SSC CGL Tier 1 2011 General Intelligence & Reasoning Questions with Solutions

Explanation

The relationship between the first two sets of letters is based on a positional shift in the English alphabet. Each letter in the first set is moved forward by 12 positions to obtain the corresponding letter in the second set:

C(3) + 12 = 15 (O) F(6) + 12 = 18 (R) I(9) + 12 = 21 (U) L(12) + 12 = 24 (X)

Applying the same logic to the third set (GDJM), we find the letters for the fourth set. Using the numerical positions of the letters:

G(7) + 12 = 19 (S) D(4) + 12 = 16 (P) J(10) + 12 = 22 (V) M(13) + 12 = 25 (Y)

The resulting letters are P, S, V, and Y. Arranging these in the sequence provided in the options gives PSVY.

Explanation

The relationship between the first pair of letter groups, BEHK and YVSP, is based on the concept of opposite letters in the English alphabet. Two letters are considered opposites if the sum of their positions from the start and end of the alphabet is 27. For BEHK, the positions are B=2, E=5, H=8, and K=11. Their opposites are Y (27 - 2 = 25), V (27 - 5 = 22), S (27 - 8 = 19), and P (27 - 11 = 16), forming YVSP.

Applying this same logic to DGJM, where the positions are D=4, G=7, J=10, and M=13: The opposite of D (4) is 27 - 4 = 23, which is W. The opposite of G (7) is 27 - 7 = 20, which is T. The opposite of J (10) is 27 - 10 = 17, which is Q. The opposite of M (13) is 27 - 13 = 14, which is N. Combining these results yields the sequence WTQN.

Explanation

The relationship between the first pair of numbers is established by a constant multiplier. By dividing the second term by the first term, we find the ratio: 60 / 24 = 2.5. To find the missing number in the second pair, the same multiplier must be applied to the third term: 120 × 2.5 = 300. This can also be viewed as a proportion where 24 : 60 simplifies to 2 : 5. Applying this ratio to the second set, if 2 units represent 120, then 1 unit represents 60, and 5 units represent 60 × 5 = 300.

Explanation

The relationship follows the pattern x : y, where y = 2 √(x / 2). Applying this to the first pair, we divide 392 by 2 to get 196. The square root of 196 is 14, and multiplying this by 2 gives the second number 28.

392 → 392 / 2 = 196 → √(196) = 14 → 14 × 2 = 28

Applying the same logic to 722, we divide 722 by 2 to get 361. The square root of 361 is 19, and multiplying this by 2 results in 38.

722 → 722 / 2 = 361 → √(361) = 19 → 19 × 2 = 38

Explanation

The relationship between the numbers is based on the square of the sum of the digits of the first number. For the first pair, the sum of the digits of 123 is 1 + 2 + 3 = 6, and squaring this sum yields 6² = 36. Applying this same pattern to the second pair, the sum of the digits of 221 is 2 + 2 + 1 = 5. Squaring this result gives 5² = 25.

Explanation

The relationship established in the analogy is between an animal and its most commonly attributed characteristic trait in folklore and literature. In this context, the ass is traditionally associated with being timid or submissive. Following the same logic, the fox is the animal universally characterized by its cunning, slyness, and craftiness. This metaphorical association is a standard convention used in fables and idiomatic expressions to represent specific human personality traits through animal archetypes.

Explanation

The relationship between the words in the first pair is that of antonyms. Ecstasy refers to a state of overwhelming happiness or joyful excitement, whereas Gloom refers to a state of depression or despondency. Similarly, Humiliation and Exaltation are opposites. Humiliation involves the loss of pride, self-respect, or dignity, while Exaltation refers to the action of elevating someone in rank or power, or a state of extreme happiness and pride. Since both pairs consist of words with diametrically opposed meanings, the second pair maintains the same logical analogy as the first.

Explanation

The analogy follows the relationship of a professional and the final product of their craft. An architect is a specialist who designs and plans the construction of a building. Similarly, a sculptor is an artist who carves or models materials like stone, clay, or metal to produce a three-dimensional figure or work of art. The term provided represents the physical form or artistic creation that results from the sculptor's labor.

