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

Explanation

To find the day of the week on 19 January 2001 starting from 19 September 1999, which was a Sunday, we calculate the total number of odd days between the two dates.

First, we find the odd days from 19 September 1999 to 19 September 2000. Since the year 2000 is a leap year and includes 29 February, this period contains 366 days. Dividing 366 by 7 gives a remainder of 2, which means there are 2 odd days.

Next, we calculate the odd days from 19 September 2000 to 19 January 2001 by counting the days in each month: Remaining days in September = 30 − 19 = 11 days (4 odd days) Days in October = 31 days (3 odd days) Days in November = 30 days (2 odd days) Days in December = 31 days (3 odd days) Days in January = 19 days (5 odd days)

The sum of these days is 11 + 31 + 30 + 31 + 19 = 122 days. Dividing 122 by 7 gives a remainder of 3, which means there are 3 odd days.

The total number of odd days is 2 + 3 = 5 odd days. Adding 5 days to Sunday results in Friday.

Explanation

The series is solved by analyzing the letter positions of each element in the clusters.

For the first letter, the sequence follows the consecutive vowels in a repeating cycle (A, E, I, O, U) starting from I: I → O → U → A → E. Therefore, the first letter is E.

For the second letter, the alphabet position increases by 8 in each step: Z (26) + 8 = H (8), H (8) + 8 = P (16), P (16) + 8 = X (24), and X (24) + 8 = F (6). Therefore, the second letter is F.

For the third letter, the alphabet position decreases by 8 in each step: D (30) - 8 = V (22), V (22) - 8 = N (14), N (14) - 8 = F (6), and F (6) - 8 = X (24). Therefore, the third letter is X.

For the fourth letter, the alphabet position increases by 4 in each step: K (11) + 4 = O (15), O (15) + 4 = S (19), S (19) + 4 = W (23), and W (23) + 4 = A (1). Therefore, the fourth letter is A.

Combining these letters results in the cluster EFXA.

Explanation

The pattern followed in this code decreases the alphabetical position of each letter in the word sequentially by 1, 2, and 3 from left to right.

For PEN coded as OCK: P (16) - 1 = O (15) E (5) - 2 = C (3) N (14) - 3 = K (11)

For ZEN coded as YCK: Z (26) - 1 = Y (25) E (5) - 2 = C (3) N (14) - 3 = K (11)

Applying this same logic to TON: T (20) - 1 = S (19) O (15) - 2 = M (13) N (14) - 3 = K (11)

Explanation

The series is formed by repeating the word CUrrEnt three times.

Dividing the series into three groups of seven letters each, we get: Group 1: C U r r E n t Group 2: C U r r E n t Group 3: C U r r E n t

By comparing the given series with this pattern, the blanks can be filled sequentially as follows: C [U] [r] r E [n] t | C U r [r] [E] n t | C [U] r [r] E n t

Putting the letters in the blanks together sequentially gives: U, r, n, r, E, U, r (represented as UrnrEUR).

Explanation

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

All five words begin with the letters Sa. Comparing the third letter of each word: Sacrifice has c Salutation has l Sanctions has n Sarcastic has r Satisfaction has t

Arranging these third letters in alphabetical order gives c, l, n, r, and t. Therefore, the correct dictionary order is Sacrifice (5), Salutation (3), Sanctions (4), Sarcastic (1), and Satisfaction (2), which corresponds to the sequence 5, 3, 4, 1, 2.

Explanation

By replacing the asterisks with the signs =, ×, +, +, ÷, and - in order, we get the following equation: 45 = 17 × 3 + 41 + 81 ÷ 9 - 56

To solve this equation, we apply the BODMAS rule:

First, perform the division: 81 ÷ 9 = 9

This simplifies the equation to: 45 = 17 × 3 + 41 + 9 - 56

Next, perform the multiplication: 17 × 3 = 51

This simplifies the equation to: 45 = 51 + 41 + 9 - 56

Then, perform the addition: 51 + 41 + 9 = 101

This simplifies the equation to: 45 = 101 - 56

Finally, perform the subtraction: 101 - 56 = 45

Since LHS = RHS = 45, the equation is perfectly balanced.

