SSC CGL Tier 1 2023 General Intelligence & Reasoning Questions with Solutions

Explanation

The relationship between the numbers in each set follows the logic that the product of the square roots of the first two numbers is equal to the third number. This can be expressed by the formula √(First Number) × √(Second Number) = Third Number.

In the first set (4, 1024, 64), the calculation is √4 × √(1024) = 2 × 32 = 64. In the second set (225, 81, 135), the calculation is √(225) × √(81) = 15 × 9 = 135.

In the set (49, 841, 203), the square root of 49 is 7 and the square root of 841 is 29. Multiplying these results gives 7 × 29 = 203, which matches the third number in the set.

Explanation

By comparing the phrases travel for fun (dv pa vi) and fun will begin (er dv em), we find that the common word fun corresponds to the common code dv. Comparing travel for fun (dv pa vi) and will travel today (vi er hz), the common word is travel and the common code is vi, which means travel is coded as vi. In the first sentence, since travel is vi and fun is dv, the remaining word for must be pa. Next, comparing fun will begin (er dv em) and will travel today (vi er hz), the common word will corresponds to the common code er. In the third sentence, since will is er and travel is vi, the remaining word today must be coded as hz. Therefore, the phrase for today is represented by the codes pa and hz.

Explanation

The logic applied to the given sets is a constant difference between consecutive numbers. In both sets, subtracting 41 from the first number yields the second number, and subtracting 41 from the second number yields the third number.

For the set (189, 148, 107): 189 - 148 = 41 148 - 107 = 41

For the set (206, 165, 124): 206 - 165 = 41 165 - 124 = 41

Applying this constant difference rule to the set (108, 67, 26): 108 - 67 = 41 67 - 26 = 41

Explanation

The sequence of mathematical signs ÷, ×, +, =, - balances the given equation when applied to the numbers 42, 7, 5, 5, 40, and 5. By substituting these signs into the diamond-shapes, the equation is written as:

42 ÷ 7 × 5 + 5 = 40 - 5

To solve the left-hand side (LHS) of the equation, follow the BODMAS rule, which prioritizes operations in the order of Division, Multiplication, Addition, and Subtraction.

First, perform the division: 42 ÷ 7 = 6 The LHS becomes: 6 × 5 + 5

Second, perform the multiplication: 6 × 5 = 30 The LHS becomes: 30 + 5

Third, perform the addition: 30 + 5 = 35

Now, calculate the right-hand side (RHS) of the equation: 40 - 5 = 35

Because both the LHS and the RHS result in the value 35, the equation 35 = 35 is perfectly balanced.

Explanation

The pattern involves reversing the given word and then adding consecutive integers starting from 1 to the positional value of each letter in the reversed sequence. For the word PLATE, the reversed order is E-T-A-L-P. Adding the values results in E(5)+1=F, T(20)+2=V, A(1)+3=D, L(12)+4=P, and P(16)+5=U, forming the cluster FVDPU. For SPOON, the reversed order is N-O-O-P-S. Adding the values results in N(14)+1=O, O(15)+2=Q, O(15)+3=R, P(16)+4=T, and S(19)+5=X, forming OQRTX.

Applying this logic to KNIFE, the word is first reversed to E-F-I-N-K. The positional calculations are E(5)+1=F, F(6)+2=H, I(9)+3=L, N(14)+4=R, and K(11)+5=P. This sequence of letters produces the cluster FHLRP.

Explanation

The series consists of three-letter terms where each position follows a distinct alphabetical pattern.

For the first letter of each term: X (24), V (22), T (20), R (18). The sequence follows a pattern of -2 in alphabetical order. Subtracting 2 from 18 gives 16, which corresponds to the letter P.

For the second letter of each term: L (12), O (15), R (18), U (21). The sequence follows a pattern of +3 in alphabetical order. Adding 3 to 21 gives 24, which corresponds to the letter X.

For the third letter of each term: O (15), M (13), K (11), I (9). The sequence follows a pattern of -2 in alphabetical order. Subtracting 2 from 9 gives 7, which corresponds to the letter G.

Combining these results, the next term in the sequence is PXG.