Explanation

The relationship between the letter groups MKQO and LNPR is based on a specific numerical shift for each corresponding letter in the English alphabet. Specifically, M - 1 = L, K + 3 = N, Q - 1 = P, and O + 3 = R. Applying this same pattern of -1, +3, -1, +3 to find the letters that precede XVTZ, we calculate the source letters as follows: Y - 1 = X, S + 3 = V, U - 1 = T, and W + 3 = Z. Mapping these results together gives the sequence YSUW.

Explanation

The letter groups in this set follow a specific alphabetical progression where the difference between consecutive letters is +1, +2, and +2 respectively. BCQN is the odd one out because it deviates from this pattern. In BCQN, the alphabetical positions are B(2), C(3), Q(17), and N(14). This results in positional increments of +1 (from B to C), +14 (from C to Q), and -3 (from Q to N), which does not align with the uniform +1, +2, +2 logic found in the other alternatives.

Explanation

In the given letter groups, the pattern consists of two sets of consecutive letters. In the first three options, the first two letters are consecutive in alphabetical order, and the last two letters are also consecutive in alphabetical order. Specifically, the pairs are A-B and Y-Z, C-D and W-X, and E-F and U-V. However, in GHTV, while the first two letters G-H are consecutive, the last two letters T and V are not consecutive, as T is the 20ᵗʰ letter and V is the 22ⁿᵈ letter of the alphabet. This difference in the internal sequence of the second pair makes this group the odd one out.

Explanation

The value 841 is a perfect square, as it is the product of 29 × 29. The other numbers provided in the set do not share this property and instead follow a uniform pattern of n² + 1. For instance, 626 is derived from 25² + 1, where 25² = 625. Similarly, 962 is 31² + 1, based on 31² = 961, and 1090 is 33² + 1, based on 33² = 1089. Since 841 is the only number that is an exact square of an integer without any increment, it does not fit the common mathematical characteristic shared by the rest.

Explanation

The number 4270 is the odd one because the sum of its digits is 13 (4 + 2 + 7 + 0 = 13). In the other numbers provided, the sum of the digits is consistently 14, as seen in 5 + 7 + 2 + 0 = 14, 6 + 7 + 1 + 0 = 14, and 2 + 6 + 6 + 0 = 14. This difference in the digit sum distinguishes 4270 from the rest of the set.

Explanation

Driving is the odd one out because it is a land-based activity that involves the operation of a motor vehicle on a solid surface. It is distinct from the other alternatives as it does not take place in or on a water medium.

Explanation

Perception, Discernment, and Penetration are all synonyms used to describe mental sharpness, insight, or the ability to understand something clearly. Insinuation is the odd one out as it refers to an indirect, usually negative, hint or suggestion.

Explanation

The numbers in the given set (4, 25, 81) are all perfect squares of integers, specifically 2² = 4, 5² = 25, and 9² = 81. The set (16, 64, 100) follows the same mathematical pattern, as each of its elements is a perfect square: 4² = 16, 8² = 64, and 10² = 100.

Explanation

The series follows a rule where the number of letters skipped between consecutive terms increases by one. Let Pₙ be the position of the nᵗʰ letter in the English alphabet. The alphabetical positions for the letters in this series are P₁ = 1 (A), P₂ = 3 (C), P₃ = 6 (F), P₄ = 10 (J), P₅ = 15 (O), and P₆ = 21 (U). The number of letters skipped between terms is calculated by the formula Sₙ = Pₙ₊₁ - Pₙ - 1. Applying this to the sequence results in S₁ = 3 - 1 - 1 = 1 letter skipped (B), S₂ = 6 - 3 - 1 = 2 letters skipped (D, E), S₃ = 10 - 6 - 1 = 3 letters skipped (G, H, I), S₄ = 15 - 10 - 1 = 4 letters skipped (K, L, M, N), and S₅ = 21 - 15 - 1 = 5 letters skipped (P, Q, R, S, T). The sequence of skipped letters 1, 2, 3, 4, 5 follows a consistent arithmetic progression.