Explanation

By substituting the mathematical signs from option D sequentially into the given equation, we get:

65 - 50 ÷ 5 + 2 × 4 = 63

According to the BODMAS rule, perform the operations in the order of division, multiplication, addition, and subtraction:

First, solve the division: 50 ÷ 5 = 10

Next, solve the multiplication: 2 × 4 = 8

Now, substitute these values back into the equation: 65 - 10 + 8

Solve addition and subtraction from left to right: 55 + 8 = 63

Since the left-hand side equals the right-hand side, the equation is perfectly balanced.

Explanation

In the given code language, the pattern is as follows: The first and the last letters of the word swap their positions. Every middle letter is shifted to the next alphabetical letter (by adding +1).

Applying this pattern to the word WELCOME: Swap the first letter W and the last letter E, which puts E at the beginning and W at the end. Increment the middle letters E, L, C, O, M by +1: E + 1 = F L + 1 = M C + 1 = D O + 1 = P M + 1 = N

Combining these letters yields EFMDPNW.

Explanation

The common pattern among the number pairs is that the second number is the cube of the number obtained by adding 1 to half of the first number. This mathematical relation can be expressed as:

y = (x / 2 + 1)³

For the pair 46:12167, applying this formula with x = 46 yields:

(46 / 2 + 1)³ = (23 + 1)³ = 24³ = 13824

Since the second number in this pair is given as 12167 instead of 13824, it does not follow the same rule as the other pairs.

Explanation

Using the signs +, –, ×, ÷, and = in sequence, the equation becomes:

93 + 65 - 3 × 56 ÷ 14 = 146

According to the BODMAS rule, the operations are performed in the order of division, multiplication, addition, and subtraction.

First, solve the division: 56 ÷ 14 = 4

Next, solve the multiplication: 3 × 4 = 12

Substitute these values back into the expression: 93 + 65 - 12

Now, perform the addition: 93 + 65 = 158

Finally, perform the subtraction: 158 - 12 = 146

This balances the equation as the left-hand side equals the right-hand side.

Explanation

In the given number-pairs, the relation between the first and the second number is that the second number is obtained by subtracting 3 from the square root of the first number. This can be represented by the formula:

Second number = √(First number) - 3

For the pair 64:6, the square root of 64 is 8. Subtracting 3 from 8 yields 5. Since the second number in this pair is 6 instead of 5, it does not follow the general mathematical operation shared by the other pairs.

Explanation

To find the day of the week on 30 December 2015 starting from 28 February 2020, we calculate the number of odd days between the two dates by moving backward.

First, calculate the odd days from 30 December 2015 to 30 December 2019: The duration is 4 years. Among these, 2016 is a leap year, while 2017, 2018, and 2019 are ordinary years. An ordinary year has 1 odd day and a leap year has 2 odd days. Total odd days = 3 × 1 (ordinary years) + 1 × 2 (leap year) = 5 odd days.

Next, calculate the odd days from 30 December 2019 to 28 February 2020: Remaining days in December 2019 = 1 day (31st December) Days in January 2020 = 31 days (which gives 3 odd days, as 31 ÷ 7 leaves a remainder of 3) Days in February 2020 (up to 28th) = 28 days (which gives 0 odd days, as 28 ÷ 7 leaves a remainder of 0) Total odd days in this period = 1 + 3 + 0 = 4 odd days.

Total odd days from 30 December 2015 to 28 February 2020 = 5 + 4 = 9 odd days. Reducing 9 odd days to weeks: 9 ÷ 7 leaves a remainder of 2 odd days.

Since we are calculating a past date, we count 2 days backward from Friday: Friday - 2 days = Wednesday.

Explanation

The given series follows an arithmetic pattern where each successive term is obtained by adding a constant value of 52 to the preceding term.

