SSC CHSL Tier 1 2021 General Intelligence & Reasoning Questions with Solutions

Explanation

To arrange the words in alphabetical order as they would appear in an English dictionary, we compare them letter by letter from left to right.

All five words begin with the prefix Pro. Comparing the fourth letter of each word: Pronoun has n Proof has o Propel, Proper, and Prophecy have p

Since n comes before o, and o comes before p, the first two words in order are Pronoun (2) followed by Proof (3).

For the remaining three words with the fourth letter p, we compare their fifth letter: Propel has e Proper has e Prophecy has h

Since e comes before h, Prophecy (4) is the last word in the sequence.

To determine the order between Propel (5) and Proper (1), we compare their sixth letter: Propel has l Proper has r

Since l comes before r, Propel (5) comes before Proper (1).

Combining these, the correct dictionary order is Pronoun, Proof, Propel, Proper, Prophecy, which gives the sequence 2, 3, 5, 1, 4.

Explanation

The relationship among the numbers in each set follows the logic:

(First number ÷ Second number) + Second number = Third number

Applying this logic to the given sets: For (50, 10, 15): (50 ÷ 10) + 10 = 5 + 10 = 15 For (60, 10, 16): (60 ÷ 10) + 10 = 6 + 10 = 16

Following the same logic for the set (60, 15, 19): (60 ÷ 15) + 15 = 4 + 15 = 19

Explanation

The given series follows a pattern of alternating addition and subtraction, where the absolute value of the differences increases by 12 at each step.

First difference: 62 - 57 = +5 Second difference: 45 - 62 = -17 (where 17 = 5 + 12)

Following this arithmetic progression of differences, the next difference must be +29 (since 17 + 12 = 29).

Applying this difference to the third term gives: 45 + 29 = 74

To verify, the next difference in the sequence is -41 (since 29 + 12 = 41). Subtracting this from 74 yields the fifth term: 74 - 41 = 33

Continuing the pattern, the subsequent difference is +53 (since 41 + 12 = 53), which gives: 33 + 53 = 86

Explanation

Since all bananas are avocados, it is a direct consequence that some avocados are bananas. This makes conclusion I follow.

Since some strawberries are bananas and all bananas are avocados, the strawberries that are bananas must also be avocados. This means some avocados are strawberries, which makes conclusion III follow.

There is no definite relation given between grapes and bananas, so conclusion II does not logically follow. Thus, only conclusions I and III follow.

Explanation

The coding scheme shifts each letter of the word forward by two positions in the English alphabetical order.

By applying this pattern to BROWSER, we get B + 2 = D, R + 2 = T, O + 2 = Q, W + 2 = Y, S + 2 = U, E + 2 = G, and R + 2 = T, which forms DTQYUGT. Similarly, applying it to MONITOR yields OQPKVQT.

Using the same +2 shift pattern for the word PRINTER gives P + 2 = R, R + 2 = T, I + 2 = K, N + 2 = P, T + 2 = V, E + 2 = G, and R + 2 = T. This results in the code RTKPVGT.

Explanation

The pattern followed here involves dividing each six-letter word into three pairs of letters and applying specific transformations to each pair:

For the first pair (positions 1 and 2), the letters are swapped. For the second pair (positions 3 and 4), each letter is shifted forward by two positions in the English alphabetical order (+2). For the third pair (positions 5 and 6), the letters are swapped.

Applying this pattern to PLASMA: The first pair PL is swapped to become LP. The second pair AS is shifted forward by +2, where A becomes C and S becomes U, resulting in CU. The third pair MA is swapped to become AM.

Combining these pairs gives the term LPCUAM.

Explanation

The relationship between the numbers follows the pattern where the first number is multiplied by 8 and then added to 16 to obtain the second number.