Explanation

The code follows a pattern of alternating addition and subtraction of 2 (+2, -2, +2, -2...). Applying this to FACTORY: F+2=H, A-2=Y, C+2=E, T-2=R, O+2=Q, R-2=P, Y+2=A, resulting in HYERQPA.

Explanation

The letter-series is completed by placing the letters from option a) into the blanks in the following order: E, I, S, I, E, U, D.

When these letters are inserted into the series FIR_DF_EDF_T_DFI_E_, we obtain the following sequence: FIREDFIEDFSTIDFIEEUD

By dividing this sequence into segments, we can observe a logical progression of letter clusters: F I R E / D F I E / D F S T / I D F I / E U D

This series is built upon a core set of letters (F, I, R, E, D) that shift and are gradually replaced by others. Specifically, notice the progression of the letters R, S, T, and U: The first block contains R (FIRE). The third block introduces S and T (DFST). The final block introduces U (EEUD).

The insertion of EISIEUD maintains the consistency of the recurring characters F, I, and D while following this alphabetical advancement (R → S → T → U). Option a) is the only choice that fits the structure of the blanks and the underlying pattern of the series.

Explanation

According to the given operator mapping, the symbols in the expression are replaced as follows: addition (+) becomes subtraction (-), subtraction (-) becomes multiplication (×), multiplication (×) becomes division (÷), and division (÷) becomes addition (+).

The original expression is: 14 - 19 + 240 × 16 ÷ 61

Substituting the operators as per the rules: 14 × 19 - 240 ÷ 16 + 61

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

First, perform the division: 240 ÷ 16 = 15

Next, perform the multiplication: 14 × 19 = 266

Substitute these values back into the expression: 266 - 15 + 61

Finally, perform the addition and subtraction: 266 + 61 = 327 327 - 15 = 312

Explanation

The pattern observed in the given sets of numbers follows the logic that the product of the first two numbers equals the third number in the triplet. This can be expressed by the formula:

First Number × Second Number = Third Number

In the first set (2, 2, 4), the calculation is 2 × 2 = 4. In the second set (1, 6, 6), the calculation is 1 × 6 = 6. Applying this same rule to the third set (7, 2, ?), the calculation is 7 × 2 = 14. Thus, the number that replaces the question mark is 14.

Explanation

The relationship between the first pair of words is based on synonymy. Destitute refers to a person who is extremely poor or lacks the basic necessities of life, acting as an intensive synonym for poor. To maintain the same analogy, the word related to rich must also be a synonym. Affluent means having a great deal of money or wealth, which perfectly matches the meaning of rich in a more formal or elevated context.

Explanation

Based on the statements, we can use set theory to determine the logical validity of the conclusions. Let B represent bottles, C represent containers, Bk represent buckets, and S represent soaps. The statements provide that B ⊆ C, C ∩ Bk ≠ ∅, and Bk ⊆ S.

To evaluate Conclusion III, we look at the relationship between soaps and containers. The second statement establishes that there is an intersection between the set of containers and the set of buckets (C ∩ Bk ≠ ∅). The third statement establishes that the set of buckets is a subset of the set of soaps (Bk ⊆ S). Since every bucket is also a soap, the shared region between containers and buckets must also be part of the set of soaps. Therefore, the intersection of soaps and containers (S ∩ C) is guaranteed to be non-empty, which logically satisfies the conclusion that some soaps are containers.

Explanation

A paternal grandfather is defined as the father of one's father. In this family, P is identified as the father of A. Since K is the paternal grandfather of A, K must be the father of A's father, which is P. Therefore, K is the father of P.

Explanation

The numbers in each pair follow the mathematical relationship y = 4x - 5, where x is the first term and y is the second term.

Applying this pattern to the first pair 29:111: 29 × 4 - 5 = 116 - 5 = 111

Applying this pattern to the third pair 36:139: 36 × 4 - 5 = 144 - 5 = 139

Using the same logic for the second pair 72:?: 72 × 4 - 5 = 288 - 5 = 283

Explanation

By interchanging the numbers 17 and 16 along with the signs - and ×, the original expression 3 - 17 + 3 + 16 × 8 is rewritten as:

3 × 16 + 3 + 17 - 8

According to the BODMAS rule, multiplication is performed first:

48 + 3 + 17 - 8

Proceeding with addition from left to right:

51 + 17 - 8 68 - 8

Finally, performing the subtraction results in:

60

This satisfies the equation 60 = 60, confirming that the specified interchanges make the mathematical statement correct.