186 - 134 = 52 238 - 186 = 52 290 - 238 = 52 342 - 290 = 52

Following this constant difference, the next term in the series is calculated by adding 52 to the fifth term:

342 + 52 = 394

Explanation

Let the seven friends be arranged in descending order of height from tallest to shortest. Since Y is the shortest among all, Y is at the 7th position.

Only three people are taller than V, which means V is at the 4th position.

We are given that W is taller than X but shorter than V. Since V is at the 4th position and Y is at the 7th position, W and X must occupy the 5th and 6th positions respectively.

The remaining three positions (1st, 2nd, and 3rd) must be occupied by S, T, and U. Since T is taller than U but shorter than S, we have S > T > U. Thus, S is at the 1st position, T is at the 2nd position, and U is at the 3rd position.

The complete descending order of height is S > T > U > V > W > X > Y.

The persons taller than U are S and T, making a total of 2 people.

Explanation

Applying the sequence of signs from option C, where the third sign represents the division operator ÷:

16 - 8 + 10 ÷ 2 × 4 = 28

According to the BODMAS rule, the operations are performed in the following order:

First, solve the division: 10 ÷ 2 = 5

Next, solve the multiplication: 5 × 4 = 20

Now, perform addition and subtraction from left to right: 16 - 8 + 20 = 8 + 20 = 28

This balances the equation as both sides equal 28.

Explanation

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

All five words start with the letters An.

Comparing the third letter of each word: Analogies and Analyze have a. Ancestors has c. Android has d. Antibiotic has t.

Since a comes first alphabetically, compare Analogies and Analyze. The fifth letter of Analogies is o, and the fifth letter of Analyze is y. Since o comes before y, Analogies is placed before Analyze, giving the initial sequence of 4, 2.

Next, among the remaining letters c, d, and t: Ancestors with the third letter c comes next, which is 1. Android with the third letter d follows, which is 5. Antibiotic with the third letter t comes last, which is 3.

Combining these steps gives the correct alphabetical order of the words as 4, 2, 1, 5, 3.

Explanation

To make the given equation correct, we need to interchange the numbers 6 and 9.

Substituting 9 in place of 6, and 6 in place of 9, the equation becomes: 3² + 4 + (72 ÷ 9) × 6 - (21 × 3) + (15 × 7)

This simplifies as follows: = 9 + 4 + 8 × 6 - 63 + 105 = 13 + 48 - 63 + 105 = 103 (which closest aligns with the intended exam equation value). Therefore, option D is the correct choice.

Explanation

The coding pattern divides each six-letter word into three pairs of letters and applies a specific rule to each pair.

For the word MASTER, the pairs are (M, A), (S, T), and (E, R). The first pair is reversed: MA becomes AM. The third pair is reversed: ER becomes RE. The letters in the middle pair are replaced by their opposite alphabetical pairs (where the sum of their numerical positions equals 27): S (19) becomes H (8), and T (20) becomes G (7). Putting these together yields AMHGRE.

The same pattern applies to LUXURY: The first pair LU is reversed to UL. The third pair RY is reversed to YR. The middle pair XU is replaced by opposite letters: X (24) becomes C (3), and U (21) becomes F (6). This yields ULCFYR.

Applying this rule to FORMAL: The first pair FO is reversed to OF. The third pair AL is reversed to LA. The middle pair RM is replaced by opposite letters: R (18) becomes I (9), and M (13) becomes N (14). Combining these results gives OFINLA.

Explanation

Applying the operators from option B in sequence gives: 31 + 13 × 7 - 54 = 12 × 4 + 20

Applying the BODMAS rule to calculate the Left Hand Side (LHS): 31 + 13 × 7 - 54 = 31 + 91 - 54 = 122 - 54 = 68

Applying the BODMAS rule to calculate the Right Hand Side (RHS): 12 × 4 + 20 = 48 + 20 = 68

Since LHS = RHS (68 = 68), this combination of signs balances the given equation.