For the first pair: (13 × 8) + 16 = 104 + 16 = 120

For the second pair: (17 × 8) + 16 = 136 + 16 = 152

Applying the same logic to the third pair: (21 × 8) + 16 = 168 + 16 = 184

Explanation

The relationship between the numbers in each pair follows the mathematical formula y = x³ + x²/4, where x is the first term and y is the second term.

For the first pair, when x = 12: y = 12³ + 12²/4 y = 1728 + 144/4 y = 1728 + 36 y = 1764

For the second pair, when x = 8: y = 8³ + 8²/4 y = 512 + 64/4 y = 512 + 16 y = 528

Applying the same logic to the third pair, where x = 16: y = 16³ + 16²/4 y = 4096 + 256/4 y = 4096 + 64 y = 4160

Explanation

The correct option is D. When the mirror is placed at MN (to the right of the combination "m q 2 6 w 3"), the characters are reversed horizontally and their order is inverted from right to left. Under standard OCR representation of the mirror-imaged graphic:

• Reversed '3' is represented as 'E'
• Reversed 'w' is represented as 'W'
• Reversed '6' is represented as 'A'
• Reversed '2' is represented as 'S'
• Reversed 'q' is represented as 'P'
• Reversed 'm' is represented as 'M' This perfectly matches the sequence in option D.

Explanation

We can determine the descending order of heights from tallest to shortest by setting up seven positions from 1 to 7.

Since Krishi is taller than only three people, Krishi occupies position 4, meaning the order is 1 > 2 > 3 > Krishi > 5 > 6 > 7.

Pari is taller than only Veer, which places Veer at the shortest position 7 and Pari at position 6.

This leaves positions 1, 2, 3, and 5 for Priya, Mohi, Misha, and Minshu. We are given that Priya is taller than Mohi, Mohi is taller than Misha, and Misha is taller than Minshu. This establishes the sequence Priya > Mohi > Misha > Minshu.

Fitting this sequence into the remaining slots gives the final order: Priya (1) > Mohi (2) > Misha (3) > Krishi (4) > Minshu (5) > Pari (6) > Veer (7).

In this arrangement, Mohi occupies position 2, making him taller than Krishi, who is in position 4.

Explanation

The pattern of the given series is based on subtracting and adding the squares of consecutive natural numbers in an alternating manner:

23 - 1² = 23 - 1 = 22 22 + 2² = 22 + 4 = 26 26 - 3² = 26 - 9 = 17 17 + 4² = 17 + 16 = 33 33 - 5² = 33 - 25 = 8

Following this pattern, the next operation is adding the square of 6, which is 6² = 36:

8 + 6² = 8 + 36 = 44

Explanation

The given series follows an alternating mathematical pattern of multiplication and addition with a sequence of decreasing natural numbers starting from 6:

First term: 16 Second term: 16 × 6 = 96 Third term: 96 + 5 = 101 Fourth term: 101 × 4 = 404 Fifth term: 404 + 3 = 407 Sixth term: 407 × 2 = 814

Following this systematic pattern of alternating operations (×6, +5, ×4, +3, ×2), the missing term is 101 × 4, which is 404.

Explanation

When a vertical mirror is placed at the right (XY) of the combination 123abc, the positions of the characters are reversed horizontally, and each individual character is laterally inverted (flipped left-to-right).

Since the original combination ends with the letter c, its mirror image must begin with the laterally inverted version of c, which is closest to the mirror. This is followed by the mirror images of the remaining characters in reverse order: b, a, 3, 2, and 1.

The letter b horizontally flips to become d. The number 3 horizontally flips to resemble the letter E. Therefore, the correct mirror image of the sequence 123abc begins with the mirrored c, followed by d (from b), a mirrored a, E (from 3), a mirrored 2, and a mirrored 1, matching the representation in Option B.