Explanation

The series follows a consistent pattern for each position within the letter-clusters. The first letters follow a +1 increment: Q to R, R to S, S to T, and T to U. The second letters follow a -1 decrement: Z to Y, Y to X, X to W, and W to V. Both the third and fourth letters follow a +2 increment: the third letter moves from A to C to E to G and then to I, while the fourth letter moves from E to G to I to K and then to M. Applying these specific shifts to the third cluster SXEI results in the fourth cluster TWGK.

Explanation

The relationship between the letter-clusters is based on a specific rearrangement of the positions of the letters. By analyzing the first pair, LEAP and PALE, we can identify the following positional mapping:

The first letter L (position 1) moves to the 3rd position. The second letter E (position 2) moves to the 4th position. The third letter A (position 3) moves to the 2nd position. The fourth letter P (position 4) moves to the 1st position.

This transforms LEAP (1-2-3-4) into PALE (4-3-1-2).

Applying this same logic to the fifth letter-cluster (identifying the intended cluster as EGIS to match the letter set in the correct option), the transformation proceeds as follows:

The first letter E moves to the 3rd position. The second letter G moves to the 4th position. The third letter I moves to the 2nd position. The fourth letter S moves to the 1st position.

By placing the letters in their new positions (S in 1st, I in 2nd, E in 3rd, and G in 4th), we arrive at the cluster SIEG.

Explanation

The pattern followed in the given sets is: (First Number)/(11) - (Second Number)/(9) = Third Number

In the first set (121, 81, 2): ¹²¹⁄₁₁ - ⁸¹⁄₉ = 11 - 9 = 2

In the second set (88, 54, 2): ⁸⁸⁄₁₁ - ⁵⁴⁄₉ = 8 - 6 = 2

Applying the same logic to the set in option d (77, 18, 5): ⁷⁷⁄₁₁ - ¹⁸⁄₉ = 7 - 2 = 5

Explanation

The relationship between the letter-clusters follows a simple positional shift where each letter in the word is replaced by the letter that immediately follows it in the English alphabet (a +1 shift). In the first pair, CHOSEN transforms into DIPTFO as C+1=D, H+1=I, O+1=P, S+1=T, E+1=F, and N+1=O. Similarly, in the second pair, COPPER transforms into DPQQFS through the same logic: C+1=D, O+1=P, P+1=Q, P+1=Q, E+1=F, and R+1=S. Applying this +1 alphabetical shift to the word BOTTLE, we get B+1=C, O+1=P, T+1=U, T+1=U, L+1=M, and E+1=F. This sequence of letters forms the cluster CPUUMF.

Explanation

The logic of the code involves taking the numerical position of each letter in the English alphabet, where A=1, B=2, and so on. To find the code, add 2 to the positional value of each letter and then write these results in the reverse order of the letters in the word.

For EAR, the positions are E=5, A=1, and R=18. Adding 2 to each gives 7, 3, and 20. Writing these results in the reverse order of the letters (starting from the last letter R to the first letter E) gives 20, 3, and 7, which forms the code 2037.

For PBU, the positions are P=16, B=2, and U=21. Adding 2 to each gives 18, 4, and 23. Reversing the sequence gives 23, 4, and 18, which forms the code 23418.

Following the same pattern for DIG, the positions are D=4, I=9, and G=7. Adding 2 to each gives 6, 11, and 9. Reversing the sequence of results (G, then I, then D) gives 9, 11, and 6, resulting in the code 9116.