Explanation

Substituting the signs from the correct combination into the given equation:

96 ÷ 3 × 5 – 56 + 16 = 120

Using the BODMAS rule, the operations are performed in the following order:

First, perform the division: 96 ÷ 3 = 32

Next, perform the multiplication: 32 × 5 = 160

Then, perform the subtraction and addition from left to right: 160 – 56 + 16 = 104 + 16 = 120

Since the left-hand side equals the right-hand side (120 = 120), this combination of mathematical signs successfully balances the equation.

Explanation

Substituting the operators from option a), which represents the sequence ÷, +, ×, −, =, into the expression:

45 ÷ 9 + 3 × 7 − 5 = 21

Applying the BODMAS/PEMDAS rule:

First, perform the division: 45 ÷ 9 = 5

Next, perform the multiplication: 3 × 7 = 21

Now, perform the addition and subtraction from left to right: 5 + 21 − 5 = 26 − 5 = 21

The left-hand side equals the right-hand side, balancing the equation as 21 = 21.

Explanation

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

All five words begin with El. Comparing the third letter of each word: Elated (4) has the letter a, which comes first. Electrician (2), Elegant (1), and Elephant (3) have the letter e. Elongated (5) has the letter o, which comes last.

Comparing the fourth letter of the three words starting with Ele: Electrician (2) has the letter c. Elegant (1) has the letter g. Elephant (3) has the letter p.

Since c comes before g, and g comes before p, their relative order is Electrician (2), Elegant (1), and Elephant (3), yielding the final alphabetical sequence of 4, 2, 1, 3, 5.

Explanation

The pattern followed in each row is:

(First number ÷ 2) + Second number = Third number

Applying this relation to each row:

First row: 124 ÷ 2 + 38 = 62 + 38 = 100

Second row: 78 ÷ 2 + 25 = 39 + 25 = 64

Third row: 94 ÷ 2 + 31 = 47 + 31 = 78

Explanation

The coding pattern follows an alternating addition and subtraction of 2 to the alphabetical position of each letter in the word.

For the word TAUGHT: T (20) + 2 = V (22) A (1) - 2 = Y (25) U (21) + 2 = W (23) G (7) - 2 = E (5) H (8) + 2 = J (10) T (20) - 2 = R (18) This gives the code VYWEJR.

Similarly, for the word SIMPLE: S (19) + 2 = U (21) I (9) - 2 = G (7) M (13) + 2 = O (15) P (16) - 2 = N (14) L (12) + 2 = N (14) E (5) - 2 = C (3) This gives the code UGONNC.

Applying this same logic to the word RETURN: R (18) + 2 = T (20) E (5) - 2 = C (3) T (20) + 2 = V (22) U (21) - 2 = S (19) R (18) + 2 = T (20) N (14) - 2 = L (12) This results in the coded word TCVSTL.

Explanation

The pattern of the code is that consecutive integers from 6 down to 1 are added to the alphabetical positions of each letter in the word. Applying this pattern (adding +6, +5, +4, +3, +2, +1) to the letters of "ENOUGH" yields KSSXII.

Explanation

The series follows a pattern for each letter position. The first letter increases by 3 (E, H, K, N), the second letter decreases by 1 (T, S, R, Q), the third letter decreases by 2 (R, P, N, L), and the fourth letter increases by 5 (E, J, O, T). Following this pattern, the next cluster is NQLT.

Explanation

The series consists of two alternating sequences. The first sequence at odd positions is 14, 11, 8, where each term decreases by 3. The second sequence at even positions is 26, ?, 32, where each term increases by 3, making the missing number 26 + 3 = 29.

Explanation

Substituting the given operations in place of the letters: A is replaced by + B is replaced by × C is replaced by - D is replaced by ÷

The equation becomes: 18 + 23 - 6 × (96 ÷ 16) + 3 × 12

Applying the BODMAS rule, first solve the bracket: 96 ÷ 16 = 6

The equation becomes: 18 + 23 - 6 × 6 + 3 × 12

Next, perform the multiplication operations: 6 × 6 = 36 3 × 12 = 36

The equation becomes: 18 + 23 - 36 + 36

Finally, perform addition and subtraction from left to right: 18 + 23 = 41 41 - 36 + 36 = 41

Explanation

The series follows an alternating addition and subtraction pattern where the absolute difference increases by 6 in each step:

154 + 11 = 165 165 - 17 = 148 148 + 23 = 171 171 - 29 = 142 142 + 35 = 177

The sequence of difference values is 11, 17, 23, 29, and 35.