Explanation

The sequence follows the logical progression of water flow and the increasing size of water bodies. A glacier (4) acts as the primary source of freshwater as it melts. This meltwater first forms a rivulet (2), which is a very small stream. As several rivulets and streams converge, they form a larger river (5). The river eventually discharges its water into a sea (3), which is a large body of saline water. Finally, multiple seas comprise or flow into the ocean (1), which is the largest expanse of water on Earth. This order represents the natural journey of water from its mountain source to its ultimate destination.

Explanation

To arrange words in dictionary order, we compare letters from left to right at each position where they differ. All five words begin with the prefix Pre. Comparing the fourth letter, word (2) Preoperatively contains the letter o, whereas words (1), (3), (4), and (5) all contain the letter p. In alphabetical order, o comes before p, so word (2) is the first in the sequence.

Among the remaining words (1), (3), (4), and (5), the first five letters Prepo are identical. We move to the sixth letter to find a difference. Word (4) Preponderate has the letter n, while words (1), (3), and (5) have the letter s. Since n precedes s in the alphabet, word (4) is the second in the sequence.

Finally, we compare words (1) Preposition, (3) Preposterous, and (5) Prepossess, which all share the first six letters Prepos. Comparing their seventh letters, we find i in word (1), t in word (3), and s in word (5). Sorting these alphabetically, i comes first, followed by s, and then t. Consequently, word (1) is third, word (5) is fourth, and word (3) is fifth. This results in the final dictionary order: 2, 4, 1, 5, 3.

Explanation

The series follows a logical pattern consisting of two alternating four-letter blocks: acac and abab. By dividing the series into groups of four, the structure of the sequence becomes clear:

Group 1: ac_c To complete the pattern acac, the missing letter is a.

Group 2: ab_b To complete the pattern abab, the missing letter is a.

Group 3: aca_ To complete the pattern acac, the missing letter is c.

Group 4: aba_ To complete the pattern abab, the missing letter is b.

Group 5: aca_ To complete the pattern acac, the missing letter is c.

Sequentially placing these letters (a, a, c, b, c) into the gaps completes the series as acacababacacababacac.

Explanation

The letters in each term of the series follow a consistent mathematical progression where each position increases by 3 in the alphabetical sequence to form the subsequent term. Specifically, for the second term DREQ to the third term GUHT: D (4) + 3 = G (7), R (18) + 3 = U (21), E (5) + 3 = H (8), and Q (17) + 3 = T (20). Similarly, from the third term GUHT to the fourth term JXKW: G (7) + 3 = J (10), U (21) + 3 = X (24), H (8) + 3 = K (11), and T (20) + 3 = W (23).

To find the missing first term, the same logic is applied in reverse by subtracting 3 from each letter of the second term DREQ. For the first letter, D (4) - 3 = 1, which corresponds to A. For the second letter, R (18) - 3 = 15, which corresponds to O. For the third letter, E (5) - 3 = 2, which corresponds to B. For the fourth letter, Q (17) - 3 = 14, which corresponds to N. Combining these results gives the term AOBN.

Explanation

The sequence follows a pattern of increasing differences. Calculating the first differences between consecutive terms, we find: 90 - 56 = 34 132 - 90 = 42 184 - 132 = 52 248 - 184 = 64

By examining these first differences (34, 42, 52, 64), we calculate the second differences: 42 - 34 = 8 52 - 42 = 10 64 - 52 = 12

The second differences are increasing by a constant value of 2. Following this logic, the next second difference should be 12 + 2 = 14. To find the next first difference, we add this to the previous one: 64 + 14 = 78. The missing number is then calculated by adding this value to the last term of the sequence: 248 + 78 = 326.

Explanation

The numerical series follows a recursive pattern where each term is calculated as twice the sum of the two terms immediately preceding it. The mathematical rule governing the progression is Tₙ = 2(Tₙ₋₁ + Tₙ₋₂) for n ≥ 3. We can verify this by observing the transitions provided in the sequence: the third term is 2(0 + 4) = 8, the fourth term is 2(4 + 8) = 24, the fifth term is 2(8 + 24) = 64, and the sixth term is 2(24 + 64) = 176. Following this logic, the seventh term is obtained by summing the fifth and sixth terms and multiplying the result by two. The calculation is 2(64 + 176) = 2(240) = 480.