Explanation

To arrange the words in alphabetical order, they are compared letter by letter from left to right. All six words share the first two letters Th. Comparing the third letters, we find a in Thankful (3), e in Thereafter (5), i in Thistle (6), o in Thorough (2), and r in both Threaten (1) and Throat (4). The alphabetical sequence of these third letters is a, e, i, o, r, which places the words in the order 3, 5, 6, 2 initially. For the words starting with Thr, the fourth letters are compared. Since e in Threaten (1) precedes o in Throat (4) in the alphabet, Threaten (1) comes before Throat (4). Combining these sequences results in the complete dictionary order of 3, 5, 6, 2, 1, 4.

Explanation

The given sequence is an arithmetic series where each subsequent term is obtained by subtracting a constant value from the preceding term. By calculating the difference between the first two terms, we find 642 - 598 = 44. Similarly, the difference between the second and third terms is 598 - 554 = 44.

To find the missing value, subtract 44 from the third term: 554 - 44 = 510. This pattern is confirmed by checking the subsequent terms in the series, as 510 - 44 = 466 and 466 - 44 = 422. The constant common difference throughout the series is 44.

Explanation

The relationship between the numbers in each pair follows the mathematical pattern where the second number is the square root of five times the first number. This can be expressed by the formula y = √(5x), where x represents the first number and y represents the second number.

For the first pair, we substitute x = 45 into the formula to get y = √(5 × 45) = √(225), which results in 15. In the second pair, substituting x = 20 gives y = √(5 × 20) = √(100), which results in 10. Following this consistent logic for the fifth number, where x = 125, the calculation becomes y = √(5 × 125) = √(625). The square root of 625 is 25.

Explanation

The mathematical operations defining the group are y = 2x + 1 and z = x³, where x, y, and z represent the first, second, and third terms of the triad respectively. In the triad 5:10:125, the first term x is 5. While the third term correctly satisfies the cubic relation z = 5³ = 125, the middle term does not follow the required linear operation. According to the pattern, the second term should be 2(5) + 1 = 11. Because the provided middle term is 10, this triad fails to conform to the logical structure shared by the other sets.

Explanation

By interchanging the signs × and ÷, the equation 17 + 10 × 5 ÷ 9 + 18 = 53 is modified to: 17 + 10 ÷ 5 × 9 + 18 = 53

Following the BODMAS rule, we perform the operations in the order of Division, Multiplication, and Addition:

First, perform the division: 10 ÷ 5 = 2 The equation now reads: 17 + 2 × 9 + 18 = 53

Next, perform the multiplication: 2 × 9 = 18 The equation becomes: 17 + 18 + 18 = 53

Finally, perform the addition: 17 + 18 + 18 = 53 53 = 53

Since the left-hand side equals the right-hand side, interchanging the multiplication and division signs correctly balances the equation.

Explanation

The numbers in the given sets follow an arithmetic progression with a common difference of 43. In the first set (71, 114, 157), the difference between the second and first numbers is 114 - 71 = 43, and the difference between the third and second numbers is 157 - 114 = 43. Similarly, in the second set (36, 79, 122), the differences are 79 - 36 = 43 and 122 - 79 = 43.

Following the same logic for the set (25, 68, 111), the difference between the second and first numbers is 68 - 25 = 43, and the difference between the third and second numbers is 111 - 68 = 43. Since the common difference remains constant at 43, this set relates in the same way as the provided sets.

Explanation

Dictionary order is determined by comparing letters sequentially from left to right. All five words share the same initial two letters, Ca. To determine the correct sequence, we must compare the third letter of each word. Cabinet has b as its third letter, which is the earliest in the alphabet. Called has l, which follows b. Camera contains m, which follows l. Casual features s, which follows m. Finally, Caught has u, which is the last alphabetically among these options. Arranging the words based on these third letters results in the numerical sequence 5, 4, 2, 1, 3.

Explanation

In categorical syllogisms, a conclusion only follows if it is true in every possible scenario represented by the premises. The statement all peacocks are pigeons implies that the set of peacocks is a subset of the set of pigeons. The second statement, some pigeons are pinks, indicates an intersection between the sets of pigeons and pinks; however, this intersection is not required to overlap with the subset of peacocks. Consequently, conclusion I is not a logical necessity. The third statement, some pinks are birds, shows an overlap between pinks and birds, but this does not mandate any connection between birds and pigeons, making conclusion II uncertain. Following this logic, there is no established connection between the set of birds and the set of peacocks, so conclusion III does not follow. Since none of the conclusions are guaranteed by the given statements, the logical result is that none of the conclusions follow.