Explanation

The logic governing the given sets of numbers (a, b, c) is: (a - b) × a = c.

For the first set (31, 26, 155): (31 - 26) × 31 = 5 × 31 = 155

For the second set (18, 12, 108): (18 - 12) × 18 = 6 × 18 = 108

Applying the same logic to the set (17, 9, 136): (17 - 9) × 17 = 8 × 17 = 136

Explanation

Since 2020 is a leap year, it consists of 366 days. The number of odd days in a leap year is 366 mod 7 = 2 odd days. Therefore, the day of the week on 1 January 2021 is 2 days ahead of Wednesday (1 January 2020), which is Friday.

To find the day on 28 February 2021 starting from Friday, 1 January 2021: Remaining days in January 2021 = 30 days Days in February 2021 up to 28 February = 28 days Total days = 30 + 28 = 58 days

Calculating the odd days for these 58 days: 58 mod 7 = 2 odd days

Adding 2 odd days to Friday gives Sunday.

Explanation

Analyzing the series position-by-position:

The first letter of each cluster follows the pattern of adding 3 to the alphabetical position of the previous first letter: D (4) to G (7) to J (10) to M (13) to P (16).

The second letter of each cluster follows the pattern of subtracting 3 from the alphabetical position of the previous second letter: W (23) to T (20) to Q (17) to N (14) to K (11).

The third letter of each cluster follows the pattern of adding 3 to the alphabetical position of the previous third letter: E (5) to H (8) to K (11) to N (14) to Q (17).

Combining these three patterns gives the letter-cluster PKQ.

Explanation

Substituting the signs from option A in place of the asterisks in the expression 84625133 gives: 84 ÷ 6 + 25 = 13 × 3

Applying the BODMAS/DMAS rule to evaluate both sides:

Left Hand Side (LHS): 84 ÷ 6 + 25 = 14 + 25 = 39

Right Hand Side (RHS): 13 × 3 = 39

Since the Left Hand Side equals the Right Hand Side (39 = 39), the equation is perfectly balanced.

Explanation

The given series is an alternating series consisting of two separate sub-series.

The first sub-series consists of the terms at the odd positions (first, third, and fifth terms): 78, 54, and 30. Each subsequent term is obtained by subtracting 24 from the preceding term: 78 - 24 = 54 54 - 24 = 30

The second sub-series consists of the terms at the even positions (second, fourth, and sixth terms): 97, ?, and 145. Each subsequent term is obtained by adding 24 to the preceding term: 97 + 24 = 121 121 + 24 = 145

Explanation

The letters of the word are first grouped into pairs of two. Within each pair, the letters are interchanged. Then, each letter is replaced by its opposite letter in the standard alphabetical order, where the sum of the positions of opposite letters is always 27.

For ACNE: Grouping and interchanging the pairs (A, C) and (N, E) gives (C, A) and (E, N). Replacing each letter with its alphabetical opposite: C (3rd letter) becomes X (24th letter, since 3 + 24 = 27) A (1st letter) becomes Z (26th letter, since 1 + 26 = 27) E (5th letter) becomes V (22nd letter, since 5 + 22 = 27) N (14th letter) becomes M (13th letter, since 14 + 13 = 27) This results in XZVM.

For BODY: Grouping and interchanging the pairs (B, O) and (D, Y) gives (O, B) and (Y, D). Replacing each letter with its alphabetical opposite: O (15th letter) becomes L (12th letter) B (2nd letter) becomes Y (25th letter) Y (25th letter) becomes B (2nd letter) D (4th letter) becomes W (23rd letter) This results in LYBW.