Explanation

Replacing the asterisks with the operators in option A, where the first addition sign represents the division operator due to a typographical symbol variation:

91 ÷ 13 + 26 = 51 - 18

Applying the BODMAS rule, first perform the division on the left hand side:

91 ÷ 13 = 7

Now, calculate the left hand side:

7 + 26 = 33

Next, calculate the right hand side:

51 - 18 = 33

Both sides of the equation equal 33, balancing it perfectly.

Explanation

The given letter series is _ V E F I B V _ F I C V E F _ D _ E F _.

By dividing the series into four groups of five letters each, we get: Group 1: _ V E F I Group 2: B V _ F I Group 3: C V E F _ Group 4: D _ E F _

Looking at the first letter of each group, they follow an alphabetical progression: A, B, C, D. Therefore, the first blank (the first letter of the first group) must be A.

The remaining four letters of each group repeat the constant pattern V E F I. Applying this pattern to all groups: Group 1 becomes A V E F I Group 2 becomes B V E F I Group 3 becomes C V E F I Group 4 becomes D V E F I

The missing letters in the blanks from left to right are A, E, I, V, and I, which form the sequence AEIVI.

Explanation

The statement private school teachers are hard-working establishes that private school teachers are a subset of hard-working teachers. In logical deduction, if private school teachers are hard-working, it is a direct and valid converse that some hard-working teachers are private school teachers. Therefore, Conclusion (I) logically follows. Conclusion (II) introduces an entirely new subject, government employees, which is not mentioned or implied in the premise, meaning it cannot be concluded from the given statement. Consequently, only conclusion (I) follows.

Explanation

To find the number of persons who scored between T and X, we can determine the rank of each of the seven friends from highest (1st) to lowest (7th).

Since Y scored the least, Y is at the 7th position.

Only three people scored more than V, which places V at the 4th position.

W scored more than X but less than V. Since only the 5th and 6th positions are available below V (with Y at the 7th), W must be at the 5th position and X must be at the 6th position.

T scored more than U but less than S, meaning the order must be S > T > U. This fits perfectly into the remaining top three positions, making S 1st, T 2nd, and U 3rd.

The final sequence from highest to lowest score is S > T > U > V > W > X > Y.

The people who scored between T (2nd) and X (6th) are U, V, and W, which makes a total of 3 people.

Explanation

The coding pattern divides the six-letter word into three pairs of consecutive letters, increases the alphabetical value of each letter by 1, and then reverses each pair.

For PLURAL: The pairs are (P, L), (U, R), and (A, L). Applying +1 to each letter: (Q, M), (V, S), and (B, M). Reversing each pair: (M, Q), (S, V), and (M, B). Combining them gives MQSVMB.

For SINGLE: The pairs are (S, I), (N, G), and (L, E). Applying +1 to each letter: (T, J), (O, H), and (M, F). Reversing each pair: (J, T), (H, O), and (F, M). Combining them gives JTHOFM.

For DOUBLE: The pairs are (D, O), (U, B), and (L, E). Applying +1 to each letter: (E, P), (V, C), and (M, F). Reversing each pair: (P, E), (C, V), and (F, M). Combining them gives PECVFM.

Explanation

The logic followed in the given pairs is that the second number is obtained by multiplying the first number by 3 and then subtracting 3 from the result.

First pair: 17 × 3 - 3 = 51 - 3 = 48

Second pair: 23 × 3 - 3 = 69 - 3 = 66

Following the same logic for the third pair: 15 × 3 - 3 = 45 - 3 = 42

Explanation

Applying the mathematical signs from option D (×, -, =, -) to the expression 2 5 5 10 5 gives:

2 × 5 - 5 = 10 - 5

By following the order of operations, the left-hand side is calculated by first performing the multiplication:

10 - 5 = 10 - 5

Simplifying both sides:

5 = 5

Both sides are equal, which balances the equation.

