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

Explanation

The series consists of 20 characters which can be divided into four identical groups of five letters each. By observing the distribution of the letters N, M, L, and J, it is determined that each group follows the repeating sequence NMLJJ.

First group: N M L (J) J Second group: N (M) L J J Third group: (N) M L J (J) Fourth group: N M (L) J J

By substituting the letters from the first option into the blanks at positions 4, 7, 11, 15, and 18, the pattern NMLJJ is consistently formed across all four segments. This results in the complete series NMLJJNMLJJNMLJJNMLJJ. Thus, the letters that complete the series from left to right are J, M, N, J, and L.

Explanation

To balance the equation 9 16 64 8 2 = 9, we substitute the signs + , ÷ , × , - , = into the respective positions. Following the BODMAS rule, we prioritize operations in the order of division, multiplication, addition, and then subtraction.

Substituting the signs, the expression becomes: 9 + 16 ÷ 64 × 8 - 2 = 9

First, we calculate the division part 16 ÷ 64, which simplifies to ¼ or 0.25. The equation now looks like this: 9 + ¼ × 8 - 2 = 9

Next, we perform the multiplication ¼ × 8, which results in 2. The equation simplifies further to: 9 + 2 - 2 = 9

Finally, by executing the addition and subtraction from left to right, we get 11 - 2 = 9. Since the value of the left-hand side matches the right-hand side (9 = 9), the combination of signs correctly balances the mathematical statement.

Explanation

The relationship can be decoded by breaking down the description step by step. R's maternal grandfather is the father of R's mother. The only granddaughter of R's maternal grandfather would be either R herself, if R is female, or R's sister, if R is male. In either scenario, the father of this granddaughter is R's father. Consequently, the person with whom the children were left is R's father.

Explanation

To find the code for the letter N, we compare the two given words and their numerical codes. The word BENT is coded as 3198, and the word DEBT is coded as 8316. By observing the common letters between BENT and DEBT, we find that B, E, and T are present in both words. Correspondingly, we look for the common digits in their respective codes, 3198 and 8316, which are 3, 1, and 8.

The only letter in the word BENT that is not present in the word DEBT is N. Similarly, the only digit in the code for BENT (3198) that is not present in the code for DEBT (8316) is 9. Through this process of elimination by comparing the sets of letters and digits, it is determined that the digit 9 represents the letter N.

Explanation

The relationship between the numbers in the given sets follows the formula n1 × n3 × 2 = n2, where n1 is the first number, n2 is the second number, and n3 is the third number.

In the first set (25, 150, 3), the calculation is: 25 × 3 × 2 = 75 × 2 = 150

In the second set (18, 180, 5), the calculation is: 18 × 5 × 2 = 90 × 2 = 180

Applying this same logic to the set (52, 728, 7): 52 × 7 × 2 = 364 × 2 = 728

Explanation

To determine the day of the week on 30 January 2013, we first calculate the number of odd days from 31 January 2009 to 31 January 2013. In a calendar, an ordinary year of 365 days has 1 odd day (365 7 = 1), and a leap year of 366 days has 2 odd days (366 7 = 2).

The period from 31 January 2009 to 31 January 2013 covers exactly 4 years. Within this span, the year 2012 is a leap year. Because the date 29 February 2012 falls between 31 January 2009 and 31 January 2013, we count one leap year and three ordinary years.

Total odd days = (3 × 1) + (1 × 2) = 5 odd days.

Adding 5 days to the reference day (Saturday): Saturday + 1 = Sunday Saturday + 2 = Monday Saturday + 3 = Tuesday Saturday + 4 = Wednesday Saturday + 5 = Thursday

Thus, 31 January 2013 was a Thursday. Since 30 January 2013 is the day immediately preceding 31 January 2013, the day was a Wednesday.

Explanation

The logic followed in the given number pairs is n : n(n - 2). For the first pair, 7 × (7 - 2) = 7 × 5 = 35. For the second pair, 21 × (21 - 2) = 21 × 19 = 399. Applying the same logic to the fifth number, we calculate 4 × (4 - 2) = 4 × 2 = 8.

Explanation

The relationship between the numbers in each pair follows the pattern where the second number is the square of the first number minus 2. This can be expressed by the formula y = x² - 2.