Explanation

The series follows a specific alternating subtraction pattern based on the alphabetical positions of the letters. Assigning numerical values to the letters where A = 1, B = 2, ..., Z = 26, the sequence is as follows:

W = 23 T = 20 (23 - 3) P = 16 (20 - 4) M = 13 (16 - 3) I = 9 (13 - 4) F = 6 (9 - 3) B = 2 (6 - 4)

The pattern of subtraction is -3, -4, -3, -4, -3, -4. Following this logic, the next subtraction should be -3.

Calculating the next letter: 2 - 3 = -1. In the circular alphabet, -1 corresponds to 25 (since 26 is Z, 1 is A, 0 is Z, and -1 is Y), which is the letter Y.

The subsequent subtraction is -4. Calculating the next letter: 25 - 4 = 21, which corresponds to the letter U.

Therefore, the next two letters in the sequence are Y and U.

Explanation

To find when the same date falls on the same day of the week, the total number of odd days between the two dates must be a multiple of 7. A non-leap year has 365 days, which equals 52 weeks and 1 odd day. A leap year has 366 days, which equals 52 weeks and 2 odd days.

Starting from 30th September 1997, we count the odd days for each subsequent year: 1998: 1 odd day 1999: 1 odd day 2000: 2 odd days (Leap year) 2001: 1 odd day 2002: 1 odd day 2003: 1 odd day

Summing these odd days: 1 + 1 + 2 + 1 + 1 + 1 = 7.

Since the sum of odd days becomes 7 (a multiple of 7) in the year 2003, 30th September 2003 will fall on the same day as 30th September 1997, which is Tuesday.

Explanation

A standard clock covers 60 minutes of time in one hour of real time. This faulty clock gains 5 minutes every hour, which means it covers 65 minutes of clock-time for every 60 minutes of actual time. This implies the clock's mechanism, including the second hand, moves faster than a normal clock by a factor of 65/60.

In a normal clock, the second hand traverses 360° in one minute. For this specific clock, the angle traversed by the second hand in one minute of real time is determined by multiplying the standard rotation by the speed ratio:

Angle = ⁶⁵⁄₆₀ × 360°

Angle = 65 × 6°

Angle = 390°

Since the clock is gaining time, the second hand must cover more than the standard 360° within a single real-time minute to account for the extra 5 minutes gained over the course of an hour.

Explanation

To determine the age hierarchy, we represent the ages of the individuals using algebraic relations based on the given statements. Let the age of D be x.

According to the statement that C is twice as old as D, C = 2x. Since C is half the age of A, it follows that A = 2C, so A = 2(2x) = 4x. The statement that B is twice as old as A (interpreting odd as old in this context of age comparison) gives B = 2A = 2(4x) = 8x. Finally, since B is twice younger than F, F must be twice as old as B, meaning F = 2B = 2(8x) = 16x.

Arranging the individuals in descending order of age based on these values results in F (16x) > B (8x) > A (4x) > C (2x) > D (x). In this sequence, F is the oldest and B is the second oldest.

Explanation

The total number of ways to form a committee consisting of one male and one female from a group of five males and three females is calculated by multiplying the number of choices for each position. The number of ways to select one male from five is ⁵C₁ = 5, and the number of ways to select one female from three is ³C₁ = 3. Thus, the total possible combinations without any restrictions are 5 × 3 = 15.

The constraint specifies that Ms. A refuses to be a member if Mr. B is included. This means the specific pairing of Mr. B and Ms. A is the only prohibited combination. To find the number of valid committees, we subtract this one restricted case from the total possible combinations.

Number of ways = (Total possible committees) - (Committees with both Mr. B and Ms. A) Number of ways = 15 - 1 = 14.

