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

Explanation

The relationship between the terms in each pair follows the pattern where the second term is twice the cube of the first term.

Formula: Second term = 2 × (First term)³

For the first pair: 2 × 4³ = 2 × 64 = 128

For the third pair: 2 × 7³ = 2 × 343 = 686

Applying the same logic to the second pair with the first term 5: 2 × 5³ = 2 × 125 = 250

Explanation

The logic of the series is based on a constant difference of 4 between the successive differences of the consecutive terms.

To find the pattern, calculate the differences between the known consecutive terms at the end of the series: 123 - 82 = 41 168 - 123 = 45 217 - 168 = 49

The differences are 41, 45, and 49, which increase by 4 at each step. Continuing this arithmetic progression of differences backwards, the preceding differences must be: 41 - 4 = 37 37 - 4 = 33

Applying these differences to the initial terms of the series: 12 + 33 = 45 45 + 37 = 82

This satisfies the sequence, confirming that the missing number is 45.

Explanation

In this code language, the symbols represent the following relationships: A ÷ Z means A is the daughter of Z A + Z means A is the mother of Z A - Z means A is the brother of Z A × Z means A is the sister of Z

To find the relationship between J and L in the expression J ÷ K + L - T × R: First, J ÷ K indicates that J is the daughter of K. Second, K + L indicates that K is the mother of L.

Since K is the mother of both J and L, and J is female, J is the sister of L.

Explanation

To find the day of the week on 15 July 2017, we calculate the total number of odd days from 21 May 2009 to 15 July 2017.

First, calculate the odd days between 21 May 2009 and 21 May 2017: The number of years between 2009 and 2017 is 8 years. Among these, the years 2012 and 2016 are leap years (containing 2 odd days each), while the other 6 are ordinary years (containing 1 odd day each). Total odd days in 8 years = 6 × 1 + 2 × 2 = 10 odd days. Since 10 divided by 7 leaves a remainder of 3, there are 3 odd days.

Next, calculate the remaining days from 21 May 2017 to 15 July 2017: Days left in May = 31 - 21 = 10 days. Days in June = 30 days. Days in July = 15 days. Total days = 10 + 30 + 15 = 55 days. Since 55 divided by 7 leaves a remainder of 6, there are 6 odd days.

Total odd days = 3 + 6 = 9 odd days. Since 9 divided by 7 leaves a remainder of 2, the net shift is 2 days.

Adding 2 days to Thursday results in Saturday.

Explanation

The statement all tankers are ships means that the entire set of tankers lies inside the set of ships. The statement some tankers are guns implies there is an intersection between the set of tankers and the set of guns. Since this intersecting group of tankers and guns must also lie within the larger set of ships, it is logically certain that some guns are ships. This makes conclusion I definitely true.

The statement some ships are rockets only establishes an intersection between ships and rockets. This intersection does not necessarily have to overlap with the subset of tankers. Because there is no direct or guaranteed connection between tankers and rockets, conclusion II does not logically follow. Hence, only conclusion I is true.

Explanation

The pattern followed in the given pairs is a constant shift of -2 for each letter in the alphabetical positions:

For FJM : DHK: F - 2 = D J - 2 = H M - 2 = K

For OQR : MOP: O - 2 = M Q - 2 = O R - 2 = P

Applying this same -2 pattern to the pair NTW : LRU: N - 2 = L T - 2 = R W - 2 = U

Explanation

The first statement tells us that some mangoes are apples, meaning the set of mangoes and the set of apples overlap. The second statement says that all apples are grapes, which means the entire set of apples is contained within the set of grapes. Since some mangoes are apples and all apples are grapes, that overlapping portion of mangoes and apples must also be grapes. This guarantees that some grapes are mangoes, making conclusion (I) logically follow.

The third statement states that no pears are mangoes, meaning these two sets are completely disjoint. While the set of grapes contains all apples and overlaps with mangoes, there is no statement that restricts the remaining portion of the set of grapes from overlapping with pears. Therefore, we cannot definitely conclude that no grapes are pears, meaning conclusion (II) does not logically follow. Thus, only conclusion (I) follows.