In the first pair, 7² - 2 = 49 - 2 = 47. In the second pair, 11² - 2 = 121 - 2 = 119. Applying this same logic to the fifth number, we calculate 3² - 2 = 9 - 2 = 7.

Explanation

The relationship between the first two words is that a pot is a container specifically used for housing and growing a plant. Similarly, an aquarium is a tank or container designed to house and maintain fish in a controlled environment. Both pairs follow the pattern of a living organism and its common man-made containment vessel.

Explanation

The series consists of two interleaved alternate sequences.

The first sequence comprises terms at odd positions: 57, 88, 150, and 243. The differences between consecutive terms in this sequence follow a pattern of multiples of 31. 88 - 57 = 31 × 1 = 31 150 - 88 = 31 × 2 = 62 243 - 150 = 31 × 3 = 93

The second sequence comprises terms at even positions: 69, 112, 186, and the required term. The differences between consecutive terms in this sequence increase by a constant value of 31. 112 - 69 = 43 186 - 112 = 74 The difference between these increments is 74 - 43 = 31. Following this arithmetic progression for the differences, the next increment should be 74 + 31 = 105.

Applying this to the last known term of the even sequence, we find the missing number: 186 + 105 = 291

Explanation

The coding follows a specific arithmetic pattern based on the positions of letters in the English alphabet (A=1, B=2, ..., Z=26). The word is divided into three parts: the first two letters, the middle letter, and the last two letters.

For the middle letter, a constant shift of +4 is applied: In RELAX, the middle letter L(12) + 4 = 16(P). In STAKE, the middle letter A(1) + 4 = 5(E). In WINDS, the middle letter N(14) + 4 = 18(R).

For the first two letters, the sum of the letter and its corresponding code letter is equal to (Sum of the first two letters of the original word - 2): RELAX: R(18) + E(5) = 23. Target sum = 23 - 2 = 21. Code: R(18) + 3(C) = 21 and E(5) + 16(P) = 21. STAKE: S(19) + T(20) = 39. Target sum = 39 - 2 = 37. Code: S(19) + 18(R) = 37 and T(20) + 17(Q) = 37. WINDS: W(23) + I(9) = 32. Target sum = 32 - 2 = 30. Code: W(23) + 7(G) = 30 and I(9) + 21(U) = 30.

For the last two letters, the sum of the letter and its corresponding code letter is equal to (Sum of the last two letters of the original word + 2): RELAX: A(1) + X(24) = 25. Target sum = 25 + 2 = 27. Code: A(1) + 26(Z) = 27 and X(24) + 3(C) = 27. STAKE: K(11) + E(5) = 16. Target sum = 16 + 2 = 18. Code: K(11) + 7(G) = 18 and E(5) + 13(M) = 18. WINDS: D(4) + S(19) = 23. Target sum = 23 + 2 = 25. Code: D(4) + 21(U) = 25 and S(19) + 6(F) = 25.

Combining these results for WINDS, we get G, U, R, U, F.

Explanation

The relationship between the numbers in each pair follows the mathematical pattern n₁ = 6 × (n₂)³, where n₁ is the first number and n₂ is the second number of the pair.

For the first pair, 750:5, substituting the values gives 6 × 5³ = 6 × 125 = 750. For the second pair, 384:4, substituting the values gives 6 × 4³ = 6 × 64 = 384.

Applying this logic to the third pair, 3072:?, we set up the equation 3072 = 6 × x³. Dividing both sides by 6, we get x³ = 3072 / 6 = 512. Taking the cube root of both sides, x = ³√(512) = 8.

Explanation

The mathematical relationship between the numbers in the pairs follows the logic y = (x × 11) + 7, where x is the first number and y is the second number. For the pair (23, 270), applying this formula gives 23 × 11 + 7 = 253 + 7 = 260. Since the second number provided in this pair is 270 instead of the expected 260, it does not follow the operation consistent across the other pairs.

Explanation

The relationship in the given pair is based on an animal and the primary natural resource or product it provides for human use. A cow is a domesticated animal that serves as a primary source of milk. Similarly, a sheep is a domesticated animal primarily raised for its fleece, which is harvested to produce wool.

Explanation

Based on the family relationships, B is identified as the wife of A and the daughter of D. Since C is the daughter of A, and B is A's wife, C is also the daughter of B. Given that B is the daughter of D, C is the daughter of D's daughter. This makes C the granddaughter of D, specifically through D's daughter.

