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

Explanation

Substituting the sequence of signs from Option D, with the first sign representing the division operator (÷), the equation becomes:

60 ÷ 6 - 3 × 18 + 49 = 5

Applying the BODMAS rule to solve the expression on the left-hand side:

First, perform the division: 60 ÷ 6 = 10

Next, perform the multiplication: 3 × 18 = 54

Now, substitute these values back into the equation: 10 - 54 + 49 = 5

Perform the addition and subtraction: 10 + 49 - 54 = 5 59 - 54 = 5 5 = 5

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

Explanation

The coding pattern involves adding consecutive natural numbers to the alphabetical positions of each letter in the word, starting from 1 for the first letter, 2 for the second, and so on.

For PENCIL: P (16) + 1 = 17 E (5) + 2 = 7 N (14) + 3 = 17 C (3) + 4 = 7 I (9) + 5 = 14 L (12) + 6 = 18 This gives the code 1771771418.

For ERASER: E (5) + 1 = 6 R (18) + 2 = 20 A (1) + 3 = 4 S (19) + 4 = 23 E (5) + 5 = 10 R (18) + 6 = 24 This gives the code 6204231024.

Applying the same logic to SHARPNER: S (19) + 1 = 20 H (8) + 2 = 10 A (1) + 3 = 4 R (18) + 4 = 22 P (16) + 5 = 21 N (14) + 6 = 20 E (5) + 7 = 12 R (18) + 8 = 26

Combining these values yields 201042221201226.

Explanation

The pattern followed in each row is: 3 * (First number) - 4 * (Second number) = Third number.

Row 1: 3 * 67 - 4 * 25 = 201 - 100 = 101 Row 2: 3 * 55 - 4 * 17 = 165 - 68 = 97 Row 3: 3 * 45 - 4 * 19 = 135 - 76 = 59

Explanation

Dario and Rihana are married as husband and wife. Since Ronaldo and Jorge are the sons of Rihana, and Sheila is the daughter of Dario, they are all siblings. This means Jorge and Sheila are brother and sister.

The wife of Jorge is the brother's wife to Sheila. In family relationships, a brother's wife is referred to as a sister-in-law.

Explanation

Analyzing the alphabetical progression of each letter position in the clusters reveals the following patterns:

For the first letter, the sequence is G (7), J (10), M (13), P (16), which increases by 3 each time. The next letter is P + 3, which is S (19).

For the second letter, the sequence is O (15), M (13), K (11), I (9), which decreases by 2 each time. The next letter is I - 2, which is G (7).

For the third letter, the sequence is D (4), A (1), X (24), U (21), which decreases by 3 each time. The next letter is U - 3, which is R (18).

For the fourth letter, the sequence is T (20), V (22), X (24), Z (26), which increases by 2 each time. The next letter is Z + 2, which wraps around the alphabet to B (2).

Combining these results gives the letter cluster SGRB.

Explanation

The relationship between the numbers is determined by adding the digits of the first number together and then adding 4 to the resulting sum.

For the first pair: 6789 → (6 + 7 + 8 + 9) + 4 = 30 + 4 = 34

For the second pair: 1786 → (1 + 7 + 8 + 6) + 4 = 22 + 4 = 26

Applying the same rule to the fifth term: 4327 → (4 + 3 + 2 + 7) + 4 = 16 + 4 = 20

Explanation

Using Venn diagrams or logical deduction: The statement Some books are pens means that the set of books and the set of pens share a common overlapping region. The statement All pens are pencils means the entire set of pens lies inside the set of pencils. Since the overlapping region of books and pens is entirely inside the set of pencils, it is certain that some books are pencils. Since some books are pencils, it logically follows that some pencils are books. Therefore, conclusion I is definitely true. On the other hand, from the given positive statements, we cannot definitely conclude any negative relationship such as some books are not pencils, because there is a possibility that all books are pencils. Thus, conclusion II does not follow.

Explanation

The standard pattern across the number-pairs is y = x² - 1, where x is the first number and y is the second number. For the first number 8, the expected second number is 8² - 1 = 63. Since the given second number in this pair is 66, it does not follow the established rule.

Explanation

The given series follows an alternating pattern of multiplication and addition with decreasing numbers, starting from 6.

The sequence of operations is: 23 × 6 = 138 138 + 5 = 143 143 × 4 = 572 572 + 3 = 575 575 × 2 = 1150

Applying this pattern, the missing number is obtained by multiplying the third term by 4, which gives 143 × 4 = 572. Adding 3 to this result gives the next term 575, confirming the validity of the pattern.

