establish a relationship between animals and elephants, and between elephants and tigers, but they do not provide a direct definitive link between animals and tigers. In syllogistic logic, when the relationship between two terms is uncertain, all possible scenarios must be considered. Conclusion I (Some animals are tigers) is a particular positive statement, while Conclusion II (No tiger is an animal) is a universal negative statement. These two conclusions form a complementary pair because they cover all possibilities regarding the intersection of the set of animals and the set of tigers. Since animals and tigers either have at least one common member or they have no common members at all, one of these two conclusions must be true. This satisfies the criteria for the either-or logic, where the subject and predicate are the same in both conclusions and they represent a pair of a particular positive and a universal negative.

Explanation

The series is composed of 21 characters that follow a cyclical pattern involving the letters k, l, and m. By substituting the letters from option c (k, l, k, l, m) into the blanks, the series can be organized into four distinct groups.

The first three groups contain five letters each. In these groups, the starting letter is doubled, the next letter in the cycle (k to l to m) is single, and the third letter is doubled. The starting letter shifts forward in the cycle for each subsequent group: Group 1: k k l m m (doubled k, single l, doubled m) Group 2: l l m k k (doubled l, single m, doubled k) Group 3: m m k l l (doubled m, single k, doubled l)

The final group consists of six letters and completes the logic by doubling every letter in the cycle: Group 4: k k l l m m

When the groups are combined, the completed sequence is: kk l mm ll m kk mm k ll kk ll mm.

Explanation

The relationship between the words is based on a solution and the condition it addresses. Medicine is the remedial substance used to treat or cure a disease. Similarly, food is the substance consumed to alleviate or satisfy the state of hunger. Just as medicine acts as the antidote to an ailment, food acts as the direct requirement to resolve the physical sensation of being hungry.

Explanation

The series follows a consistent mathematical pattern for each position within the letter-clusters based on their alphabetical ranks.

For the first letter, there is a constant increment of 5. Starting with C (rank 3), the sequence is 3 + 5 = 8 (H), 8 + 5 = 13 (M), and 13 + 5 = 18 (R). Applying the same logic to the last known term, 18 + 5 = 23, which corresponds to the letter W.

For the second letter, there is a constant decrement of 3. Starting with X (rank 24), the sequence is 24 - 3 = 21 (U), 21 - 3 = 18 (R), and 18 - 3 = 15 (O). Following this pattern, 15 - 3 = 12, which corresponds to the letter L.

For the third letter, there is a constant increment of 7. Starting with B (rank 2), the sequence is 2 + 7 = 9 (I), 9 + 7 = 16 (P), and 16 + 7 = 23 (W). Extending this further, 23 + 7 = 30. Since the English alphabet has only 26 letters, we subtract 26 from the total to find the cyclic position: 30 - 26 = 4, which corresponds to the letter D. Combining these individual results yields the cluster WLD.

Explanation

The relationship between the numbers follows the logic that the second number in each pair is obtained by dividing the square of the first number by 2. This can be expressed by the formula:

y = x²{2}

Applying this to the first pair where x = 12: y = 12²{2} = ¹⁴⁴⁄₂ = 72

Applying this to the third pair where x = 22: y = 22²{2} = ⁴⁸⁴⁄₂ = 242

Following the same pattern for the third number 18: y = 18²{2} = ³²⁴⁄₂ = 162

Explanation

The relationship established in the given pair is that of a measuring instrument and the specific physical quantity it is designed to quantify. A clock is the standard instrument used to measure the passage of time. Similarly, an ammeter is a device used to measure the magnitude of electric current flowing through a circuit, typically expressed in amperes. This matches the instrument-to-quantity relationship perfectly.

Explanation

Applying the specified interchanges to the equation 67 - 76 + 43 = 100, we replace the digit 6 with 7 and the digit 7 with 6, while also swapping the signs + and -. The number 67 transforms into 76, and 76 transforms into 67. The number 43 and the result 100 remain the same as they do not contain the digits 6 or 7. The modified equation becomes:

76 + 67 - 43 = 100

Calculating the left-hand side: 76 + 67 = 143 143 - 43 = 100

The resulting value matches the right-hand side exactly.