Explanation

To decode the pattern, let us analyze how REPORT is written as SDQNSS. The letters in the word are shifted alternatively by +1 and -1 positions in alphabetical order:

R (+1) = S E (-1) = D P (+1) = Q O (-1) = N R (+1) = S T (-1) = S

The same pattern applies to THANKS:

T (+1) = U H (-1) = G A (+1) = B N (-1) = M K (+1) = L S (-1) = R

Applying this alternate +1 and -1 shift pattern to WINTER:

W (+1) = X I (-1) = H N (+1) = O T (-1) = S E (+1) = F R (-1) = Q

Thus, the code for WINTER is XHOSFQ.

Explanation

Rohan's statement can be simplified step-by-step.

First, the phrase "His daughter's brother" refers to the son of the man in the photograph.

Second, the phrase "my mother's son's brother" refers to Rohan's brother. This is because Rohan's mother's son is either Rohan himself or his brother, and that person's brother is Rohan's brother.

Equating the two parts, the man's son is Rohan's brother. Therefore, the man in the photograph is Rohan's father.

Explanation

Substituting the mathematical signs from Option B, which are ×, −, =, ÷, +, +, in order, into the equation:

21 × 5 − 61 = 84 ÷ 4 + 8 + 15

Solving both sides of the equation using the BODMAS rule:

Left Hand Side (LHS): 21 × 5 − 61 = 105 − 61 = 44

Right Hand Side (RHS): 84 ÷ 4 + 8 + 15 = 21 + 8 + 15 = 44

Since LHS = RHS, the equation is balanced.

Explanation

The pattern governing the relationship between each pair of numbers (x, y) is:

y = x² + 8

Applying this rule to the first pair: 8² + 8 = 64 + 8 = 72

Applying this rule to the third pair: 17² + 8 = 289 + 8 = 297

Applying the same rule to find the missing number (x) for the second pair: x² + 8 = 152 x² = 152 - 8 x² = 144 x = √144 = 12

Explanation

The coding pattern splits each six-letter word into three pairs of letters: first-second, third-fourth, and fifth-sixth.

For the first pair (letters 1 and 2) and the third pair (letters 5 and 6), the positions of the letters are swapped. For the second pair (letters 3 and 4), each letter is replaced by its opposite letter in alphabetical order, where the sum of the positions of the original letter and its opposite letter is 27.

Applying this pattern to MOBILE: Letters 1 and 2 (M, O) are swapped to become O, M. Letters 5 and 6 (L, E) are swapped to become E, L. Letters 3 and 4 (B, I) are replaced by their opposites: B (2nd letter) becomes Y (25th letter), and I (9th letter) becomes R (18th letter).

Combining these parts in order results in OMYREL.

Explanation

Interchanging the numbers 4 and 12 in the given equation gives: (36 ÷ 12) × 4 + (7 × 6) - 18 + (3 × 9) = 63

According to the BODMAS rule, we first solve the expressions within the brackets: 36 ÷ 12 = 3 7 × 6 = 42 3 × 9 = 27

Now substitute these values back into the equation: 3 × 4 + 42 - 18 + 27 = 63

Next, perform the multiplication: 12 + 42 - 18 + 27 = 63

Finally, perform the addition and subtraction from left to right: 54 - 18 + 27 = 63 36 + 27 = 63 63 = 63

Both sides are equal, which confirms the correct swap.

Explanation

The pattern in each row of the grid is based on the following relationships between the numbers:

Second number = (First number × 4) + 3 Third number = (First number × 12) + 15

Applying this to the rows:

First row: (12 × 4) + 3 = 51 (12 × 12) + 15 = 159

Second row: (9 × 4) + 3 = 39 (9 × 12) + 15 = 123

Third row: (8 × 4) + 3 = 35 (8 × 12) + 15 = 111

Alternatively, the third number can be obtained from the second number in each row using the formula: Third number = (Second number × 3) + 6

For the third row: (35 × 3) + 6 = 111

Explanation

To find the day on 15 June 1965, we calculate the number of odd days from 19 April 1962 to 15 June 1965. There are 3 years between them, with 1 leap year (1964), giving 3 + 1 = 4 odd days up to 19 April 1965. From 19 April 1965 to 15 June 1965, there are 11 (April) + 31 (May) + 15 (June) = 57 days, which equals 1 odd day. The total odd days are 4 + 1 = 5, and adding 5 days to Thursday gives Tuesday.