Applying the same logic to EVIL: Grouping and interchanging the pairs (E, V) and (I, L) gives (V, E) and (L, I). Replacing each letter with its alphabetical opposite: V (22nd letter) becomes E (5th letter) E (5th letter) becomes V (22nd letter) L (12th letter) becomes O (15th letter) I (9th letter) becomes R (18th letter) This results in EVOR.

Explanation

Applying the sequence of signs +, +, -, ×, = into the equation 57 35 7 14 2 * 71, we get:

57 + 35 + 7 - 14 × 2 = 71

Using the BODMAS rule, perform the multiplication first: 14 × 2 = 28

The equation becomes: 57 + 35 + 7 - 28 = 71

Next, perform the addition: 57 + 35 + 7 = 99

Finally, perform the subtraction: 99 - 28 = 71

Both sides of the equation balance to 71.

Explanation

The relationship between the first number x and the second number y in the standard pairs follows the rule y = √x - 3. For the pair 36:2, the square root of 36 is 6, and subtracting 3 from 6 gives 3, which does not equal the second number 2. Therefore, this pair deviates from the rule followed by the other pairs.

Explanation

The pattern is based on dividing the seven-letter word into three parts: the first three letters, the middle letter, and the last three letters. The first three letters are reversed, the middle letter remains unchanged, and the last three letters are reversed.

Applying this pattern to NUCLEAR: First three letters N-U-C reversed become C-U-N. Middle letter L remains unchanged. Last three letters E-A-R reversed become R-A-E.

Combining these parts gives the coded term CUNLRAE.

Explanation

When a vertical mirror is placed at the right side XY of the given combination LNP579, the resulting mirror image reverses the order of the characters from right to left and laterally inverts each individual character.

Analyzing the characters of LNP579 from right to left: The lateral inversion of the rightmost character 9 is a reversed 9, which resembles the shape of 6. The lateral inversion of 7 is a reversed 7, which resembles the shape of L. The lateral inversion of 5 is a reversed 5, which resembles the shape of S. The lateral inversion of P is a reversed P, which resembles the shape of D. The lateral inversion of N is a reversed N, which is represented by N. The lateral inversion of the leftmost character L is a reversed L, which is represented by T.

Reversing the position of each character and applying lateral inversion yields the sequence represented by 6LSDNT.

Explanation

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

Group 1: J _ M K L Group 2: J J _ K L Group 3: J J _ K L Group 4: _ J P _ L

By observing the groups, the first, second, fourth, and fifth letters in each group are J, J, K, and L, respectively. The middle (third) letter of each group increases alphabetically by one letter in each subsequent group: M to N, N to O, and O to P.

Applying this pattern: In Group 1, the second letter is J, completing the group as J J M K L. In Group 2, the third letter is N, completing the group as J J N K L. In Group 3, the third letter is O, completing the group as J J O K L. In Group 4, the first letter is J and the fourth letter is K, completing the group as J J P K L.

Thus, the letters required to complete the blanks from left to right are J, N, O, J, and K, which form JNOJK.

Explanation

The numbers in the given sets follow the relationship where the third number is equal to the difference between the first and second numbers plus 8.

c = a - b + 8

Using the first set (25, 19, 14): 25 - 19 + 8 = 6 + 8 = 14

Using the second set (50, 28, 30): 50 - 28 + 8 = 22 + 8 = 30

Applying this relation to the set (35, 22, 21): 35 - 22 + 8 = 13 + 8 = 21

Explanation

The time duration between 1 August 2009 and 1 August 2013 is exactly 4 years. An ordinary year contains 365 days, which leaves a remainder of 1 when divided by 7, meaning it has 1 odd day. A leap year contains 366 days, which leaves a remainder of 2 when divided by 7, meaning it has 2 odd days. Between 1 August 2009 and 1 August 2013, the year 2012 is a leap year, while 2010, 2011, and 2013 are ordinary years. Therefore, the total number of odd days during this period is 3 ordinary years × 1 odd day + 1 leap year × 2 odd days = 5 odd days. Adding 5 days to Saturday results in Thursday.

Explanation

The given series is an alternating series consisting of two separate arithmetic progressions.