Explanation

The series follows the general term formula aₙ = n² + 4n for n = 1, 2, 3, 4, 5, 6. By substituting the values of n into the formula, we find a₆ = 6² + 4(6) = 60, a₅ = 5² + 4(5) = 45, a₄ = 4² + 4(4) = 32, a₃ = 3² + 4(3) = 21, and a₂ = 2² + 4(2) = 12. For the first term where n = 1, the value should be a₁ = 1² + 4(1) = 5. The presence of 6 instead of 5 breaks this mathematical progression. Alternatively, the differences between consecutive terms are 60 - 45 = 15, 45 - 32 = 13, 32 - 21 = 11, and 21 - 12 = 9. These differences form a sequence of consecutive odd numbers. To maintain this pattern, the difference between the second and first term should be 9 - 2 = 7. Subtracting 7 from the second term gives 12 - 7 = 5, confirming that 6 is the wrong number in the series.

Explanation

To find the number of students between Ramesh and Suresh, we first determine their numerical positions from the same end of the sequence. Ramesh is ranked 13th from the top. Suresh has 5 students below him, which means his position from the top is 33 - 5 = 28.

The number of students between two positions P₁ and P₂ is calculated using the formula: Students Between = (P₂ - P₁) - 1

Substituting the known values: Students Between = (28 - 13) - 1 Students Between = 15 - 1 = 14

This calculation accounts for the exclusion of both Ramesh and Suresh from the count, leaving exactly 14 students in the interval between them.

Explanation

Let x represent the age of Naresh's brother. The expression twice the age of his brother translates mathematically to 2x. To find a value that is 4 years less than this amount, 4 must be subtracted from the product. Therefore, the equation representing Naresh's age is 2x - 4.

Explanation

Rohit is the son of Rani's brother, and since the problem states that Ram is Rani's brother, Rohit is Ram's son. Suresh's sister is the wife of Ram, which means Rohit is the son of Suresh's sister. In family relations, the son of one's sister is defined as a nephew.

Explanation

Using the principle of inclusion-exclusion for two sets, the percentage of people who own at least one of the items (either a car or a TV) is calculated using the formula P(C ∪ T) = P(C) + P(T) - P(C ∩ T). Substituting the given values, we have 70% + 75% - 55% = 90%. This figure represents the portion of the surveyed population that owns at least one of the two devices. The percentage of those who do not own either a car or a TV is the complement of this set, which is calculated as 100% - 90% = 10%.

Explanation

The coding pattern follows an alternating sequence of adding 3 and subtracting 3 to the numerical positions of the letters in the English alphabet. For the word DANCE, the transformations are D (4) + 3 = 7 (G), A (1 or 27) - 3 = 24 (X), N (14) + 3 = 17 (Q), C (3) - 3 = 0 or 26 (Z), and E (5) + 3 = 8 (H). Applying this same alternating +3, -3 pattern to the word RIGHT yields the following results: R (18) + 3 = 21 (U), I (9) - 3 = 6 (F), G (7) + 3 = 10 (J), H (8) - 3 = 5 (E), and T (20) + 3 = 23 (W). Combining these letters results in the coded form UFJEW.

Explanation

The coding follows a direct letter-to-digit mapping. From the code LOSE = 1357, we identify L = 1, O = 3, S = 5, and E = 7. From the code GAIN = 2468, we identify G = 2, A = 4, I = 6, and N = 8.

To decode the figures 84615, we substitute the corresponding letters for each digit: 8 = N 4 = A 6 = I 1 = L 5 = S

By arranging these letters in order, the figures 84615 represent the word NAILS.

Explanation

Argument I is strong because a primary objective of modern education is to equip individuals with the specialized skills and qualifications necessary to secure gainful employment and sustain themselves financially. From a developmental perspective, preparing a person for a career is a fundamental expectation of formal schooling. Argument II is also strong as it reinforces the concept of self-reliance, asserting that the end goal of education should be to enable a person to become independent and economically stable upon graduation. Both arguments correctly identify the essential vocational and utilitarian functions of education that are critical for individual survival and the overall economic health of a nation.