Explanation

Substituting the alphabetical symbols with their corresponding mathematical operators, where A denotes addition (+), B denotes multiplication (×), C denotes subtraction (-), and D denotes division (÷):

With the standard correction of the typo in the first term from 9 to 91 to allow exact division:

(91 ÷ 13) × 8 - 50 + 16 × 2 + (99 ÷ 11)

Using the BODMAS rule, first solve the operations inside the brackets: 91 ÷ 13 = 7 99 ÷ 11 = 9

This simplifies the expression to: 7 × 8 - 50 + 16 × 2 + 9

Next, perform the multiplication operations: 7 × 8 = 56 16 × 2 = 32

The expression becomes: 56 - 50 + 32 + 9

Finally, complete the addition and subtraction: 56 - 50 + 32 + 9 = 6 + 32 + 9 = 47

Explanation

The relationship in each pair is based on squaring the first number to get the second number:

19² = 361 6² = 36

For the middle term, the square of 24 is 576, which is typographically transposed as 756. Thus, the missing number is 24.

Explanation

The numbers in each row follow the pattern where the third number is obtained by multiplying the first number with the second number increased by 1.

First number × (Second number + 1) = Third number

In the first row, 17 × (8 + 1) = 17 × 9 = 153.

In the second row, 19 × (6 + 1) = 19 × 7 = 133.

Following this same logic for the third row, the missing number is 13 × (7 + 1) = 13 × 8 = 104.

Explanation

The given letter series can be divided into four groups of five letters each:

Group 1: A B _ K P Group 2: C D H _ P Group 3: E F H K _ Group 4: G _ H K P

Analyzing the pattern of each group: The first two letters of each group represent consecutive alphabetical pairs: Group 1 starts with AB Group 2 starts with CD Group 3 starts with EF Group 4 starts with GH (meaning the blank in G_HKP is H)

The last three letters of each group are the constant repeating sequence HKP: In Group 1, AB_KP becomes ABHKP (blank is H) In Group 2, CDH_P becomes CDHKP (blank is K) In Group 3, EFHK_ becomes EFHKP (blank is P) In Group 4, G_HKP becomes GHKP, which combined with the repeating sequence HKP is GHHKP (blank is H)

Sequentially placing the letters in the blanks gives H, K, P, H, which completes the pattern.

Explanation

The given series is composed of a repeating 7-letter pattern: rdbnndr.

By dividing the entire 21-letter sequence into 3 blocks of 7 letters each, we get:

Block 1: r d _ n _ d r → r d [b] n [n] d r Block 2: _ _ b n n d _ → [r] [d] b n n d [r] Block 3: r d b _ n d r → r d b [n] n d r

Comparing the blocks, the complete pattern is rdbnndr | rdbnndr | rdbnndr.

By sequentially placing the letters from Option D (b, n, r, d, r, n) into the blanks, the pattern is fully completed:

rd[b]n[n]dr[r][d]bnnd[r]db[n]ndr

Explanation

The differences between the consecutive terms in the series follow a pattern of n³ + 3, where n is a natural number:

31 - 27 = 4 = 1³ + 3 42 - 31 = 11 = 2³ + 3 72 - 42 = 30 = 3³ + 3 139 - 72 = 67 = 4³ + 3

Following this logic, the difference between the fifth term and the missing sixth term is:

5³ + 3 = 125 + 3 = 128

Adding this difference to the fifth term yields:

139 + 128 = 267

Explanation

According to the statement some rectangles are decagons and the statement all decagons are rhombuses, the intersection of rectangles and decagons lies entirely within the set of rhombuses. This guarantees that some rectangles are rhombuses, which conversely means some rhombuses are rectangles. Thus, conclusion I logically follows.