Explanation

The relationship established in the first pair is that of a product and its professional creator. A farmer is the individual responsible for the cultivation and production of crops. Following this logic, a chef is the professional specifically trained and responsible for the preparation and production of food. Both terms represent the person whose primary occupation is the creation of the respective product mentioned.

Explanation

The series follows a specific mathematical pattern for each letter in the cluster based on its position in the English alphabet. For the first letter, the sequence is q (17), n (14), k (11), h (8), decreasing by 3 in each step. The next letter is 8 - 3 = 5, which corresponds to e. For the second letter, the sequence is D (4), H (8), L (12), P (16), increasing by 4 in each step. The next letter is 16 + 4 = 20, which corresponds to T. For the third letter, the sequence is x (24), s (19), n (14), i (9), decreasing by 5 in each step. The next letter is 9 - 5 = 4, which corresponds to d. Combining these, the next cluster in the series is eTd.

Explanation

To determine the dictionary order, we compare the words letter by letter from left to right. All words begin with W. Comparing the second letter, Weaver, Weather, Weekly, Weight, and Weird contain e, while Wielded contains i. Since e precedes i in the alphabet, Wielded is positioned 6th.

Among the five words starting with We, we compare the third letters: a (Weather, Weaver), e (Weekly), and i (Weight, Weird). Alphabetically, a comes before e, and e comes before i. Between Weather and Weaver, the fourth letter t comes before v, so Weather is 1st and Weaver is 2nd. Weekly, having e as its third letter, is 3rd. Finally, we compare the third and fourth letters of Weight and Weird. Both have i as the third letter, but the fourth letter g in Weight comes before the fourth letter r in Weird. This places Weight 4th and Weird 5th in the sequence.

Explanation

The pair 28, 5 is distinct because it is the only pair where one of the numbers is odd. In the other three pairs, 16, 8; 36, 2; and 14, 8, both numbers in each pair are even. This difference in parity means that the sum of the numbers in the other pairs is always an even number (16 + 8 = 24, 36 + 2 = 38, and 14 + 8 = 22), whereas the sum in the pair 28, 5 is an odd number (28 + 5 = 33). Additionally, the product of the numbers in the other pairs results in a multiple of 8, as 16 × 8 = 128, 36 × 2 = 72, and 14 × 8 = 112. In contrast, the product of the numbers in the fourth pair is 28 × 5 = 140, which is not divisible by 8.

Explanation

To achieve equality between the two expressions, we interchange the numbers 6 and 8. The original equation is 4 + 6 × 7 - 27 ÷ 3 = 7 × 8 - 4 + 39 ÷ 3. After interchanging 6 and 8, the equation becomes 4 + 8 × 7 - 27 ÷ 3 = 7 × 6 - 4 + 39 ÷ 3.

Applying the BODMAS rule to the left-hand side (LHS): LHS = 4 + (8 × 7) - (27 ÷ 3) LHS = 4 + 56 - 9 LHS = 60 - 9 = 51

Applying the BODMAS rule to the right-hand side (RHS): RHS = (7 × 6) - 4 + (39 ÷ 3) RHS = 42 - 4 + 13 RHS = 38 + 13 = 51

Since both sides result in a value of 51, the interchange of 6 and 8 makes the equation correct.

Explanation

The coding logic follows an incremental shift pattern where each letter in the word is moved forward in the alphabet by its position in the string. For HAMMER, the transformations are H+1=I, A+2=C, M+3=P, M+4=Q, E+5=J, and R+6=X.

Applying this same sequence of +1, +2, +3, +4, +5, +6 to the letters of WRENCH: W (23) + 1 = 24 (X) R (18) + 2 = 20 (T) E (5) + 3 = 8 (H) N (14) + 4 = 18 (R) C (3) + 5 = 8 (H) H (8) + 6 = 14 (N)

The resulting code is XTHRHN.