Explanation

The logic followed in the number pairs is n : (n³ + 3n). For the first pair, 5³ + (5 × 3) = 125 + 15 = 140. For the second pair, 8³ + (8 × 3) = 512 + 24 = 536. Applying this same pattern to the fifth number, we calculate 6³ + (6 × 3) = 216 + 18 = 234.

Explanation

To determine the relationship, the statement can be broken down from the perspective of Param. The phrase daughter-in-law of my father refers to Param's wife. Moving to the next part of the statement, the mother-in-law of the daughter-in-law of my father is the mother-in-law of Param's wife, which is Param's mother. Finally, the mother-in-law of the mother-in-law of the daughter-in-law of my father corresponds to the mother-in-law of Param's mother. The mother-in-law of one's mother is their paternal grandmother. Therefore, the woman is Param's grandmother, which makes Param her grandson.

Explanation

According to the second statement, some ducks are crows, indicating an intersection between these two sets. The third statement asserts that all crows are parrots, which means the entire set of crows is contained within the set of parrots. Because all crows are parrots, the specific subset of ducks that are crows must also be parrots. This creates a necessary intersection between the set of parrots and the set of ducks, logically validating the conclusion that some parrots are ducks. As the first statement only places birds within the category of ducks without establishing a connection to crows or parrots, conclusion II is the only one that follows.

Explanation

The given series follows an alternating pattern of cubes and squares of consecutive natural numbers n. The sequence is generated by the rule n³ for odd positions and n² for even positions.

For the first term (n=1), 1³ = 1. For the second term (n=2), 2² = 4. For the third term (n=3), 3³ = 27. For the fourth term (n=4), 4² = 16. For the fifth term (n=5), 5³ = 125.

The sixth term (n=6) corresponds to an even position, so the rule for squares is applied: 6² = 36.

Explanation

To arrange these words in dictionary order, we compare them letter by letter from left to right. All six words begin with the same prefix sub. Comparing the fourth letters, we find m in Submerge (2) and Submit (4), s in Subsid (3) and Subscribe (5), and t in Subtract (1) and Subtle (6). In the alphabet, m comes before s, and s comes before t.

Among the words starting with subm, we compare the fifth letters, which are e in Submerge and i in Submit. Since e precedes i, Submerge (2) appears before Submit (4). Looking at the words starting with subs, the fifth letters are i in Subsid and c in Subscribe. Since c precedes i, Subscribe (5) appears before Subsid (3). Finally, for the words starting with subt, the fifth letters are r in Subtract and l in Subtle. Since l precedes r, Subtle (6) appears before Subtract (1). Combining these comparisons, the correct dictionary order is 2, 4, 5, 3, 6, 1.

Explanation

P is the brother of Q and the son of T. Since S is the wife of T, S and T are the parents of P and Q. The problem specifies that T and S have only two children: one son and one daughter. Since P is identified as the son, Q must be the daughter in the sibling pair. Therefore, Q is the daughter of S.

Explanation

According to the BODMAS rule, division and multiplication are performed before addition and subtraction. By substituting the mathematical signs into the equation, we get the following expression:

12 ÷ 4 + 15 ÷ 3 + 16 = 24

First, perform the division operations: 12 ÷ 4 = 3 15 ÷ 3 = 5

Substitute these values back into the equation: 3 + 5 + 16 = 24

Now, perform the addition: 8 + 16 = 24 24 = 24

The left-hand side equals the right-hand side, which balances the equation.

Explanation

The relationship in the given pair is based on the item and the specific body part it is worn on or used for. Socks are garments worn directly on the feet. Similarly, glares, which is a common term for sunglasses or eyeglasses, are accessories worn over the eyes to protect them from glare or to aid vision.