Explanation

Noor's father's wife is Noor's mother. The son-in-law of Noor's mother is the husband of Noor's sister. The wife of this son-in-law is Noor's sister. Therefore, the woman on the stage is Noor's sister.

Explanation

The relationship between the terms is based on reversing the order of the letters of each word.

In the first pair, the word BRIGHT is written in reverse order to form THGIRB.

In the second pair, the word DANGER is written in reverse order to form REGNAD.

Applying this same rule to the fifth term, the letters of the word FOREST written in reverse order from last to first give TSEROF.

Explanation

The sequence follows a double-difference pattern. First, find the differences between consecutive terms: 21 - 4 = 17 41 - 21 = 20 66 - 41 = 25 98 - 66 = 32 141 - 98 = 43 197 - 141 = 56 270 - 197 = 73

Next, find the differences between these consecutive differences: 20 - 17 = 3 25 - 20 = 5 32 - 25 = 7 43 - 32 = 11 56 - 43 = 13 73 - 56 = 17

The second-level differences are the sequence of consecutive prime numbers: 3, 5, 7, 11, 13, 17. The next prime number in this sequence is 19.

Adding 19 to the last first-level difference (73) yields: 73 + 19 = 92

Adding this value to the last term of the given series (270) gives the missing number: 270 + 92 = 362

Explanation

The relationship between the terms is established by calculating the sum of the digits of the four-digit number and then subtracting 4 from that sum to obtain the related two-digit number.

For the first pair, the sum of the digits of 9876 is 9 + 8 + 7 + 6 = 30. Subtracting 4 from this sum yields 30 - 4 = 26.

For the second pair, the sum of the digits of 8671 is 8 + 6 + 7 + 1 = 22. Subtracting 4 from this sum yields 22 - 4 = 18.

Applying the same logic to the fifth term 3427, the sum of the digits is 3 + 4 + 2 + 7 = 16. Subtracting 4 from this sum yields 16 - 4 = 12.

Explanation

In this coding scheme, each letter of the word is represented by its corresponding numerical position in the English alphabet, where A = 1, B = 2, C = 3, and so on.

For TABLE: T is 20 A is 1 B is 2 L is 12 E is 5 Combining these numbers sequentially gives 2012125.

For CHAIR: C is 3 H is 8 A is 1 I is 9 R is 18 Combining these numbers sequentially gives 381918.

Applying the same pattern to STAND: S is 19 T is 20 A is 1 N is 14 D is 4 Combining these positions sequentially yields 19201144.

Explanation

The coding pattern rearranges the positions of the letters in each four-letter word. By numbering the positions of the letters in the original word as 1-2-3-4, the transformation can be observed.

For the word SPOT: S is 1, P is 2, O is 3, T is 4. The coded word POST rearranges these to the sequence 2-3-1-4.

For the word PLOT: P is 1, L is 2, O is 3, T is 4. The coded word LOPT rearranges these to the same sequence of 2-3-1-4.

Applying this 1-2-3-4 to 2-3-1-4 rearrangement rule to the word SINK: S is 1, I is 2, N is 3, K is 4. Rearranging these letters into the 2-3-1-4 positions gives I, N, S, K, resulting in the coded word INSK.

Explanation

To find the missing letter-cluster, we analyze the alphabetical position of each letter in the sequence of clusters: QTGC, RBVY, ?, TRZQ, UZOM.

For the first letter: Q (17) → R (18) → ? → T (20) → U (21) The pattern is +1. The missing letter at position 19 is S.

For the second letter: T (20) → B (2 or 28) → ? → R (18) → Z (26) The pattern is +8. The missing letter at position 10 (2 + 8) is J.

For the third letter: G (7) → V (22) → ? → Z (26) → O (15) The pattern is -11. The missing letter at position 11 (22 - 11) is K.

For the fourth letter: C (3 or 29) → Y (25) → ? → Q (17) → M (13) The pattern is -4. The missing letter at position 21 (25 - 4) is U.

Combining these letters yields SJKU.

Explanation

The given series is a geometric progression where each successive term is obtained by multiplying the previous term by 2.5.