Explanation

The pattern followed in the given numerical analogy is that the second number is 1.5 times the first number, representing a ratio of 2:3.

In the first pair, the relationship is 78 × 1.5 = 117. In the third pair, the relationship is 108 × 1.5 = 162.

Applying the same logic to the second pair where the first number is 90, the calculation is 90 × 1.5 = 135. This can also be solved by adding half of the number to itself: 90 + (90 / 2) = 90 + 45 = 135.

Explanation

The coding logic follows the positional value of each letter in the English alphabet, where A=1, B=2, ..., Z=26. If a letter has a double-digit positional value, its digits are added together to form a single-digit number (the digital root). For the word BREATHER, the positions are B(2), R(18), E(5), A(1), T(20), H(8), E(5), and R(18). These convert to 2, 1+8=9, 5, 1, 2+0=2, 8, 5, and 1+8=9, resulting in 29512859.

Applying this pattern to AVIATION: A is 1, which remains 1. V is 22, and 2+2=4. I is 9, which remains 9. A is 1, which remains 1. T is 20, and 2+0=2. I is 9, which remains 9. O is 15, and 1+5=6. N is 14, and 1+4=5.

Stringing these single digits together results in the code 14912965.

Explanation

The expression R + S × T - V ÷ U establishes the family structure through sequential relationships. The segment S × T indicates that S is the brother of T, while T - V shows that T is the sister of V. Together, these confirm that S, T, and V are siblings. The initial part R + S defines R as the father of S, making R the father of all three siblings. The final part V ÷ U identifies V as the daughter of U. Since R is already established as the father of V, U must be the mother and the spouse of R. As S is a male sibling (brother) within this group of children belonging to R and U, S is the son of U.

Explanation

The series follows an alternating pattern of addition and multiplication using consecutive odd numbers starting from 1. The sequence of operations is +1, × 3, +5, × 7, +9, and so on.

The first term is 11. The second term is 11 + 1 = 12. The third term is 12 × 3 = 36. The fourth term is 36 + 5 = 41. The fifth term is calculated by multiplying the fourth term by the next consecutive odd number, which is 7. Therefore, 41 × 7 = 287.

To verify the pattern, the sixth term is obtained by adding the next consecutive odd number, 9, to the fifth term. Thus, 287 + 9 = 296, which matches the final number in the given series.

Explanation

Brass is categorized as an alloy, which is a metallic substance produced by combining two or more chemical elements. Specifically, brass is a mixture consisting primarily of copper and zinc. Unlike the other options provided, which are pure chemical elements found on the periodic table with distinct atomic numbers, brass does not have a single type of atom and is instead a solid solution. This fundamental difference in chemical composition makes it the odd word among the group.

Explanation

The pattern follows a row-wise logic where the difference between the fourth number and the second number results in a square of consecutive odd numbers for the first, third, and fourth rows.

Row 1: 5 - 4 = 1 = 1²

Row 3: 12 - 3 = 9 = 3²

Row 4: 65 - 16 = 49 = 7² (using option b)

The progression of the square roots follows the sequence of odd numbers 1, 3, 5, 7. While Row 2 (25 - 7 = 18) does not fit a perfect square, the established progression for the other rows identifies 16 as the most consistent value to complete the pattern in the final row.

Alternatively, examining the sum of the numbers in each row: Row 1: 10 + 4 + 7 + 5 = 26 (Sum of digits: 2 + 6 = 8) Row 2: 15 + 7 + 8 + 25 = 55 (Sum of digits: 5 + 5 = 10) Row 3: 14 + 3 + 6 + 12 = 35 (Sum of digits: 3 + 5 = 8) Row 4: 10 + 16 + 14 + 65 = 105 (Sum of digits: 1 + 0 + 5 = 6)

The digit sums follow a symmetrical/sequential decrease (8, 10, 8, 6), confirming 16 as the correct replacement.

Explanation

Conclusion I logically follows from the first statement through the rule of conversion. In categorical syllogisms, a universal affirmative statement of the form All A are B implies that Some B are A. Since all books are magazines, it is an immediate valid inference that some magazines are books.