Explanation

Following the BODMAS rule, we substitute the plus and multiplication signs in the given equation 162 ÷ 3 + 5 × 6 - 2 = 274. Replacing + with × and × with + yields the expression 162 ÷ 3 × 5 + 6 - 2.

First, perform the division: 162 ÷ 3 = 54. Next, perform the multiplication: 54 × 5 = 270. Finally, perform the addition and subtraction: 270 + 6 - 2 = 276 - 2 = 274.

Since the calculated result matches the value on the right-hand side of the equation, this interchange makes the equation mathematically correct.

Explanation

The logic followed in the given sets is that the third number is obtained by adding the second number to twice the first number. The relationship can be expressed by the formula 2 × n₁ + n₂ = n₃.

In the first set (12, 5, 29), the calculation is 12 × 2 + 5 = 24 + 5 = 29. In the second set (19, 12, 50), the calculation is 19 × 2 + 12 = 38 + 12 = 50.

Applying the same mathematical pattern to the set in the correct option (15, 14, 44), we perform the operation 15 × 2 + 14 = 30 + 14 = 44. This set perfectly adheres to the identified rule.

Explanation

The relationship between the numbers in each pair follows the mathematical pattern x × (ˣ⁄₂ + 1), where x is the first number in the pair.

For the first pair, 16 : 144: 16 × (¹⁶⁄₂ + 1) = 16 × (8 + 1) = 16 × 9 = 144

For the third pair, 14 : 112: 14 × (¹⁴⁄₂ + 1) = 14 × (7 + 1) = 14 × 8 = 112

Applying this same logic to the second pair, where x = 22: 22 × (²²⁄₂ + 1) = 22 × (11 + 1) = 22 × 12 = 264

An alternative way to express this pattern is (x²{2} + x). Substituting 22 into this formula gives 22²{2} + 22 = ⁴⁸⁴⁄₂ + 22 = 242 + 22 = 264.

Explanation

To arrange words in dictionary order, we compare the letters of each word from left to right. All the given words start with the same first three letters, Can. Therefore, the sequence is determined by comparing the fourth letter of each word.

In Cancer (6), the fourth letter is c. In Candidly (2), the fourth letter is d. In Cannibal (5), the fourth letter is n. In Canopy (4), the fourth letter is o. In Canteen (3), the fourth letter is t. In Canvas (1), the fourth letter is v. Arranging these fourth letters in alphabetical order gives the sequence c, d, n, o, t, v. Consequently, the words follow the order 6, 2, 5, 4, 3, 1.

Explanation

Sonal and her brother share the same paternal grandmother, Seeta. A paternal grandmother is defined as the mother of one's father. The problem specifies that Seeta is accompanied by her only son. Since she has only one son, that individual must be the father of Sonal and her brother. In genealogical terms, the male child of a paternal grandmother who has no other sons is the father of the grandchildren. Therefore, Seeta's son is Sonal's father.

Explanation

By interchanging the signs ÷ and ×, the given equation becomes:

60 ÷ 4 + 9 × 3 - 8 = 34

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

First, perform the division: 15 + 9 × 3 - 8 = 34

Next, perform the multiplication: 15 + 27 - 8 = 34

Then, perform the addition: 42 - 8 = 34

Finally, perform the subtraction: 34 = 34

Since the LHS equals the RHS, the equation is satisfied.

Explanation

The series is formed by the continuous repetition of the seven-letter block STNFIRG. By dividing the series into these uniform segments, we can identify the missing letters in each position:

Block 1: ST [N] FIR [G] Block 2: STNF [I] RG Block 3: STN [F] IRG Block 4: [S] [T] NF I [R] G

By filling the blanks sequentially from left to right: The first blank (position 3) requires N to complete the first STN segment. The second blank (position 7) requires G to complete the first STNFIRG block. The third blank (position 12) requires I to complete the second STNFIRG block. The fourth blank (position 18) requires F to complete the third STNFIRG block. The fifth, sixth, and seventh blanks (positions 22, 23, and 27) require S, T, and R respectively to complete the fourth STNFIRG block (where the letter I appears as L due to a typographical variation).

The sequential letters are N, G, I, F, S, T, R.

Explanation

The coding logic divides the eight-letter word into two equal halves of four letters each.