600 × 2.5 = 1500 1500 × 2.5 = 3750 3750 × 2.5 = 9375

Applying this constant multiplier to the last term yields: 9375 × 2.5 = 23437.50

Explanation

In the standard pattern, the second number is obtained by multiplying the first number by 1.25, which is equivalent to adding one-fourth of the first number to itself. Applying this rule to the first number 48 gives 48 + 48/4 = 60. Since the pair contains 62 instead of 60, it violates the rule and is the odd pair.

Explanation

By replacing the * signs with the operators from option D, which sequentially represent Addition (+), Division (÷), Subtraction (-), Multiplication (×), and Equality (=), we get:

75 + 85 ÷ 17 - 12 × 6 = 8

Following the BODMAS rule:

First, division is performed: 85 ÷ 17 = 5

The equation becomes: 75 + 5 - 12 × 6 = 8

Next, multiplication is performed: 12 × 6 = 72

The equation becomes: 75 + 5 - 72 = 8

Then, addition is performed: 75 + 5 = 80

The equation becomes: 80 - 72 = 8

Finally, subtraction is performed: 80 - 72 = 8

Since 8 = 8, the equation is balanced.

Explanation

The numbers in each row follow a specific mathematical relation:

Third number = (First number × 2) - (Second number ÷ 5)

Applying this relation to each row:

First row: (12 × 2) - (25 ÷ 5) = 24 - 5 = 19

Second row: (35 × 2) - (50 ÷ 5) = 70 - 10 = 60

Third row: (24 × 2) - (70 ÷ 5) = 48 - 14 = 34

Explanation

The pattern of the given series is based on the differences between consecutive terms: 17 - 14 = 3 23 - 17 = 6 35 - 23 = 12 59 - 35 = 24

The differences form a geometric sequence where each subsequent difference is multiplied by 2: 3 × 2 = 6 6 × 2 = 12 12 × 2 = 24

Following this pattern, the next difference in the series is: 24 × 2 = 48

Adding this difference to the last term gives: 59 + 48 = 107

Explanation

The coding pattern follows a rule where the letters at odd-numbered positions (1st, 3rd, 5th, 7th, 9th) remain unchanged, while the letters at even-numbered positions (2nd, 4th, 6th, 8th) are shifted forward by one position (+1) in the alphabetical order.

For the word BREAK: B (1st) remains B R (2nd) becomes S (+1) E (3rd) remains E A (4th) becomes B (+1) K (5th) remains K This results in BSEBK.

For the word FAST: F (1st) remains F A (2nd) becomes B (+1) S (3rd) remains S T (4th) becomes U (+1) This results in FBSU.

Applying the same logic to the word BREAKFAST: B (1st) remains B R (2nd) becomes S (+1) E (3rd) remains E A (4th) becomes B (+1) K (5th) remains K F (6th) becomes G (+1) A (7th) remains A S (8th) becomes T (+1) T (9th) remains T

This gives the final coded output as BSEBK GATT.

Explanation

The given series follows a pattern where the differences between consecutive terms are alternating additions of cubes of consecutive odd numbers and subtractions of squares of consecutive even numbers.

The differences between consecutive terms are:

133 - 132 = +1, which is +1³ 129 - 133 = -4, which is -2² 156 - 129 = +27, which is +3³ 140 - 156 = -16, which is -4² 265 - 140 = +125, which is +5³

Following this pattern, the next difference must be the subtraction of the square of 6:

-6² = -36

Calculating the next term:

265 - 36 = 229

Explanation

Replacing the asterisks sequentially with the mathematical signs +, ÷, -, +, ÷, and = yields the following equation:

26 + 56 ÷ 4 - 17 + 49 ÷ 7 = 30

Applying the BODMAS rule, perform the division operations first: 56 ÷ 4 = 14 49 ÷ 7 = 7

Substitute these division results back into the equation: 26 + 14 - 17 + 7 = 30

Now, solve the remaining addition and subtraction operations from left to right: 40 - 17 + 7 = 30 23 + 7 = 30 30 = 30

The equation is perfectly balanced.

Explanation

From the first statement, there is an intersection between the set of chairs and the set of racks. The third statement tells us that the set of racks is entirely contained within the set of beds. Since all racks are beds, the portion of chairs that overlaps with racks must also overlap with beds. Therefore, it is guaranteed that some chairs are beds, which makes conclusion I logically follow.

Explanation

The coding pattern involves shifting the positions of the letters of the word as follows: The first letter is shifted forward by 1 position (+1). The second letter is shifted forward by 2 positions (+2). The third letter is shifted forward by 3 positions (+3). The remaining letters in the word remain unchanged.