Explanation

The relationship between the letter pairs is established by shifting the English alphabetical position of each letter forward by 6 places (modulo 26).

Applying this +6 positional shift logic to the letters of the given word:

First letter: E (5) + 6 = 11, which corresponds to K Third letter: U (21) + 6 = 27 (27 - 26 = 1), which corresponds to A Fourth letter: O (15) + 6 = 21, which corresponds to U

This gives the pattern K_AU, which uniquely matches KPAU.

Explanation

First number = Second number + 2 × Third number

For the set (85, 13, 36): 13 + 2 × 36 = 13 + 72 = 85

Explanation

The relationship between the first and the second number in each pair follows the pattern where the second number is obtained by squaring the first number and adding 3 to the result.

Using the formula: Second number = (First number)² + 3

For the pair 4, 19: 4² + 3 = 16 + 3 = 19

For the pair 11, 124: 11² + 3 = 121 + 3 = 124

Applying this same mathematical operation to the pair 13, 172: 13² + 3 = 169 + 3 = 172

Explanation

By interchanging '+' with '×' and '÷' with '-', the equation becomes 9 × 11 - 2 + 36 ÷ 12. Following the BODMAS rule, we first perform the division (36 ÷ 12 = 3), then the multiplication (9 × 11 = 99), and finally the addition and subtraction (99 - 2 + 3 = 100).

Explanation

The series consists of 15 letters, which can be divided into three blocks of five letters each. By filling the blanks with the letters from option B (V, A, A, V, Z, Z, V, Z) in sequence, we get:

Block 1: V Z V A Z Block 2: A A V V Z Block 3: A Z V A Z

This division reveals a highly consistent, symmetrical pattern across the three blocks: The third letter in every block is always V. The fifth letter in every block is always Z. The second and fourth letters of the blocks alternate systematically, with Z and A in Blocks 1 and 3, and A and V in Block 2.

Explanation

The relation between the numbers in the given pairs follows the mathematical formula x : x² + 1.

For the first pair: 5 : 5² + 1 = 25 + 1 = 26

For the second pair: 9 : 9² + 1 = 81 + 1 = 82

Applying this formula to the pair 2:5: 2 : 2² + 1 = 4 + 1 = 5

Explanation

By replacing the letters with their respective mathematical operators in the equation 83 A 7 C 539 D 49 B 29:

83 + 7 × 539 ÷ 49 - 29

Applying the BODMAS rule:

First, perform the division: 539 ÷ 49 = 11

Next, perform the multiplication: 7 × 11 = 77

Now, substitute these values back into the expression: 83 + 77 - 29

Finally, perform the addition and subtraction: 160 - 29 = 131

Explanation

The relationship between the family members can be mapped step-by-step. Since B is the father of C and C is the brother of Q, B is the father of Q.

Next, Q is the son of M's son. Since B is already established as the father of Q, B must be the son of M.

It is given that M is married to T, and B is the only son of T. Since T is the mother of U, T is female, which means M is male. Since T is married to M, and B is their son, T is the mother of B.

Because B is the father of Q and T is the mother of B, T is the grandmother of Q from the paternal side, which means T is Q's father's mother.

Explanation

L is the sister of T, and T is the daughter of R. This means that L is also the daughter of R, which makes R the father of L.

R is the brother of P, which means R and P are siblings.

P is married to N, and N is the father of Q. Since N is a father, N is male, which makes his spouse P female.

Since P is a female sibling of L's father R, P is the sister of R. Therefore, P is L's father's sister.

Explanation

To find the relationship between T and O, we trace the family tree:

N is the father of O.

S is the father of N and is married to T. Since S is male and married to T, T is female and must be the mother of N.

Since N is the father of O, and T is the mother of N, T is the father's mother of O.