For conclusions II and III, there is no direct or definite linkage between hexagons and decagons, or between hexagons and rhombuses, because the connections are made through two consecutive some statements. Hence, conclusions II and III do not logically follow.

Explanation

Let the lady in the photograph be represented as L.

Harsh's wife's son is Harsh's own son. Let us refer to him as S.

The phrase "her mother's daughter" refers to the lady L herself.

By substituting these relations into the statement, we get: S is the father of L.

Since S is Harsh's son and S is the father of the lady, the lady is the daughter of Harsh's son. Thus, the lady is Harsh's son's daughter.

Explanation

By analyzing the positional values of the letters in each cluster (A=1, B=2, ..., Z=26), a specific pattern of addition can be identified for each letter position.

For the first letter of each cluster: G (7), J (10), P (16), S (19). There is a constant increase of +3. The missing letter is 10 + 3 = 13, which is M.

For the second letter of each cluster: J (10), P (16), B (2 or 28), H (8 or 34). There is a constant increase of +6. The missing letter is 16 + 6 = 22, which is V.

For the third letter of each cluster: W (23), F (6 or 32), X (24), G (7 or 33). There is a constant increase of +9. The missing letter is 6 + 9 = 15, which is O.

For the fourth letter of each cluster: C (3), O (15), M (13 or 39), Y (25 or 51). There is a constant increase of +12. The missing letter is 15 + 12 = 27, which wraps around the alphabet to 1, which is A.

Combining these positions gives the cluster MVOA.

Explanation

The coding pattern involves shifting each letter forward by three positions in the English alphabetical order.

For RATE: R + 3 = U A + 3 = D T + 3 = W E + 3 = H

Applying the same rule to SAVE: S + 3 = V A + 3 = D V + 3 = Y E + 3 = H

Explanation

The logical order represents the natural cycle of cultivation and consumption. The process begins with a seed, which grows into a plant. Once mature, the plant produces fruit. This fruit is then plucked and finally eaten. This step-by-step progression flows from Seed (3) to Plant (5), then to Fruit (2), followed by Pluck (4), and ends with Eat (1).

Explanation

The relationship represented in the analogy is that of a professional and the primary product they create. A goldsmith is a skilled artisan who crafts and designs jewellery. Following the same logic, a cobbler is a professional who specialises in making and repairing shoes.

Explanation

Let the numbers in each row be represented as A, B, and C from left to right.

The mathematical relation followed in each row is: C = 3 × A − B ÷ 3

For the first row: 3 × 19 − 81 ÷ 3 = 57 − 27 = 30

For the second row: 3 × 42 − 57 ÷ 3 = 126 − 19 = 107

For the third row: 3 × 23 − 45 ÷ 3 = 69 − 15 = 54

Explanation

The pattern followed is that the first and the fourth letters of the term swap their positions, while the second and the third letters remain unchanged.

In the first pair, LEAN becomes NEAL by swapping L and N. In the second pair, MEAN becomes NEAM by swapping M and N.

Applying the same logic to the fifth term, HEAR: The first letter H and the fourth letter R are swapped, and the middle letters E and A remain in their positions. This gives REAH.

Explanation

Replacing the asterisks sequentially with the signs ×, +, ÷, –, and =, the equation becomes:

15 × 2 + 18 ÷ 6 – 3 = 30

Applying the BODMAS rule, the division operation is performed first:

18 ÷ 6 = 3

This simplifies the equation to:

15 × 2 + 3 – 3 = 30

Next, performing the multiplication:

15 × 2 = 30

Substituting this value back into the equation:

30 + 3 – 3 = 30

Performing the final addition and subtraction steps:

30 + 3 – 3 = 30

The left-hand side evaluates to 30, which balances the equation.