Explanation

The movement can be tracked by calculating the net change in direction from the starting point. The man starts facing West. A right turn is a 90-degree clockwise rotation, which changes his direction from West to North. A second right turn is another 90-degree clockwise rotation, changing his direction from North to East. Finally, a left turn is a 90-degree counter-clockwise rotation. Rotating 90 degrees counter-clockwise from East brings the man back to facing North. Alternatively, two right turns (180 degrees) followed by one left turn (-90 degrees) results in a net 90-degree clockwise turn from the starting direction of West, which is North.

Explanation

Sudha starts at a point and moves 8 km South. Turning right while facing South means she now heads West, where she travels for 4 km. A second right turn while facing West directs her 8 km North. Since the first leg (8 km South) and the third leg (8 km North) are of equal length and opposite in direction, she returns to the same horizontal line (latitude) as her starting point. Her final position is shifted only by the length of the second leg, which is 4 km West of the start. The path describes three sides of a rectangle with dimensions 8 km by 4 km, leaving her exactly 4 km away from the origin.

Explanation

The word COMPREHENSION consists of the letters C, O, M, P, R, E, H, N, S, and I. In order to construct the word PREACH, the letter A is necessary. An examination of the letters available in the parent word shows that the letter A is absent. Consequently, the word PREACH cannot be formed from the letters of the word COMPREHENSION.

Explanation

The word LIMITATION can be formed using the letters available in MULTIPLICATION. By counting the letters in the source word, we find M (1), U (1), L (2), T (2), I (3), P (1), C (1), A (1), O (1), and N (1). The word LIMITATION requires one L, three Is, one M, two Ts, one A, one O, and one N. Since each of these letters is present in MULTIPLICATION in the required quantity, the word can be successfully constructed from it.

Explanation

According to the logic of the question, the operational symbols are redefined as follows: - represents division (÷), + represents subtraction (-), ÷ represents multiplication (×), and × represents addition (+). Applying these substitutions to the equation in option b, the expression 70 - 2 + 4 ÷ 5 × 6 is rewritten as:

70 ÷ 2 - 4 × 5 + 6

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

First, perform the division: 70 ÷ 2 = 35 Next, perform the multiplication: 4 × 5 = 20 The expression now is: 35 - 20 + 6 Finally, perform the addition and subtraction: 35 - 20 = 15 and 15 + 6 = 21

The calculated result is 21, which matches the value provided in the equation.

Explanation

The system used to solve these equations is based on the sum of the square roots of the two numbers being multiplied. In the first equation, 324 × 289 = 35, the calculation is √(324) + √(289) = 18 + 17 = 35.

Applying this same logic to the next equation, 441 × 484 = 43 is obtained by calculating √(441) + √(484) = 21 + 22 = 43. Similarly, for the third equation, 625 × 400 = 45, the calculation is √(625) + √(400) = 25 + 20 = 45.

To find the value for the unsolved equation 256 × 729, take the square root of each number and add them together. The square root of 256 is 16, and the square root of 729 is 27. Therefore, the sum is 16 + 27 = 43.

Explanation

The pair 86-99 does not belong to the group because it fails to satisfy the 8:9 ratio property. In this mathematical pattern, the first number in the pair is 8/9 of the second number. When this ratio is applied to the second value 99, the required first value is calculated as 99 × (8/9) = 88. Since the pair provides the number 86 instead of 88, it does not possess the common property that characterizes the group.

Explanation

The sequence CXFUIR follows a rule where the number of letters skipped between consecutive characters decreases by 3 at each step. By assigning numerical values to the letters based on their alphabetical positions (C=3, X=24, F=6, U=21, I=9, R=18), the number of skipped letters is calculated using the formula Skip = |Positionₙ₊₁ - Positionₙ| - 1.

Between C and X, there are |24 - 3| - 1 = 20 letters skipped. Between X and F, there are |6 - 24| - 1 = 17 letters skipped. Between F and U, there are |21 - 6| - 1 = 14 letters skipped. Between U and I, there are |9 - 21| - 1 = 11 letters skipped. Finally, between I and R, there are |18 - 9| - 1 = 8 letters skipped. The resulting sequence of skipped letters (20, 17, 14, 11, 8) decreases by exactly 3 at each interval, which confirms that this option observes the rule.