Explanation

The relationship between the three numbers (a - b - c) in each set follows the mathematical pattern where the third number is obtained by adding 20 to the product of the first two numbers.

Formula: c = (a × b) + 20

Applying this logic to the given sets: For the first set (12 - 15 - 200): (12 × 15) + 20 = 180 + 20 = 200

For the second set (10 - 12 - 140): (10 × 12) + 20 = 120 + 20 = 140

Following the same pattern for the correct option (6 - 9 - 74): (6 × 9) + 20 = 54 + 20 = 74

Explanation

The given series follows a pattern where the differences between consecutive terms are consecutive perfect squares starting from 2².

The difference between the first two terms is: 246 - 242 = 4 = 2²

The difference between the next two terms is: 255 - 246 = 9 = 3²

Following this pattern, the next difference must be 4² = 16. Adding this to the third term yields: 255 + 16 = 271

We can verify this by checking the next transition in the series using 5² = 25: 271 + 25 = 296

This matches the final term of the series.

Explanation

The given series consists of five groups of letters, where each group follows a specific alphabetical sequence:

Group 1: ABMN (consists of the consecutive pairs AB and MN) Group 2: CDOP (consists of the consecutive pairs CD and OP) Group 3: EFQR (consists of the consecutive pairs EF and QR) Group 4: GHST (consists of the consecutive pairs GH and ST) Group 5: IJUV (consists of the consecutive pairs IJ and UV)

Each group is formed by pairing consecutive letters from the first half of the alphabet with consecutive letters from the second half of the alphabet: First pairs: AB (1-2) → CD (3-4) → EF (5-6) → GH (7-8) → IJ (9-10) Second pairs: MN (13-14) → OP (15-16) → QR (17-18) → ST (19-20) → UV (21-22)

Comparing this pattern with the given series: AB_N requires M to form ABMN. _DOP requires C to form CDOP. E_QR requires F to form EFQR. HST requires G to form GHST. IU requires V to form IUV.

Sequentially placing these letters in the blanks gives M, C, F, G, V.

Explanation

By comparing the given coded sentences, the code for each word can be uniquely identified.

From the first sentence 'ear eyes nose chin cheeks' coded as 'si ei ki ri ni' and the third sentence 'eyes ear hands' coded as 'ri si di', the common words 'eyes' and 'ear' correspond to 'si' and 'ri'.

From the fourth sentence 'legs cheeks eyes' coded as 'ki gi si', 'eyes' is identified as 'si' since it is common to all three sentences, which leaves 'ear' as 'ri'. The word 'cheeks' is common to the first and fourth sentences, and the common code is 'ki'.

From the second sentence 'nose legs hands fingers' coded as 'gi fi di ei', the word 'nose' is common to the first and second sentences, and the common code is 'ei'.

In the first sentence 'ear eyes nose chin cheeks', the codes for 'ear' (ri), 'eyes' (si), 'nose' (ei), and 'cheeks' (ki) are known. This leaves the remaining word 'chin' to be coded as the remaining code 'ni'.

Explanation

The given series is 0, 5, 12, 21, ?, 45, 60 where the number 7 is a typographical error representing the question mark.

The differences between consecutive terms are: 5 - 0 = 5 12 - 5 = 7 21 - 12 = 9

These differences form an arithmetic progression of consecutive odd numbers: 5, 7, 9, 11, 13, 15.

Following this pattern, the next difference must be 11: 21 + 11 = 32

To verify, adding the next odd number 13 to 32 yields: 32 + 13 = 45

And adding 15 to 45 yields: 45 + 15 = 60

This perfectly completes the series.

Explanation

To find the number of letters whose positions will be changed, write down the word ACQUIRE and its letters in alphabetical order, then compare the positions:

Original word: A C Q U I R E Alphabetical order: A C E I Q R U

Comparing each position: The letter A remains at the 1st position. The letter C remains at the 2nd position. The letter Q at the 3rd position changes to E. The letter U at the 4th position changes to I. The letter I at the 5th position changes to Q. The letter R remains at the 6th position. The letter E at the 7th position changes to U.