Applying this pattern to ABILITY: A (+1) → B B (+2) → D I (+3) → L The letters L, I, T, and Y remain unchanged as L, I, T, and Y. Thus, ABILITY is coded as BDLLITY.

Applying the same pattern to DISPLAY: D (+1) → E I (+2) → K S (+3) → V The letters P, L, A, and Y remain unchanged as P, L, A, and Y. Thus, DISPLAY is coded as EKVPLAY.

Explanation

The given symbols represent the following mathematical operations: M represents - (subtraction) N represents ÷ (division) O represents × (multiplication) P represents + (addition)

Substituting these operators into the given equation: (14 O 7) P 41 M (26 O 3) P (176 N 2) = (14 × 7) + 41 - (26 × 3) + (176 ÷ 2)

According to the BODMAS rule, solving the operations inside the brackets first: 14 × 7 = 98 26 × 3 = 78 176 ÷ 2 = 88

Substituting these calculated values back into the equation: 98 + 41 - 78 + 88

Performing addition: 98 + 41 + 88 = 227

Performing subtraction: 227 - 78 = 149

Explanation

The given series follows a pattern where consecutive terms are obtained by alternately adding and subtracting the cubes of consecutive descending integers starting from 6.

Let the terms of the series be denoted by T₁, T₂, T₃, T₄, T₅, and T₆.

T₂ = T₁ + 6³ = 192 + 216 = 408

T₃ = T₂ - 5³ = 408 - 125 = 283

T₄ = T₃ + 4³ = 283 + 64 = 347

T₅ = T₄ - 3³ = 347 - 27 = 320

Following this established sequence, the next term is obtained by adding the cube of 2:

T₆ = T₅ + 2³ = 320 + 8 = 328

Explanation

In each 7-letter word, the letters are rearranged in a specific pattern. The word is divided into three parts: the first three letters (positions 1-3), the middle letter (position 4), and the last three letters (positions 5-7). The rearrangement pattern shifts the last three letters to the front, keeps the middle letter in its place, and shifts the first three letters to the end. This transforms the letter position sequence from (1, 2, 3, 4, 5, 6, 7) to (5, 6, 7, 4, 1, 2, 3).

Applying this pattern to the 7-letter word QUICKLY: The last three letters (5, 6, 7) are KLY. The middle letter (4) is C. The first three letters (1, 2, 3) are QUI.

Combining these components in the pattern sequence (5, 6, 7, 4, 1, 2, 3) gives KLYCQUI.

Explanation

The series follows a specific pattern of alphabetical shifting for each letter position in the clusters:

First letters decrease by 3: A (27) → X (24) → U (21) → R (18) → O (15).

Second letters increase by 4: A (1) → E (5) → I (9) → M (13) → Q (17).

Third letters decrease by 5: V (22) → Q (17) → L (12) → G (7) → B (2).

Fourth letters increase by 6: R (18) → X (24) → D (4 or 30) → J (10) → P (16).

Combining these letters yields UILD.

Explanation

The general mathematical operation followed by the pairs is that the second number is obtained by adding 5 to the square of the first number. Applying this logic to the first number 8 gives 8² + 5 = 64 + 5 = 69. The pair 8:70 does not conform to this rule because the second number is 70 instead of 69, making it the odd one out.

Explanation

By interchanging 12 and 11, the expression becomes (132 / 11) + (6 * 12) + 18 - (64 / 16) * 8, which simplifies to 12 + 72 + 18 - 32 = 70. This makes the equation correct.

Explanation

The relationship between the numbers in each pair follows the pattern where the second number is obtained by multiplying the first number by 5 and then adding 7.

Using the relation: Second number = 5 × First number + 7

For the first pair: 5 × 12 + 7 = 60 + 7 = 67

For the second pair: 5 × 21 + 7 = 105 + 7 = 112

Applying the same pattern to the third pair: 5 × 17 + 7 = 85 + 7 = 92

Explanation

The relationship between the numbers follows the pattern where the first number of each pair is multiplied by 5, and then 7 is subtracted from the product to get the second number.

For the first pair, we have (17 × 5) - 7 = 85 - 7 = 78.

For the second pair, we have (15 × 5) - 7 = 75 - 7 = 68.

Applying the same mathematical operation to the third pair, the calculation is (28 × 5) - 7 = 140 - 7 = 133.