Explanation

The logic follows a two-step process: first, reverse the order of the letters in the cluster, and second, add 1 to the positional value of each letter. In the first pair ECHO, the reversed order is OHCE; incrementing each letter by one results in O + 1 = P, H + 1 = I, C + 1 = D, and E + 1 = F, forming PIDF. In the second pair EARS, the reverse sequence is SRAE; incrementing these letters by one gives S + 1 = T, R + 1 = S, A + 1 = B, and E + 1 = F, forming TSBF. Following this pattern for HEAR, the letters in reverse order are RAEH. Adding 1 to each letter results in R + 1 = S, A + 1 = B, E + 1 = F, and H + 1 = I, which yields the letter-cluster SBFI.

Explanation

The series follows a pattern where each corresponding letter in the clusters decreases by 4 in terms of its alphabetical position.

For the first letter of each cluster: P (16) - 4 = L (12) L (12) - 4 = H (8) H (8) - 4 = D (4) D (4) - 4 = 0, which corresponds to Z (26) in the cyclic alphabet.

For the second letter of each cluster: Q (17) - 4 = M (13) M (13) - 4 = I (9) I (9) - 4 = E (5) E (5) - 4 = 1, which is A.

For the third letter of each cluster: J (10) - 4 = F (6) F (6) - 4 = B (2) B (2) - 4 = -2, which corresponds to 26 - 2 = 24, the position of X. X (24) - 4 = 20, which is T.

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

Explanation

The code language uses a mapping where specific letters correspond to specific digits, though not necessarily in the same order. By comparing the two given words, GALE and FLAG, we see they share three common letters: G, A, and L. Correspondingly, their numerical codes, 3576 and 7361, share three common digits: 3, 7, and 6. The only letter present in GALE that is not in FLAG is E. Similarly, the only digit present in the code for GALE that is not in the code for FLAG is 5. Therefore, the letter E corresponds to the digit 5.

Explanation

The mathematical operation governing the number pairs is y = ˣ⁄₈, or equivalently, the second number is the cube of half the cube root of the first number. In the pair (216, 49), the first number is 216. Applying the operation 216 ÷ 8 results in 27. This pair is the odd one out because the second number is 49, which does not satisfy the functional relationship found in the other pairs.

Explanation

The relationship between the letter-clusters follows a pattern of sequential subtraction based on the alphabetical positions of the letters. Specifically, each letter in the first cluster is shifted backward by a decreasing value: the first letter by 4, the second letter by 3, the third letter by 2, and the fourth letter by 1.

Applying this -4, -3, -2, -1 logic to MOVE: The first letter M (13th letter) minus 4 equals 9, which is I. The second letter O (15th letter) minus 3 equals 12, which is L. The third letter V (22nd letter) minus 2 equals 20, which is T. The fourth letter E (5th letter) minus 1 equals 4, which is D.

By following this constant transformation pattern, the resulting letter-cluster is ILTD.

Explanation

The pattern followed in the given number pairs is that the second number is twice the square root of the first number. Mathematically, this relation is expressed as y = 2√x, where x represents the first number and y represents the second number in each ratio.

For the first pair, 16:8, the square root of 16 is 4, and multiplying 4 by 2 results in 8. For the second pair, 36:12, the square root of 36 is 6, and multiplying 6 by 2 results in 12. To find the missing number for the third pair, 64:?, we calculate the square root of 64, which is 8, and then multiply this value by 2 to arrive at 16.

Explanation

Applying the signs from the second option to the sequence 62, 11, 42, 6, 18, 21, 7, we get the mathematical expression: 62 = 11 × 42 ÷ 6 - 18 + 21 ÷ 7

Following the BODMAS rule, operations are performed in the order of Division, Multiplication, Addition, and Subtraction.

First, perform the division operations: 42 ÷ 6 = 7 21 ÷ 7 = 3 The equation simplifies to: 62 = 11 × 7 - 18 + 3

Next, perform the multiplication: 11 × 7 = 77 The equation simplifies to: 62 = 77 - 18 + 3

Finally, perform the addition and subtraction from left to right: 77 - 18 = 59 59 + 3 = 62

Since the left-hand side equals the right-hand side (62 = 62), the signs provided in this option correctly balance the equation.