The letters that change their positions are Q, U, I, and E, which is a total of four letters.

Explanation

The relationship between the letter-clusters in the given pairs is that each letter of the second cluster is obtained by adding 5 to the alphabetical position of the corresponding letter in the first cluster.

For XFI to CKN: X (24) + 5 = 29, which corresponds to C (3) F (6) + 5 = 11, which corresponds to K (11) I (9) + 5 = 14, which corresponds to N (14)

For PFS to UKX: P (16) + 5 = 21, which corresponds to U (21) F (6) + 5 = 11, which corresponds to K (11) S (19) + 5 = 24, which corresponds to X (24)

Applying the same logic to HPS: H (8) + 5 = 13, which corresponds to M (13) P (16) + 5 = 21, which corresponds to U (21) S (19) + 5 = 24, which corresponds to X (24)

Thus, HPS becomes MUX.

Explanation

In the alphabetical series, each letter represents a specific numerical position: A is 1, C is 3, and D is 4. The difference between consecutive letters in ACD is +2 from A to C, and +1 from C to D. This pattern of an unequal gap of +2 and +1 distinguishes it from the other groups, which all maintain a constant gap of +2 between consecutive letters.

Explanation

To find the correct pattern, substitute the letters from option B (H, G, H, I) sequentially into the blanks of the series:

G [H] J I G [G] H J G G H [H] J G G H H [I] J I

Now, divide the complete 20-letter sequence into four progressive groups:

G H J I G G H J G G H H J G G H H I J I

The pattern shows a systematic progression of doubling the letters of the set {G, H, I, J}: In the first group, each letter appears once (with J and I at the end). In the second group, the first letter (G) is doubled: G G H J. In the third group, the first two letters (G and H) are doubled: G G H H J. In the fourth group, the first three letters (G, H, and I) are doubled: G G H H I J I.

Explanation

By interchanging the signs '+' with '-' and '×' with '÷', the given equation is rewritten as:

69 + 44 ÷ 726 × 132 - 58 = ?

Applying the BODMAS rule, division and multiplication are performed first:

44 ÷ 726 × 132 = (44 / 726) × 132

Simplifying the fraction: 44 / 726 = 4 / 66

Substituting this back: (4 / 66) × 132 = 4 × 2 = 8

Now, performing the addition and subtraction:

69 + 8 - 58 = 77 - 58 = 19

Explanation

The relationship between the letter groups is established by shifting each letter forward by 5 positions in the English alphabetical order.

Applying this logic to the first pair BEH and GJM: B (2nd letter) + 5 = G (7th letter) E (5th letter) + 5 = J (10th letter) H (8th letter) + 5 = M (13th letter)

Applying the same logic to the second pair FOT and KTY: F (6th letter) + 5 = K (11th letter) O (15th letter) + 5 = T (20th letter) T (20th letter) + 5 = Y (25th letter)

Following the same pattern for LIN: L (12th letter) + 5 = Q (17th letter) I (9th letter) + 5 = N (14th letter) N (14th letter) + 5 = S (19th letter)

Explanation

By analyzing the letters at each position across the five terms of the series, we find distinct arithmetic progressions based on alphabetical positions (A = 1, B = 2, ..., Z = 26):

The first letters follow a pattern of decreasing by 3: Z (26) → W (23) → T (20) → Q (17) → N (14) This gives the third blank (first letter of the third term) as T.

The second letters follow a pattern of increasing by 4: N (14) → R (18) → V (22) → Z (26) → D (4, after wrapping around from 26) This gives the second blank as R and the fifth blank as D.

The third letters follow a pattern of decreasing by 3: G (7) → D (4) → A (1) → X (24) → U (21) This gives the first blank as G.

The fourth letters follow a pattern of increasing by 4: T (20) → X (24) → B (2) → F (6) → J (10) This gives the fourth blank as F.