For the first half (letters 1-4), add 2 to the alphabetical position of each letter: T (20) + 2 = V (22) A (1) + 2 = C (3) K (11) + 2 = M (13) E (5) + 2 = G (7) This results in the first part of the code: VCMG.

For the second half (letters 5-8), reverse the order of the letters and then add 1 to the alphabetical position of each: Original second half: O V E R Reversed order: R E V O R (18) + 1 = S (19) E (5) + 1 = F (6) V (22) + 1 = W (23) O (15) + 1 = P (16) This results in the second part of the code: SFWP.

Combining both segments, the word TAKEOVER is written as VCMGSFWP.

Explanation

The coding logic follows a two-step process: first, the word is reversed, and then specific numerical increments are added to each letter's position in the alphabet. The increments applied to the letters of the reversed word are +6, +5, +4, +3, +2, and +1 respectively.

For WINTER, the reversed string is RETNIW. R (18) + 6 = 24 (X) E (5) + 5 = 10 (J) T (20) + 4 = 24 (X) N (14) + 3 = 17 (Q) I (9) + 2 = 11 (K) W (23) + 1 = 24 (X) This results in the code XJXQKX.

For AUTUMN, the reversed string is NMUTUA. N (14) + 6 = 20 (T) M (13) + 5 = 18 (R) U (21) + 4 = 25 (Y) T (20) + 3 = 23 (W) U (21) + 2 = 23 (W) A (1) + 1 = 2 (B) This results in the code TRYWWB.

Applying this logic to SEASON: Step 1: Reverse the word to get NOSAES. Step 2: Add the corresponding increments to the alphabet positions. N (14) + 6 = 20 (T) O (15) + 5 = 20 (T) S (19) + 4 = 23 (W) A (1) + 3 = 4 (D) E (5) + 2 = 7 (G) S (19) + 1 = 20 (T) The resulting code is TTWDGT.

Explanation

The relationship is based on replacing each letter of the cluster with its two immediately preceding letters in the English alphabet, in the order of (n-1) followed by (n-2).

Applying this to LOPE: L (12th letter): The preceding letters are K (11th) and J (10th) → KJ O (15th letter): The preceding letters are N (14th) and M (13th) → NM P (16th letter): The preceding letters are O (15th) and N (14th) → ON E (5th letter): The preceding letters are D (4th) and C (3rd) → DC

Concatenating these pairs results in the cluster: KJNMONDC.

This pattern is also seen in DUCK, where each letter follows the same rule: D → CB (3, 2) U → TS (20, 19) C → BA (2, 1) K → JI (10, 9) Combined: CBTSBAJI.

Explanation

The triads in the group are formed using the mathematical operations A = C² - 1 and B = 5 × C, where the triad is represented as A:B:C. The triad 35:36:6 is the odd one out because it fails to satisfy the B = 5 × C relationship. In this triad, the middle term is the square of the third term (6 × 6 = 36), whereas the rest of the triads in the group maintain a constant multiplier of 5 for the second term (such as 5 × 5 = 25, 3 × 5 = 15, and 2 × 5 = 10). While triad b) adheres to the first-term pattern A = C² - 1 (where 35 = 6² - 1), the discrepancy in the operation for the middle term separates it from the group.

Explanation

The letter-cluster JMP is the odd one out because the first and third letters, J and P, are not alphabetical opposites. The alphabetical position of J is 10 and the position of P is 16, resulting in a sum of 10 + 16 = 26. In the English alphabet, opposite pairs must have positions that sum to 27; the opposite of J (10) is Q (17), not P (16). While the cluster JMP follows a consistent addition pattern of 3 between all consecutive letters (J+3=M and M+3=P), it deviates from the logic where the first and third characters must be an opposite-letter pair.

Explanation

The series follows a pattern where the difference between consecutive terms increases by 4 at each step. By calculating the differences between the given numbers at the end of the series, we observe: 92 - 72 = 20 72 - 56 = 16 56 - 44 = 12

The differences of 20, 16, and 12 form a sequence where each term decreases by 4 as we move toward the start of the series. Following this logic, the difference between the third term (44) and the missing second term (?) must be 12 - 4 = 8. Applying this to the sequence: 44 - 8 = 36

The first difference in the series is 8 - 4 = 4. Adding this to the first term, we get 32 + 4 = 36, which maintains the established pattern throughout the entire sequence.

Explanation

The numbers in each set follow the logic: (First Number × Second Number) + (First Number ÷ Second Number) = Third Number.