Explanation

The logical pattern followed in each row is: (First number × 3) - (Second number ÷ 2) = Third number

For the first row: (14 × 3) - (64 ÷ 2) = 42 - 32 = 10

For the second row: (7 × 3) - (18 ÷ 2) = 21 - 9 = 12

For the third row: (23 × 3) - (88 ÷ 2) = 69 - 44 = 25

Explanation

The given series follows a distinct mathematical pattern for each letter position in the clusters:

For the first letter, the pattern is to add 1 to the positional value of the previous letter: X (24) + 1 = Y (25) Y (25) + 1 = Z (26) Z (26) + 1 = A (1) A (1) + 1 = B (2)

For the second letter, the pattern is to subtract 2 from the positional value of the previous letter: Q (17) - 2 = O (15) O (15) - 2 = M (13) M (13) - 2 = K (11) K (11) - 2 = I (9)

For the third letter, the pattern is to add 3 to the positional value of the previous letter: N (14) + 3 = Q (17) Q (17) + 3 = T (20) T (20) + 3 = W (23) W (23) + 3 = Z (26)

For the fourth letter, the pattern is to subtract 4 from the positional value of the previous letter: H (8) - 4 = D (4) D (4) - 4 = Z (26) Z (26) - 4 = V (22) V (22) - 4 = R (18)

Combining these letters yields the cluster AKWV.

Explanation

The relation between the first number x and the second number y in each pair is defined by the formula:

y = 3x² - 1

Applying this formula to the first pair where x = 3: 3 × 3² - 1 = 3 × 9 - 1 = 26

Applying this formula to the third pair where x = 5: 3 × 5² - 1 = 3 × 25 - 1 = 74

Applying the same formula to the missing number where x = 7: 3 × 7² - 1 = 3 × 49 - 1 = 146

Explanation

The coding pattern simply reverses the order of the letters of the given word.

In COUNTY, reversing the letters C-O-U-N-T-Y gives Y-T-N-U-O-C. In DEFEAT, reversing the letters D-E-F-E-A-T gives T-A-E-F-E-D.

Applying this same reversing rule to FAMILY: F-A-M-I-L-Y when written in reverse order becomes Y-L-I-M-A-F.

Explanation

To find the day of the week on 28 March 2008, we calculate the total number of odd days from 13 January 2006 to 28 March 2008.

First, we calculate the odd days between 13 January 2006 and 13 January 2008. Since both 2006 and 2007 are ordinary years of 365 days each, they contribute 1 odd day each, totaling 2 odd days.

Next, we count the days from 13 January 2008 to 28 March 2008: Remaining days in January 2008: 31 - 13 = 18 days, which has 4 odd days (18 mod 7) Days in February 2008: 2008 is a leap year, so it has 29 days, which has 1 odd day (29 mod 7) Days in March 2008: 28 days, which has 0 odd days (28 mod 7)

Summing these gives 4 + 1 + 0 = 5 odd days for this period.

Adding the odd days from the years and the months gives 2 + 5 = 7 odd days. Because 7 odd days is equivalent to 0 odd days (7 mod 7 = 0), the day of the week remains unchanged.

Explanation

To solve this relation step-by-step, we break down Vishal's statement from the end: First, my sister's father is Vishal's father. Second, the wife of Vishal's father is Vishal's mother. Therefore, the statement "Her mother is the wife of my sister's father" translates to "Her mother is Vishal's mother". Since the woman in the picture and Vishal share the same mother, the woman is Vishal's sister.

Explanation

To analyze the validity of the conclusions, we can use Venn diagrams to represent the relations between the classes of sparrows, peacocks, and birds.

The first statement, "All sparrows are peacocks", means the class of sparrows is entirely contained within the class of peacocks.

The second statement, "Some peacocks are birds", means there is a common region between the class of peacocks and the class of birds.

Conclusion I, "All birds are sparrow", is invalid because there is no direct relationship established between birds and sparrows. The set of birds and the set of sparrows may not even overlap, making it impossible to definitely conclude that all birds are sparrows.

Conclusion II, "Some sparrows are not birds", is also invalid. Since both premises are positive, a definite negative conclusion cannot be drawn. It is possible for the set of sparrows to be entirely contained within the set of birds while satisfying both statements. Since this conclusion is not definitely true in all possible scenarios, it does not logically follow.

Explanation

The letters of each word are shifted by a specific pattern of positions from left to right to obtain the corresponding term. The pattern of shift is +2, +1, +3, +1, +2.