Collecting the letters for the blanks in order of their occurrence: First blank (3rd letter of 1st term) = G Second blank (2nd letter of 2nd term) = R Third blank (1st letter of 3rd term) = T Fourth blank (4th letter of 4th term) = F Fifth blank (2nd letter of 5th term) = D

The sequence of letters to fill the blanks is GRTFD.

Explanation

The series follows a consistent pattern where each letter in a cluster decreases by 3 positions in the English alphabetical order to form the corresponding letter of the next cluster.

For the first letter, the position values decrease by 3: V (22) minus 3 is S (19), S (19) minus 3 is P (16), P (16) minus 3 is M (13), and M (13) minus 3 is J (10). Thus, the first letter is P.

For the second letter, the position values decrease by 3: P (16) minus 3 is M (13), M (13) minus 3 is J (10), J (10) minus 3 is G (7), and G (7) minus 3 is D (4). Thus, the second letter is J.

For the third letter, the position values decrease by 3: A (27) minus 3 is X (24), X (24) minus 3 is U (21), U (21) minus 3 is R (18), and R (18) minus 3 is O (15). Thus, the third letter is U.

Combining these letters, the missing cluster is PJU.

Explanation

To find the relationship of B to E in the expression A - B * C / D + E, we decode the relations step-by-step from right to left:

D + E means D is the mother of E.

C / D means C is the father of D.

B * C means B is the wife of C. Since C is the father of D, his wife B is the mother of D.

Since B is the mother of D, and D is the mother of E, B is the mother of E's mother. Therefore, B is the mother's mother of E.

Explanation

The differences between consecutive terms in the series form a sequence of consecutive prime numbers starting from 71.

194 - 123 = 71 267 - 194 = 73

The next two consecutive prime numbers after 73 are 79 and 83.

Applying this pattern to find the missing number: 267 + 79 = 346

To verify the pattern with the final term: 346 + 83 = 429

Explanation

According to the rules of sign interchange, the operators are interchanged as follows:

• becomes × × becomes -

• and ÷ are interchanged

Applying these interchanges to the equation: 5 × 9 - 8 + 12 ÷ 4 = ?

Using the BODMAS rule, perform division first: 12 ÷ 4 = 3

Next, perform multiplication: 5 × 9 = 45

Now, substitute the values back to perform addition and subtraction: 45 - 8 + 3 = 40

Explanation

The given series follows a pattern where the difference between consecutive terms decreases by consecutive perfect squares.

The difference between the first two terms is: 473 - 464 = 9 = 3²

The difference between the next two terms is: 464 - 448 = 16 = 4²

Following this pattern, the next difference must be 5² = 25. Subtracting 25 from 448 gives: 448 - 25 = 423

To verify, the next difference should be 6² = 36: 423 - 36 = 387

This perfectly matches the last term of the series.

Explanation

The given series follows a pattern where the difference between consecutive terms increases progressively by 1.

The difference between the first and second terms is 39 - 38 = 1. The difference between the second and third terms is 41 - 39 = 2. The difference between the third and fourth terms is 44 - 41 = 3. The difference between the fourth and fifth terms is 48 - 44 = 4.

Following this sequence of consecutive integers, the difference between the fifth and the sixth terms must be 5. Therefore, the missing term is 48 + 5 = 53.

Explanation

The coding scheme follows an alternating pattern of adding 1 and subtracting 1 to the alphabetical position of successive letters: +1, -1, +1, -1, and so on.

For BLADE: B + 1 = C L - 1 = K A + 1 = B D - 1 = C E + 1 = F This yields CKBCF.

For CHALK: C + 1 = D H - 1 = G A + 1 = B L - 1 = K K + 1 = L This yields DGBKL.

Applying this same rule to DIGITAL: D + 1 = E I - 1 = H G + 1 = H I - 1 = H T + 1 = U A - 1 = Z L + 1 = M

This gives the final coded word EHHHUZM.