Applying this to the set (10, 5, 52): (10 × 5) + (10 ÷ 5) = 50 + 2 = 52

Applying this to the set (35, 7, 250): (35 × 7) + (35 ÷ 7) = 245 + 5 = 250

Similarly, for the set (8, 4, 34): (8 × 4) + (8 ÷ 4) = 32 + 2 = 34

Explanation

The relationship between the numbers in the given sets follows the logic that the third number is the product of the first and second numbers.

In the set (4, 14, 56): 4 × 14 = 56

In the set (6, 15, 90): 6 × 15 = 90

Applying the same logic to the set (7, 16, 112): 7 × 16 = 112

The multiplication of the first two whole numbers directly results in the third number of the set.

Explanation

The first letter of each term follows the sequence of English vowels: A, E, I, O. The next vowel in this sequence is U.

The second letter follows a pattern of increasing additions based on consecutive prime numbers. Converting letters to their numerical positions (A=1, B=2, ..., Z=26): X (24) + 2 = Z (26) Z (26) + 3 = C (3, in cyclic order where 29 mod 26 = 3) C (3) + 5 = H (8) Following the sequence of primes (2, 3, 5), the next prime number to add is 7. Therefore, H (8) + 7 = 15, which corresponds to the letter O.

The third letter follows a constant subtraction of 2 from the numerical position of the preceding letter: Y (25) - 2 = W (23) W (23) - 2 = U (21) U (21) - 2 = S (19) Continuing this pattern, S (19) - 2 = 17, which corresponds to the letter Q.

By combining the derived letters U, O, and Q, the next term in the series is UOQ.

Explanation

The coding logic follows a specific positional shift pattern. For every letter in the word, the letter is replaced by the one immediately preceding it in the English alphabet (a shift of -1), except for the middle letter (the fourth letter in a seven-letter word), which is shifted forward by two positions (a shift of +2).

In the word PDFJARS: P (-1) → O D (-1) → C F (-1) → E J (+2) → L A (-1) → Z R (-1) → Q S (-1) → R This results in the code OCELZQR.

Applying this same logic to the word MHCXBTU: M (-1) → L H (-1) → G C (-1) → B X (+2) → Z B (-1) → A T (-1) → S U (-1) → T This results in the code LGBZAST.

To find the code for ZVDGENQ: Z (-1) → Y V (-1) → U D (-1) → C G (+2) → I E (-1) → D N (-1) → M Q (-1) → P

Following this pattern, the word ZVDGENQ is written as YUCIDMP.

Explanation

The relationship between the numbers in the given sets is defined by the formula (n1 × n2) ÷ 7 = n3, where n1 is the first number, n2 is the second number, and n3 is the third number.

In the first set (49, 63, 441), the operation is (49 × 63) ÷ 7. Dividing 63 by 7 gives 9, and 49 × 9 = 441.

In the second set (7, 14, 14), the operation is (7 × 14) ÷ 7. Dividing 7 by 7 gives 1, and 1 × 14 = 14.

Following the same logic for the set in option b (14, 28, 56), the operation is (14 × 28) ÷ 7. Dividing 14 by 7 gives 2, and 2 × 28 = 56. The result matches the third number of the set, confirming it follows the same mathematical pattern.

Explanation

The series follows a pattern where the difference between consecutive terms increases by 4 at each step. By calculating the differences between the known terms towards the end of the series, we observe: 39 - 27 = 12 55 - 39 = 16 75 - 55 = 20

The differences are 12, 16, and 20, which form an arithmetic progression with a common difference of 4. To find the missing number, we extend this pattern backward from the difference of 12. The difference between the second and third terms must be 12 - 4 = 8, and the difference between the first and second terms must be 8 - 4 = 4.

Adding the first difference to the first term of the series: 15 + 4 = 19

Verifying with the next term in the sequence: 19 + 8 = 27

The calculation confirms that 19 is the missing number that maintains the constant increase in differences.

Explanation

The code is generated by reversing the string of letters in the given word and then adding 3 to the alphabetical position of each letter. For the word MANAGE, the letters in reverse order are E-G-A-N-A-M. Applying the shift: E(5)+3=8(H), G(7)+3=10(J), A(1)+3=4(D), N(14)+3=17(Q), A(1)+3=4(D), and M(13)+3=16(P), which results in HJDQDP.