Conclusion IV follows directly from the conversion of the second statement. A particular affirmative statement of the form Some A are B is logically equivalent to its converse, Some B are A. Thus, the premise that some books are novels necessitates that some novels are books.

Additionally, because all books are contained within the set of magazines and there is an overlap between books and novels, there must also be an overlap between magazines and novels, rendering any negative conclusions regarding these sets invalid. Only the affirmative relationships established by the conversion of the primary premises hold true.

Explanation

This is a direct substitution code where each letter in the given words is assigned a specific code letter. By comparing the provided examples, we can identify the mapping for each letter.

From the word VERBAL (QNMYXK) and REACH (MNXZF), we extract the following letter-to-code pairs: V maps to Q E maps to N R maps to M B maps to Y A maps to X L maps to K C maps to Z H maps to F

Using these mappings to construct the code for BRAVE: B translates to Y R translates to M A translates to X V translates to Q E translates to N

The resulting sequence for BRAVE is YMXQN.

Explanation

The letter-cluster SWIK contains only one vowel, which is I. In the given set, this distinguishes it from the other clusters, each of which contains exactly two vowels. This difference in the count of vowels makes SWIK the odd one out.

Explanation

The numbers in the given set (343, 98, 21) follow the mathematical pattern (n³, 2n², 3n) where n = 7. Calculating these values yields: n³ = 7³ = 343 2n² = 2 × 7² = 2 × 49 = 98 3n = 3 × 7 = 21

The set (1331, 242, 33) follows the identical logic for n = 11: n³ = 11³ = 1331 2n² = 2 × 11² = 2 × 121 = 242 3n = 3 × 11 = 33

By substituting the base value n = 11 into the formula, we arrive exactly at the numbers provided in the sequence. This demonstrates the consistent application of cubic, doubled square, and triple relations derived from a single integer.

Explanation

The given series consists of 24 character positions. By dividing the series into four blocks of six characters each, we can identify an alternating pattern. The structure of the four blocks is:

Group 1: _ u v w u v Group 2: _ w v t u w Group 3: _ u v w u v Group 4: _ w v _ u w

When the letter t is placed in all five blanks, the completed sequence becomes: t u v w u v, t w v t u w, t u v w u v, t w v t u w

In this arrangement, Group 1 is identical to Group 3, and Group 2 is identical to Group 4, creating an ABAB repeating pattern. The letter t consistently fills the first position of every six-character block (at indices 1, 7, 13, and 19) and the fourth position of the even-numbered blocks (at indices 10 and 22). This structural consistency confirms that the sequence is completed by the repetitive use of the letter t across all empty slots.

Explanation

The coding logic involves taking the numerical position of each letter in the English alphabetical order (A=1, B=2, …, Z=26) and multiplying that value by 2 to generate the code for that specific letter. These resulting numbers are then concatenated to form the complete code.

In the word PEN: The position of P is 16, and 16 × 2 = 32. The position of E is 5, and 5 × 2 = 10. The position of N is 14, and 14 × 2 = 28. Combining these gives 321028.

Applying the same logic to the word TUB: The position of T is 20, and 20 × 2 = 40. The position of U is 21, and 21 × 2 = 42. The position of B is 2, and 2 × 2 = 4. Combining these values in sequence results in the code 40424.

Explanation

The series follows a pattern where the difference between consecutive terms increases as multiples of 3. Calculating the differences between the first three terms, we find 58 - 55 = 3 and 64 - 58 = 6. The differences are following the sequence 3 × 1, 3 × 2, 3 × 3, 3 × 4, and so on. To find the missing term, we add the next multiple of 3, which is 9, to the third term: 64 + 9 = 73. This logic is verified by the final term, as adding the subsequent multiple of 3, which is 12, to our result gives 73 + 12 = 85.