Explanation

Each letter-cluster in the series is obtained by adding 2 to the alphabetical position of the corresponding letter in the previous cluster.

For the first letter: J (10) + 2 = L (12), L (12) + 2 = N (14), N (14) + 2 = P (16). For the second letter: O (15) + 2 = Q (17), Q (17) + 2 = S (19), S (19) + 2 = U (21). For the third letter: Q (17) + 2 = S (19), S (19) + 2 = U (21), U (21) + 2 = W (23). For the fourth letter: W (23) + 2 = Y (25), Y (25) + 2 = A (27 or 1), A (1) + 2 = C (3).

Applying this pattern of adding 2 to each letter of LQSY yields NSUA.

Explanation

The terms in the series follow a distinct pattern for the first letter, the second letter, and the number.

For the first letter, the alphabetical positions increase by 2 in each step: E (5) + 2 = G (7) G (7) + 2 = I (9) I (9) + 2 = K (11) K (11) + 2 = M (13)

For the second letter, the alphabetical positions also increase by 2 in each step, cyclically: Z (26) + 2 = B (2) B (2) + 2 = D (4) D (4) + 2 = F (6) F (6) + 2 = H (8)

For the number, there is a constant addition of 13 in each step: 10 + 13 = 23 23 + 13 = 36 36 + 13 = 49 49 + 13 = 62

Combining these three patterns gives the missing term GB 23.

Explanation

To find the code for the word come, we analyze the common words and their corresponding codes across the given sentences.

Comparing the first sentence, he will go to market (xi ui hi ni ji), and the second sentence, market is very crowded (wi ni ki di), the only common word is market and the common code is ni. Therefore, market is coded as ni.

Comparing the first sentence, he will go to market (xi ui hi ni ji), and the third sentence, come to crowded market (ui ni fi di), the common words are to and market, which share the codes ui and ni. Since market is ni, the word to is coded as ui.

Comparing the second sentence, market is very crowded (wi ni ki di), and the third sentence, come to crowded market (ui ni fi di), the common words are market and crowded, which share the codes ni and di. Since market is ni, the word crowded is coded as di.

In the third sentence, come to crowded market (ui ni fi di), the words to, crowded, and market correspond to the codes ui, di, and ni respectively. By elimination, the remaining word come is coded as the remaining code fi.

Explanation

The statement "All orchids are lilies" means the set of orchids is entirely contained within the set of lilies. The statement "No lily is a rose" means there is no overlap between the set of lilies and the set of roses. Since all orchids are inside the set of lilies, and no lily can be a rose, it logically follows that no orchid can be a rose. Therefore, conclusion II definitely follows from the given statements.

Explanation

In the letter-cluster ZAB, the alphabetical positions of the letters are Z = 26, A = 27 (or 1), and B = 28 (or 2). The difference between the consecutive letters is +1 from Z to A, and +1 from A to B. This +1, +1 progression makes it the odd one out, whereas the other groups follow a +1, +2 progression.

Explanation

The given series consists of three distinct patterns for the first letter, the second letter, and the number in each term.

For the first letter, the sequence follows consecutive alphabetical positions: X, Y, Z, A, B. Thus, the first letter of the missing term is Z.

For the second letter, the sequence also follows consecutive alphabetical positions: D, E, F, G, H. Thus, the second letter of the missing term is F.

For the numbers, the sequence is 45, 53, ?, 58, 55. This follows an alternating mathematical pattern of adding 8 and then subtracting 3: 45 + 8 = 53 53 - 3 = 50 50 + 8 = 58 58 - 3 = 55

Thus, the missing number is 50, and combining all three patterns yields ZF 50.

Explanation

First, calculate the day on 15th January 1997. Since 1996 is a leap year, it contains 366 days.

Number of odd days in 366 days = 366 mod 7 = 2 odd days.

So, 15th January 1997 is Monday + 2 days = Wednesday.