Similarly, for the word LITTLE, the letters in reverse order are E-L-T-T-I-L. Applying the shift: E(5)+3=8(H), L(12)+3=15(O), T(20)+3=23(W), T(20)+3=23(W), I(9)+3=12(L), and L(12)+3=15(O), which results in HOWWLO.

Applying this logic to the word POLICY, the letters in reverse order are Y-C-I-L-O-P. We calculate the new positions as follows: Y(25) + 3 = 28 (which corresponds to 2, or B) C(3) + 3 = 6 (F) I(9) + 3 = 12 (L) L(12) + 3 = 15 (O) O(15) + 3 = 18 (R) P(16) + 3 = 19 (S)

The resulting code for POLICY is BFLORS.

Explanation

Ophthalmology is the medical specialty concerned with the study, diagnosis, and treatment of disorders related to the eyes. In the same manner, dermatology is the branch of medicine that focuses on the health and diseases of the skin. The relationship established is between a field of medical science and the specific organ or body system it investigates.

Explanation

The numbers in the given sets (4, 6, 8) and (6, 8, 10) follow the pattern of an arithmetic progression where the middle number is the arithmetic mean of the first and third numbers. This relationship can be expressed by the formula First + Third = 2 × Second. For the set (4, 6, 8), the calculation is 4 + 8 = 12, which equals 2 × 6. For the set (6, 8, 10), the calculation is 6 + 10 = 16, which equals 2 × 8.

In the set (8, 12, 16), the same logic applies. Adding the first and third numbers gives 8 + 16 = 24. Multiplying the middle number by 2 also gives 2 × 12 = 24. Because the sum of the outer numbers is twice the middle number, the set maintains the same mathematical relationship as the provided examples, with a constant common difference of 4 between consecutive terms.

Explanation

The relationship established in the first pair is that of an animal and its offspring; a hatchling is the name for a young tortoise. Applying this same logic to the second pair, the standard term for a young rabbit is a kitten, also frequently referred to as a kit.

Explanation

The series follows a pattern where the difference between consecutive terms increases by a constant value of 6, effectively adding successive multiples of 6 to each term.

The first difference is 14 - 8 = 6. Following the pattern of adding multiples of 6 (6, 12, 18, 24, 30, 36), the next term is calculated as 14 + 12 = 26.

We can verify this pattern with the remaining terms in the series: 26 + 18 = 44 44 + 24 = 68 68 + 30 = 98 98 + 36 = 134

Since all subsequent terms satisfy the logic of adding 6 × n where n is the position of the difference, the missing number is 26.

Explanation

Interchanging the signs + and - transforms the left-hand side of the equation into 13 × 6 - 24 ÷ 6 + 17. Following the BODMAS order of operations, the division 24 ÷ 6 is calculated first, yielding 4. Then, the multiplication 13 × 6 is calculated, yielding 78. The expression simplifies to 78 - 4 + 17. Subtracting 4 from 78 gives 74, and adding 17 to 74 results in 91. Since the resulting value matches the right-hand side of the equation, the interchange of + and - makes the equation correct.

Explanation

The relationship between the terms in each pair follows the mathematical pattern (n² × 5) + 2, where n is the first number in the pair.

For the first pair 5:127: n = 5 5² × 5 + 2 = 25 × 5 + 2 = 125 + 2 = 127

For the third pair 7:247: n = 7 7² × 5 + 2 = 49 × 5 + 2 = 245 + 2 = 247

Applying the same logic to the third term 9 to find the missing fourth term: n = 9 9² × 5 + 2 = 81 × 5 + 2 = 405 + 2 = 407

Explanation

To make the equation 4 + 2 ÷ 7 + 8 × 9 = 25 correct, we interchange the numbers 4 and 9 and the signs ÷ and ×. Substituting these changes into the equation, it becomes 9 + 2 × 7 + 8 ÷ 4. Following the order of operations (BODMAS/PEMDAS), we first perform the division: 8 ÷ 4 = 2. The equation now reads 9 + 2 × 7 + 2. Next, we perform the multiplication: 2 × 7 = 14. The equation then becomes 9 + 14 + 2. Finally, performing the addition, we get 23 + 2 = 25. This matches the value on the right-hand side of the equation.