Explanation

The series is based on a constant increment in the numerical positions of the letters in the English alphabet. The positions for the given letters are J = 10, M = 13, and P = 16. By observing the sequence, there is a common difference of +3 between consecutive terms (13 - 10 = 3 and 16 - 13 = 3). Applying this logic to find the missing term, 16 + 3 = 19. The letter at the 19th position in the alphabet is S. This pattern is consistent with the rest of the series, as 19 + 3 = 22 (V) and 22 + 3 = 25 (Y).

Explanation

The pattern followed in the pairs is that the second number is six times the sum of the digits of the first number. For the pair 57 - 38, the sum of the digits of the first number is 5 + 7 = 12. When this sum is multiplied by 6, the result is 12 × 6 = 72, which does not match the second number 38.

Explanation

The relationship between the words Faculty and Teachers is that of a collective noun and its constituents. A faculty refers to the entire group of teachers or academic staff within an educational institution.

Similarly, the word Fleet is the collective noun used to describe a group of trucks, ships, or other vehicles operating together or owned by the same organization. This pair follows the same logic where the first word represents the collective group and the second word represents the individual units that make up that group.

Explanation

The series follows a pattern where the positional value of each letter in the English alphabet increases by a decreasing interval. By converting the letters into their numerical positions where A=1 and Z=26, the logic is as follows:

K = 11 Q = 17 (11 + 6) V = 22 (17 + 5) ? = 26 (22 + 4) C = 3 (26 + 3 = 29, and 29 ≡ 3 26) E = 5 (3 + 2) F = 6 (5 + 1)

The difference between consecutive terms decreases by 1 in each step (6, 5, 4, 3, 2, 1). Adding 4 to the position of V (22) results in 26, which corresponds to the letter Z.

Explanation

The series follows a specific pattern for each position of the letter-cluster. For the first letter, the pattern is +3 in the alphabetical order: D (4) + 3 = G (7), G + 3 = J (10), J + 3 = M (13), and M + 3 = P (16). For the second letter, the pattern is a simple +1 increment: Y (25) + 1 = Z (26), Z + 1 = A (1), A + 1 = B (2), and B + 1 = C (3).

For the third letter, the pattern is -2 in the alphabetical order: K (11) - 2 = I (9), I - 2 = G (7), G - 2 = E (5), and E - 2 = C (3). For the fourth letter, the pattern is +1 in the alphabetical order: M (13) + 1 = N (14), N + 1 = O (15), O + 1 = P (16), and P + 1 = Q (17). Combining these results, the next cluster in the series is PCCQ.

Explanation

The words follow the chronological sequence of a student's academic cycle. The process begins with Admission (2) into an institution, which is followed by attending the Class (1) for learning. After completing the course of study, the student appears for an Examination (4). Once the exam is conducted, the evaluation process or Marking (5) of the answer scripts takes place. Finally, the Result (3) is declared based on the marks awarded during the evaluation. This logical progression from enrollment to the final outcome establishes the order 2, 1, 4, 5, 3.

Explanation

Conclusion I follows because the statement All helmets are objects logically implies its converse, Some objects are helmets. In categorical logic, a universal affirmative statement (All A are B) always supports the particular affirmative converse (Some B are A).

Conclusion II follows from the second statement, Some helmets are vehicles. Particular affirmative statements (Some A are B) are reversible, meaning if some helmets belong to the category of vehicles, then some vehicles must also belong to the category of helmets.

Conclusion III follows by combining both statements. Since the entire set of helmets is contained within the set of objects, any entity that is a helmet is also an object. Because some vehicles are helmets, those specific vehicles must also be objects. In set theory terms, if H ⊆ O and H ∩ V ≠ ∅, then the intersection V ∩ O must also be non-empty. This proves that all three conclusions are logically valid based on the given premises.

Explanation

The series follows a pattern of increasing differences. First, calculate the difference between consecutive terms: 73 - 58 = 15, 99 - 73 = 26, 138 - 99 = 39, and 193 - 138 = 55.

Next, determine the second-level differences (the difference of the differences): 26 - 15 = 11, 39 - 26 = 13, and 55 - 39 = 16.