Now, count the days from 15th January 1997 to 30th March 1997: Remaining days in January 1997 = 31 - 15 = 16 days Days in February 1997 = 28 days Days in March 1997 = 30 days Total days = 16 + 28 + 30 = 74 days

Number of odd days in 74 days = 74 mod 7 = 4 odd days.

Adding 4 days to Wednesday gives Sunday.

Explanation

The relationship between the first number (x) and the second number (y) in the given pairs is defined by the formula:

y = 9 × x - 8

Applying this relation to the given sets: For (42, 370): 9 × 42 - 8 = 378 - 8 = 370 For (57, 505): 9 × 57 - 8 = 513 - 8 = 505

Applying the same relation to the correct option (29, 253): 9 × 29 - 8 = 261 - 8 = 253

Explanation

Decoding the given expression P × Q + R - S ÷ T step-by-step from right to left to find the relation between R, S, and T:

S ÷ T means S is the mother of T.

R - S means R is the brother of S.

Since S is the mother of T and R is the brother of S, R is the brother of T's mother. This makes R the maternal uncle of T.

Explanation

The relationship between the first number x and the second number y in the consistent pairs is defined by the formula y = x × (x + 4).

Applying this formula to the first number 2 gives: 2 × (2 + 4) = 2 × 6 = 12

Since the second number in the pair is 10 instead of 12, this pair does not follow the common pattern.

Explanation

The relation between the letters in each pair is established by shifting each letter forward by two positions (+2) in the alphabetical order.

For the first pair: J (10) + 2 = L (12) O (15) + 2 = Q (17) S (19) + 2 = U (21) V (22) + 2 = X (24) Thus, JOSV becomes LQUX.

For the second pair: E (5) + 2 = G (7) J (10) + 2 = L (12) N (14) + 2 = P (16) Q (17) + 2 = S (19) Thus, EJNQ becomes GLPS.

Applying the same +2 logic to DIMP: D (4) + 2 = F (6) I (9) + 2 = K (11) M (13) + 2 = O (15) P (16) + 2 = R (18) This yields FKOR.

Explanation

To solve the equation, the signs - and + are interchanged, and × and ÷ are interchanged.

The original equation is: 72 - 33 × 605 ÷ 110 + 70 = ?

After interchanging the signs, the expression becomes: 72 + 33 ÷ 605 × 110 - 70

Applying the BODMAS rule:

First, perform the division: 33 ÷ 605 = 33/605 = 3/55

Next, perform the multiplication: (3/55) × 110 = 3 × 2 = 6

Now, the expression becomes: 72 + 6 - 70

Perform the addition: 72 + 6 = 78

Finally, perform the subtraction: 78 - 70 = 8

Explanation

To determine the validity of the conclusions, we can analyze the relationships between the categories using set theory.

The statement that all directors are actors means the set of directors is entirely contained within the set of actors.

The statement that some actors are writers indicates an overlap between actors and writers, but this overlapping region does not necessarily intersect with the set of directors. Therefore, we cannot guarantee that any directors are writers, which means Conclusion I does not logically follow.

The statement that no writer is a producer means the sets of writers and producers are completely disjoint. However, this does not establish any direct constraint between producers and directors. The set of producers can freely overlap with the set of directors without violating any of the given statements. Since there is a possibility of overlap, the assertion that no producer is a director is not guaranteed to be true, which means Conclusion II does not logically follow.

Explanation

The number of years between 19 December 1992 and 19 December 2009 is 17 years.

Among these, the leap years are 1996, 2000, 2004, and 2008, making a total of 4 leap years. The remaining 13 years are ordinary years.

The total number of odd days in this period is calculated as: Total odd days = (13 × 1) + (4 × 2) = 13 + 8 = 21 odd days

Dividing 21 by 7 leaves a remainder of 0. Therefore, 19 December 2009 is the same day of the week as 19 December 1992, which is Saturday.

To find the day on 22 December 2009, we add the 3 remaining days from 19 December to 22 December: Saturday + 3 days = Tuesday