Explanation

The series follows a pattern where each corresponding letter of the clusters decreases by 6 in terms of their alphabetical positions. In the English alphabet, let the positions be A=1, B=2, ..., Z=26.

For the first letters: Z(26) - 6 = T(20), T(20) - 6 = N(14), N(14) - 6 = H(8). Applying the same logic, the first letter of the missing cluster is 8 - 6 = 2, which corresponds to B.

For the second letters: X(24) - 6 = R(18), R(18) - 6 = L(12), L(12) - 6 = F(6). Following the pattern, the second letter of the missing cluster is 6 - 6 = 0. In a cyclic alphabet, 0 corresponds to the 26th position, which is Z.

For the third letters: V(22) - 6 = P(16), P(16) - 6 = J(10), J(10) - 6 = D(4). Continuing the pattern, the third letter of the missing cluster is 4 - 6 = -2. In a cyclic alphabet, this is calculated as 26 - 2 = 24, which corresponds to X.

The resulting letter-cluster is BZX.

Explanation

The letter sets for the two words are {B, I, N, D} and {D, R, I, B}, while the digit sets for their respective codes are {9, 2, 1, 4} and {4, 1, 0, 9}. By comparing these two sets, the common letters are B, I, and D, and the common digits are 9, 1, and 4. The letter N is present in the first word but not in the second. Similarly, the digit 2 is present in the first code but not in the second. Since N is the unique letter in the first set compared to the second, it corresponds to the unique digit 2 in the first code set.

Explanation

The relationship in this analogy is between a medical specialty or diagnostic tool and the professional who specializes in that field. A Radiologist is a medical doctor who specializes in diagnosing and treating injuries and diseases using medical imaging procedures such as X-rays. Similarly, a Dermatologist is a medical doctor who specializes in the study, diagnosis, and treatment of conditions and diseases related to the Skin.

Explanation

The relationship between the numbers in each set follows the logic where the second number is equal to one-third of the product of the first and third numbers. This can be expressed by the formula Second Number = (First Number × Third Number)/(3).

Applying this logic to the given sets: In the set (15, 20, 4): (15 × 4)/(3) = ⁶⁰⁄₃ = 20. In the set (30, 30, 3): (30 × 3)/(3) = ⁹⁰⁄₃ = 30.

Following the same pattern for the set (60, 400, 20): (60 × 20)/(3) = ¹²⁰⁰⁄₃ = 400.

Explanation

The numerical relationship followed in the given sets is (n₁ - 10) × (n₂ - 10) = n₃, where n₁, n₂, and n₃ are the first, second, and third numbers of the set respectively.

In the first set (50, 60, 2000), the calculation is (50 - 10) × (60 - 10) = 40 × 50 = 2000. In the second set (20, 30, 200), the calculation is (20 - 10) × (30 - 10) = 10 × 20 = 200.

The numbers in option b, (21, 11, 11), follow this same logic as (21 - 10) × (11 - 10) = 11 × 1 = 11. The third number is the product of the first and second numbers after 10 has been subtracted from each.

Explanation

The relationship between the numbers follows the pattern x = y³{5}, where x is the first number and y is the second number in each pair.

For the first pair 3125:25: 25³{5} = ¹⁵⁶²⁵⁄₅ = 3125

For the second pair 1600:20: 20³{5} = ⁸⁰⁰⁰⁄₅ = 1600

Applying the same logic to the fifth number 675 to find the missing value y: 675 = y³{5} y³ = 675 × 5 y³ = 3375 y = ³√(3375) = 15

Explanation

The series consists of 28 positions including blanks. Dividing the series into groups of seven letters reveals a consistent repeating pattern based on the word BUPLESH.

The first group BUP_ESH completes to BUPLESH by adding L in the fourth position. The second group UPL_SH completes to BUPLESH by adding B at the eighth position and E at the twelfth position. The third group B_PLES completes to BUPLESH by adding U at the sixteenth position and H at the twenty-first position. The fourth group BU_LE_H completes to BUPLESH by adding P at the twenty-fourth position and S at the twenty-seventh position.

Arranging these missing letters sequentially from left to right as they appear in the original string yields the sequence L, B, E, U, H, P, S. This matches the string LBEUHPS.

Explanation

The relationship in the given pair is that of an adult animal and its offspring. A foal is the specific term used for a young horse. Similarly, a kitten is the correct term for a young cat, perfectly mirroring the parent-to-offspring relationship established in the example.