Analyzing the third-level differences reveals a simple incremental pattern: 13 - 11 = 2 and 16 - 13 = 3. Following this sequence of consecutive integers, the next third-level difference must be 4.

Applying this back up the levels, the next second-level difference is 16 + 4 = 20. Adding this to the previous first-level difference gives 55 + 20 = 75. The missing number is therefore 193 + 75 = 268.

This can be verified by extending the pattern one more step. The next third-level difference is 5, making the next second-level difference 20 + 5 = 25. The next first-level difference becomes 75 + 25 = 100, and 268 + 100 = 368, which matches the final term in the series.

Explanation

The pattern followed in the given sets is that the second number is the sum of the digits of the first number. For the pair 41263:18, the sum of the digits of the first number is 4 + 1 + 2 + 6 + 3 = 16. Since 16 is not equal to 18, this pair is the odd one out as it deviates from the logic shared by the other number-pairs where the digit sum exactly matches the second value.

Explanation

Machine is a broad, generic classification that represents an entire category of mechanical or electronic devices. It serves as a collective term for any apparatus designed to perform specific tasks. In this set, it is the overarching category to which the other three specific appliances belong, making it the odd one out as it is a general noun rather than a specific instrument.

Explanation

Interchanging the numbers 28 and 35 in the original equation 28 + 49 - 35 ÷ 7 × 4 = 68 results in the modified expression 35 + 49 - 28 ÷ 7 × 4. Following the BODMAS rule, we first perform the division: 28 ÷ 7 = 4. Substituting this back into the expression, we have 35 + 49 - 4 × 4. Next, we perform the multiplication: 4 × 4 = 16. The expression then becomes 35 + 49 - 16. Finally, we execute the addition and subtraction: 35 + 49 = 84, and 84 - 16 = 68. This matches the right-hand side of the equation.

Explanation

The pattern followed in the given analogy is that the second number is obtained by multiplying the square of the first number with the next consecutive integer. This can be represented by the mathematical relationship n : n² × (n + 1).

For the first pair, 8 : 576: 8² × (8 + 1) = 64 × 9 = 576

Applying the same logic to the third number, 4: 4² × (4 + 1) = 16 × 5 = 80

The logic can also be viewed as the sum of the cube and the square of the number, n³ + n². For the first pair, 8³ + 8² = 512 + 64 = 576. For the second pair, 4³ + 4² = 64 + 16 = 80.

Explanation

The coding logic involves splitting the word into two equal halves, reversing the sequence of letters within each half, and then incrementing each letter to the next one in the alphabetical series (+1 logic).

For the word NECTAR, the first half NEC is reversed to CEN; adding 1 to each letter (C+1=D, E+1=F, N+1=O) results in DFO. The second half TAR is reversed to RAT; adding 1 to each letter (R+1=S, A+1=B, T+1=U) results in SBU. Combining these gives the code DFOSBU.

Applying the same logic to CARPET, the first half CAR is reversed to RAC; incrementing each letter (R+1=S, A+1=B, C+1=D) results in SBD. The second half PET is reversed to TEP; incrementing each letter (T+1=U, E+1=F, P+1=Q) results in UFQ. Combining the two parts yields the code SBDUFQ.

Explanation

The relationship established in the given pair is that of an organ and a specific medical condition or ailment associated with it. Tinnitus is a sensation of noise, such as ringing or buzzing, that occurs within the Ear. Applying this logic, Acne is a physiological condition that specifically affects the Skin, occurring when hair follicles become clogged with oil and dead skin cells. In both instances, the second word describes a localized disorder or symptom experienced in the part of the body denoted by the first word.

Explanation

According to the first statement, the set of dogs is a subset of the set of lions, which can be expressed as D ⊆ L. The second statement asserts that there is no intersection between the set of elephants and the set of lions, meaning E ∩ L = ∅. Because every dog is contained within the category of lions, and no lion can be an elephant, it is logically impossible for any dog to be an elephant. This confirms that the relation D ∩ E = ∅ must hold true, making conclusion I a valid logical consequence of the given premises.