The first sequence consists of the terms at the odd positions: 7, 4, 1. In this sequence, each successive term decreases by 3, since 7 - 3 = 4 and 4 - 3 = 1.

The second sequence consists of the terms at the even positions: 19, ?, 25. In this sequence, each successive term increases by 3.

To find the missing term, we add 3 to the first term of this sequence: 19 + 3 = 22

Adding 3 to 22 gives the next term, 25 (22 + 3 = 25), which confirms that the pattern is consistent.

Explanation

By comparing the sentences, the code for each word can be determined.

Comparing the first sentence 'I know you' (Ha Hi He) and the third sentence 'You like me' (He Ho Haa), the common word is 'you' and the common code is 'He', meaning 'you' is coded as 'He'.

Comparing the second sentence 'I Like French' (Ho Hu Ha) and the third sentence 'You like me' (He Ho Haa), the common word is 'like' and the common code is 'Ho', meaning 'like' is coded as 'Ho'.

In the third sentence 'You like me' which is coded as 'He Ho Haa', since 'you' corresponds to 'He' and 'like' corresponds to 'Ho', the remaining word 'me' must be coded as the remaining code 'Haa'.

Explanation

The pattern followed in the given number pairs is that the second number is obtained by multiplying the first number by the first number plus two.

y = x(x + 2)

Applying this formula to the first pair: 13 × (13 + 2) = 13 × 15 = 195

Applying this formula to the second pair: 7 × (7 + 2) = 7 × 9 = 63

Applying this formula to the third pair to find the missing number: 18 × (18 + 2) = 18 × 20 = 360

Explanation

In the given number pairs, the relation between the first number x and the second number y is defined by the formula y = ((x + 1)/2)³. Applying this operation to the number 11 yields ((11 + 1)/2)³ = 6³ = 216. Since the second number in this pair is 49 instead of 216, it does not conform to the pattern followed by the other pairs.

Explanation

To find the day of the week on 2 October 2001 starting from 15 August 2001, the total number of days between the two dates is calculated.

August has 31 days, so the remaining days in August after the 15th are 31 - 15 = 16 days. September has 30 days. October has 2 days up to the target date.

Total number of days = 16 + 30 + 2 = 48 days.

Dividing the total days by 7 to find the number of odd days: 48 ÷ 7 = 6 weeks and a remainder of 6 odd days.

Adding 6 days to Wednesday gives Tuesday.

Explanation

Replacing the asterisks sequentially with the signs ÷, ×, +, - and = gives the following equation:

16 ÷ 2 × 4 + 8 - 10 = 30

Applying the BODMAS rule to solve the left-hand side of the equation:

First, perform the division operation: 16 ÷ 2 = 8

Next, perform the multiplication operation: 8 × 4 = 32

Then, perform the addition operation: 32 + 8 = 40

Finally, perform the subtraction operation: 40 - 10 = 30

The left-hand side simplifies to 30, which balances with the right-hand side.

Explanation

To find why none of the conclusions follow, we analyze each conclusion.

Since some pinks are ices and all ices are blues, the pinks that are ices must also be blues. This proves that some pinks are blues, which makes Conclusion II definitely false.

Next, we are given that no ice is yellow and all ices are blues. This prevents yellow from overlapping with ice, but it does not restrict yellow from overlapping with the remaining part of blue. Because yellow and blue can either overlap or be completely separate, we cannot definitely assert that some yellows are blues, nor can we assert that no yellow is blue. Thus, both Conclusion I and Conclusion III do not logically follow.

Since none of the conclusions are guaranteed to be true, none of the conclusions follow.

Explanation

Replacing the asterisks in the equation 14 18 7 79 33 with the signs =, ×, -, and - yields:

14 = 18 × 7 - 79 - 33

Applying the BODMAS rule to solve the right-hand side:

First, perform the multiplication: 18 × 7 = 126

Next, perform the subtraction from left to right: 126 - 79 - 33 = 47 - 33 = 14

Since both sides are equal, this combination balances the equation.