Applying this pattern to PLANK: P + 2 = R L + 1 = M A + 3 = D N + 1 = O K + 2 = M This gives RMDOM.

Applying this pattern to TABLE: T + 2 = V A + 1 = B B + 3 = E L + 1 = M E + 2 = G This gives VBEMG.

Applying the same pattern to ZEBRA: Z + 2 = B E + 1 = F B + 3 = E R + 1 = S A + 2 = C This gives BFESC.

Explanation

The logic followed in the given pairs is that the second number is obtained by multiplying the first number by 5 and then subtracting 1.

First pair: 34 × 5 - 1 = 170 - 1 = 169

Second pair: 42 × 5 - 1 = 210 - 1 = 209

Applying the same mathematical relation to the fifth number: 28 × 5 - 1 = 140 - 1 = 139

Explanation

The logic followed in the given analogy is: Second term = (First term - 2) × 8

Applying this logic to the given pairs: First pair: (8 - 2) × 8 = 6 × 8 = 48 Third pair: (16 - 2) × 8 = 14 × 8 = 112

Applying the same logic to the second pair: (19 - 2) × 8 = 17 × 8 = 136

Explanation

To find the day of the week on 31 August 2009 when 31 August 2000 is given as Friday, we calculate the number of odd days between these two dates.

The total number of years between 31 August 2000 and 31 August 2009 is 9 years.

Among these years, we determine the number of leap years. Since 31 August 2000 falls after February, its extra day is already passed and not counted. The leap years that fall completely within this 9-year interval are 2004 and 2008.

Thus, in this 9-year period, there are: 2 leap years, which contribute 2 odd days each 7 ordinary years, which contribute 1 odd day each

Total odd days = (2 × 2) + (7 × 1) = 4 + 7 = 11 odd days.

Dividing 11 by 7 to find the net odd days gives a remainder of 4 (11 ≡ 4 mod 7).

Adding 4 odd days to Friday results in Tuesday.

Explanation

Substituting the signs in option C into the equation 14 11 97 67 10 gives:

14 × 11 - 97 = 67 - 10

Solving the left-hand side of the equation: 14 × 11 - 97 = 154 - 97 = 57

Solving the right-hand side of the equation: 67 - 10 = 57

Both sides yield 57, balancing the equation.

Explanation

The pattern followed in each row of the given matrix is that the sum of the first two numbers, when multiplied by -3, yields the third number.

In the first row, the sum of the first two numbers is 58 + (-28) = 30. Multiplying this sum by -3 gives 30 × (-3) = -90, which is the third number.

In the second row, the sum of the first two numbers is -17 + 21 = 4. Multiplying this sum by -3 gives 4 × (-3) = -12, which is the third number.

Following the same pattern in the third row, the sum of the first two numbers is -8 + (-7) = -15. Multiplying this sum by -3 gives -15 × (-3) = 45.

Explanation

The mathematical operation followed in the number pairs is the reversal of the digits of the first number to obtain the second number. For any four-digit number represented by the digits ABCD, the corresponding second number is DCBA. Reversing the digits of 4328 should result in 8234, but the given second number is 8324, which does not follow this reversal rule.

Explanation

Comparing the first statement, 'you can do' written as 'mat hat pat', with the third statement, 'they do think' written as 'ant hat cat', the common word is 'do' and the common code is 'hat'. This means 'do' is coded as 'hat'.

Comparing the second statement, 'They can work' written as 'rat pat ant', with the third statement, 'they do think' written as 'ant hat cat', the common word is 'they' and the common code is 'ant'. This means 'they' is coded as 'ant'.

In the third statement, 'they do think' is represented by the codes 'ant hat cat'. Since 'they' is coded as 'ant' and 'do' is coded as 'hat', the remaining word 'think' must be coded as 'cat'.

Explanation

The coding pattern keeps the first and last letters of the word in their original positions while reversing the order of the remaining middle letters.

In the word PIZZA, the first letter P and the last letter A remain unchanged, while the middle letters I, Z, Z are reversed to Z, Z, I, resulting in PZZIA.

In the word CHEESE, the first letter C and the last letter E remain unchanged, while the middle letters H, E, E, S are reversed to S, E, E, H, resulting in CSEEHE.

Applying this same rule to the word PASTA, the first letter P and the last letter A remain in their positions, while the middle letters A, S, T are reversed to T, S, A, which gives PTSAA.