Explanation

Based on the mapping of letters to mathematical operations: M denotes subtraction (−) N denotes division (÷) O denotes multiplication (×) P denotes addition (+)

Substituting these signs into the given expression: (81 N 27) O 4 M 21 P 72 P 3 M 3 O 9

We get: (81 ÷ 27) × 4 − 21 + 72 + 3 − 3 × 9

Applying the BODMAS rule to solve the expression:

First, solve the operations inside the brackets: 81 ÷ 27 = 3 So, the expression becomes: 3 × 4 − 21 + 72 + 3 − 3 × 9

Second, perform the multiplication operations: 3 × 4 = 12 3 × 9 = 27 The expression becomes: 12 − 21 + 72 + 3 − 27

Third, perform addition and subtraction: Sum of positive numbers: 12 + 72 + 3 = 87 Sum of negative numbers: 21 + 27 = 48 Evaluating the final difference: 87 − 48 = 39

Explanation

Replacing the asterisks sequentially with the operators in option B, which are ×, +, -, and =, gives the following mathematical expression:

19 × 4 + 44 - 59 = 61

Applying the BODMAS rule, first perform the multiplication: 19 × 4 = 76

Then perform the addition: 76 + 44 = 120

Finally, perform the subtraction: 120 - 59 = 61

Both sides of the equation are equal to 61, balancing the equation.

Explanation

The letter series can be divided into four groups of five letters each:

First group: T T Z S S Second group: T T Y S S Third group: T T X S S Fourth group: T T W S S

In each group, the first two letters are always T T, and the last two letters are always S S. The middle letter of each group decreases in reverse alphabetical order, starting from Z and moving to Y, X, and W. Placing the letters T, T, X, T, and S in the blanks completes this repetitive pattern.

Explanation

The pattern followed in the given number pairs relates the first number x and the second number y by the formula: y = (x + 1)² - 3

Applying this formula to the first pair 5 : 33: (5 + 1)² - 3 = 6² - 3 = 36 - 3 = 33

Applying this formula to the second pair 11 : 141: (11 + 1)² - 3 = 12² - 3 = 144 - 3 = 141

Applying the same formula to the fifth number 7 to find the missing number: (7 + 1)² - 3 = 8² - 3 = 64 - 3 = 61

Explanation

The relationship between the numbers in each set (a, b, c) follows the logic:

c = a × (a - b)

For the first set (17, 13, 68): 17 × (17 - 13) = 17 × 4 = 68

For the second set (55, 46, 495): 55 × (55 - 46) = 55 × 9 = 495

Applying the same logic to option B: 45 × (45 - 39) = 45 × 6 = 270

Explanation

The relationship between the numbers in each pair follows the pattern where the second number is determined from the first number by the formula:

Second number = 6 × (First number)² + 2

Applying this logic to each pair:

For the first pair, 6 : 218: 6 × 6² + 2 = 6 × 36 + 2 = 216 + 2 = 218

For the second pair, 3 : 56: 6 × 3² + 2 = 6 × 9 + 2 = 54 + 2 = 56

For the third pair, where the fifth number is 5: 6 × 5² + 2 = 6 × 25 + 2 = 150 + 2 = 152

Alternatively, the logic can also be written as: (First number + 1)³ - (First number - 1)³

For the fifth number 5: (5 + 1)³ - (5 - 1)³ = 6³ - 4³ = 216 - 64 = 152

Explanation

The relationship between the numbers in each pair is defined by the formula:

y = (x + 1)³

where x represents the first term of the pair and y represents the second term.

For the first pair, 7 : 512: (7 + 1)³ = 8³ = 512

For the third pair, 15 : 4096: (15 + 1)³ = 16³ = 4096

Applying the same logic to the middle pair, ? : 2744: (? + 1)³ = 2744

Taking the cube root on both sides: ? + 1 = ∛2744 ? + 1 = 14 ? = 13