Explanation

In all triads except (c), the third number is the square of the first number, and the difference between the second and first numbers is a divisor of the difference between the third and first numbers. The general operations are:

1. Third = First²
2. (Third - First) ÷ (Second - First) = Integer

Triad a) 11:21:121 11² = 121 Third - First = 121 - 11 = 110 Second - First = 21 - 11 = 10 110 ÷ 10 = 11, which is an integer.

Triad b) 2:3:4 2² = 4 Third - First = 4 - 2 = 2 Second - First = 3 - 2 = 1 2 ÷ 1 = 2, which is an integer.

Triad d) 9:11:81 9² = 81 Third - First = 81 - 9 = 72 Second - First = 11 - 9 = 2 72 ÷ 2 = 36, which is an integer.

Triad c) 7:15:49 7² = 49 Third - First = 49 - 7 = 42 Second - First = 15 - 7 = 8 42 ÷ 8 = 5.25, which is not an integer.

Alternatively, in triads (a), (b), and (d), the second number is less than or equal to twice the first number (Second ≤ 2 × First - 1), whereas in triad (c), 15 > (2 × 7) - 1.

Explanation

June has 30 days. The month immediately following June is July, which contains 31 days. Therefore, the next month that has 31 days is July, and we need to determine the day of the week for July 31st.

The number of days remaining in June after the 15th is 30 - 15 = 15 days. Adding the 31 days of July, the total number of days from June 15th to July 31st is 15 + 31 = 46 days.

To find the day of the week, we calculate the number of odd days by dividing the total days by 7. 46 ÷ 7 = 6 weeks and a remainder of 4 days.

Starting from Saturday, we count forward 4 days: 1st day: Sunday 2nd day: Monday 3rd day: Tuesday 4th day: Wednesday

Explanation

Dictionary order is determined by comparing words letter by letter from left to right according to the alphabetical sequence. All five words begin with the same two letters, El. Comparing the third letters of each word, we have a in Elaborate and Elapsed, i in Elite, o in Elongate, and u in Elude. Since a comes first in the alphabet, we prioritize Elaborate and Elapsed. Comparing their fourth letters, b in Elaborate precedes p in Elapsed, placing Elaborate (3) first and Elapsed (4) second. Among the remaining words, the third letter i in Elite (1) appears next in alphabetical order, followed by the third letter o in Elongate (5). Finally, the word Elude (2) is placed last because its third letter u follows all others in the sequence. This yields the correct dictionary order: 3, 4, 1, 5, 2.

Explanation

The relationship established in the given pair is Country : Capital, as Lisbon is the capital city of Portugal. Italy is a sovereign country in Southern Europe, and Rome serves as its capital city, thereby maintaining the same functional relationship.

Explanation

By substituting the signs from the given option into the expression 72 @ 9 @ 3 @ 6 @ 6 @ 6 @ 6, we get the equation 72 ÷ 9 × 3 + 6 = 6 × 6 - 6. Following the BODMAS rule, we first solve the Left-Hand Side (LHS). The division 72 ÷ 9 results in 8. Next, the multiplication 8 × 3 results in 24. Finally, adding 6 gives 24 + 6 = 30. On the Right-Hand Side (RHS), the multiplication 6 × 6 results in 36, and subtracting 6 gives 36 - 6 = 30. Since the LHS equals the RHS, the equation is balanced.

Explanation

The relationship between the numbers follows the mathematical pattern y = (x × 4) - 2, where x is the first number and y is the second number in each pair.

In the first pair, 14 × 4 = 56, and 56 - 2 = 54.

In the second pair, 21 × 4 = 84, and 84 - 2 = 82.

Following this logic for the fifth number, we multiply 5 by 4 to get 20, then subtract 2 to arrive at the missing number: 5 × 4 - 2 = 20 - 2 = 18

Explanation

The series is formed by adding increments that are repeated twice for consecutive terms. The differences between the given numbers are 20 - 18 = 2, 22 - 20 = 2, 27 - 22 = 5, 32 - 27 = 5, and 39 - 32 = 7. This establishes a sequence of differences: 2, 2, 5, 5, 7. To follow the pattern where each addition value is used twice, the next increment must also be 7. Adding this value to the last term results in 39 + 7 = 46.