Explanation

The sequence follows a logical descending order based on the hierarchy of linguistic and literary structures. A chapter (3) is the most comprehensive unit, which is subdivided into paragraphs (5). Each paragraph is formed by a series of sentences (1). Sentences are further divided into phrases (4), which are clusters of words that function as a single unit within a sentence. Finally, the word (2) represents the most fundamental and smallest unit of construction in this hierarchy. This progression from the largest organizational unit to the smallest constituent element creates a coherent and meaningful arrangement of the given terms.

Explanation

To arrange the words in dictionary order, we compare the letters from left to right. All words begin with the prefix In. Comparing the third letters, we have f in Infatuation (5) and Influence (4), g in Ingenious (2), and h in Inhabit (1) and Inherit (3). Since f comes before g and h, we first order the words starting with Inf. The fourth letter a in Infatuation precedes the fourth letter l in Influence, placing 5 before 4. The next word is Ingenious (2) as g follows f in the alphabet. Finally, for the words starting with Inh, the fourth letter a in Inhabit precedes the fourth letter e in Inherit, placing 1 before 3. This establishes the sequence 5, 4, 2, 1, 3.

Explanation

To find the correct pattern, the letter series is divided into groups of four characters each. By sequentially placing the letters from option d (a aa ba) into the gaps, we can observe a consistent alternating pattern based on the frequency of the letters a and b.

The provided series is: _ _ a b _ _ b _ a b a _ a b a b

If we assume the first gap __ is actually a single gap _ followed by a fixed letter a (or simply fill the gaps 1, 5, 6, 8, 12), and use the letters from option d (a, a, a, b, a), the sequence becomes:

Block 1: a a a b (Positions 1 to 4) Block 2: a a b b (Positions 5 to 8) Block 3: a b a a (Positions 9 to 12) Block 4: a b a b (Positions 13 to 16)

When we analyze the composition of each block: Block 1 (aaab) contains 3 a's and 1 b. Block 2 (aabb) contains 2 a's and 2 b's. Block 3 (abaa) contains 3 a's and 1 b. Block 4 (abab) contains 2 a's and 2 b's.

The pattern follows a cycle where the count of a's and b's alternates between (3,1) and (2,2) in every successive group of four. This logical structure completes the series systematically.

Explanation

The sequence follows a pattern where the difference between consecutive terms doubles at each step. Calculating the differences between the given numbers:

19 - 14 = 5 29 - 19 = 10 49 - 29 = 20 89 - 49 = 40

The differences observed are 5, 10, 20, and 40. This indicates a geometric progression of differences with a common ratio of 2. To find the next term in the sequence, the next difference must be calculated by multiplying the previous difference by 2, which gives 40 × 2 = 80. Adding this difference to the last known term of the sequence results in the following calculation:

89 + 80 = 169

Explanation

The series is formed by applying separate arithmetic patterns to each character position within the letter clusters. For the first letter, the pattern follows an increment of +2 positions in the alphabet: B +2 D +2 F +2 H +2 J. For the second letter, the pattern follows a decrement of -1 position: M -1 L -1 K -1 J -1 I. For the third letter, the pattern follows an increment of +2 positions: R +2 T +2 V +2 X +2 Z. For the fourth letter, the pattern follows a decrement of -1 position: G -1 F -1 E -1 D -1 C. Combining these transitions results in the cluster JIZC.

Explanation

The sequence consists of the squares of integers following a specific pattern in their bases. The numbers are 11² = 121, 12² = 144, 17² = 289, 18² = 324, 23² = 529, and 24² = 576.

The sequence of the bases is 11, 12, 17, 18, 23, 24. Examining the differences between consecutive bases reveals an alternating pattern: 12 - 11 = 1 17 - 12 = 5 18 - 17 = 1 23 - 18 = 5 24 - 23 = 1

Following this +1, +5, +1, +5, +1 pattern, the next base must be 24 + 5 = 29. Therefore, the next term in the sequence is 29² = 841.