SSC CGL Tier 1 2013 General Intelligence & Reasoning Questions with Solutions

Explanation

To find the least number to be subtracted from 2486 to make it a perfect square, we find the square root of 2486 using the long division method or by identifying the nearest lower perfect square. Since 50² = 2500, we calculate the square of 49. Using the identity (a - b)² = a² - 2ab + b², we have 49² = (50 - 1)² = 2500 - 100 + 1 = 2401.

The difference between the given number and this perfect square represents the least value that must be subtracted. Performing the subtraction, we get 2486 - 2401 = 85. Using the long division method, we group the digits as 24 and 86. The largest square less than 24 is 4² = 16, leaving a remainder of 8. Bringing down 86 gives 886. Doubling the quotient 4 gives 8; the largest digit x such that (80 + x) × x ≤ 886 is 9, since 89 × 9 = 801. The final remainder is 886 - 801 = 85.

Explanation

Let the starting point be the origin (0, 0). Shiela and Belah move 10 km in opposite directions, reaching coordinates (10, 0) and (-10, 0). Shiela turns left from the positive x-axis, moving 10 km in the positive y-direction to reach (10, 10). Belah turns right from the negative x-axis, also moving 10 km in the positive y-direction to reach (-10, 10). Using the distance formula for two points (x₁, y₁) and (x₂, y₂):

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates (10, 10) and (-10, 10):

d = √((-10 - 10)² + (10 - 10)²)

d = √((-20)² + 0²) = 20 km

Explanation

The height relationships can be established step-by-step from the given statements. First, Roshan is taller than Hardik (Roshan > Hardik) and Susheel is also taller than Hardik (Susheel > Hardik). Second, the statement that Susheel is shorter than Roshan (Roshan > Susheel) confirms that Roshan is taller than both Susheel and Hardik. Third, Niza is shorter than Hardik but taller than Harry (Hardik > Niza > Harry). By combining these inequalities, the complete order from tallest to shortest is Roshan > Susheel > Hardik > Niza > Harry. In this hierarchy, Roshan is at the top.

Explanation

The word POINTER requires the letter R. Upon examining the letters available in the word DISAPPOINTMENT, which are D, I, S, A, P, O, N, T, M, and E, it is evident that the letter R is not present. Therefore, it is impossible to construct the word POINTER using the given letters.

Explanation

The word DOCTOR cannot be formed from the letters of DECOMPOSITION because the letter R is not present in the source word. While the letters D, O, C, and T are available in DECOMPOSITION, the absence of the letter R makes it impossible to construct the word DOCTOR.

Explanation

The word CANCEL cannot be formed from the letters of INTELLIGENCE because it requires the letter A, which is entirely absent from the original word. Furthermore, CANCEL requires two instances of the letter C, while the word INTELLIGENCE contains only a single letter C.

Explanation

In the series BEJQZ, the positions of the letters in the English alphabet are B (2), E (5), J (10), Q (17), and Z (26). The number of letters skipped between adjacent letters is determined by the formula n = (p₂ - p₁) - 1, where p₁ and p₂ are the numerical positions of the letters. Between B and E, the number of letters skipped is (5 - 2) - 1 = 2. Between E and J, the number of letters skipped is (10 - 5) - 1 = 4. Between J and Q, the number of letters skipped is (17 - 10) - 1 = 6. Between Q and Z, the number of letters skipped is (26 - 17) - 1 = 8. The series of skipped letters consists of 2, 4, 6, and 8, which are successive even numbers.

Explanation

According to the given instructions, the symbols are mapped as follows: x → +

• → ÷ < → -

→ ×

• → = ÷ → > = → <

To verify option (a), we substitute the mapped symbols into the expression: 5 × 8 + 4 = 10 < 4 × 8 becomes: 5 + 8 ÷ 4 < 10 - 4 + 8

Following the BODMAS rule, we evaluate the left-hand side (LHS) and the right-hand side (RHS) of the relational operator (<):

LHS: 5 + (8 ÷ 4) = 5 + 2 = 7 RHS: 10 - 4 + 8 = 6 + 8 = 14

Substituting these values back into the inequality: 7 < 14

Since 7 is indeed less than 14, the statement is true.

Explanation

The total number of questions physically appearing in the question paper is the sum of the main questions and their alternatives. There are 12 main questions listed in the paper. Six of these questions have an alternative each, which adds 6 more distinct questions to the total count. Therefore, the total number of questions printed on the paper is 12 + 6 = 18. Since each of these 18 questions consists of 4 parts, the total number of questions including parts is calculated as 18 × 4 = 72.

Explanation

The coding pattern involves shifting each letter of the word forward by a decreasing sequence of integers starting from 13. For the word MOBILE, the transformation is as follows: M + 13 = Z (13 + 13 = 26), O + 12 = A (15 + 12 = 27, which corresponds to position 1 in a 26-letter cycle), B + 11 = M (2 + 11 = 13), I + 10 = S (9 + 10 = 19), L + 9 = U (12 + 9 = 21), and E + 8 = M (5 + 8 = 13).

Applying the same logic to TUMOR: The first letter T (20) is shifted by 13: 20 + 13 = 33. Subtracting the 26 letters of the alphabet gives 7, which is G. The second letter U (21) is shifted by 12: 21 + 12 = 33. Subtracting 26 gives 7, which is G. The third letter M (13) is shifted by 11: 13 + 11 = 24, which is X. The fourth letter O (15) is shifted by 10: 15 + 10 = 25, which is Y. The fifth letter R (18) is shifted by 9: 18 + 9 = 27. Subtracting 26 gives 1, which is A.

Following these steps, TUMOR is coded as GGXYA.

Explanation

The logic of the given sequence is determined by finding the sum of all individual digits in the expression and multiplying that sum by 1.5. For 55 + 66, the calculation is (5 + 5 + 6 + 6) × 1.5 = 22 × 1.5 = 33. For 22 + 99, the calculation is (2 + 2 + 9 + 9) × 1.5 = 22 × 1.5 = 33. Following this established pattern for the target expression 44 + 88, the sum of the digits is 4 + 4 + 8 + 8 = 24. Multiplying this sum by the constant factor gives 24 × 1.5 = 36. Another way to express this shortcut is that since each number consists of two identical digits, the result is three times the sum of the unique digits, yielding (4 + 8) × 3 = 36.

Explanation

The sequence follows a mathematical pattern where each subsequent number is determined by subtracting the value formed by its first three digits from the number itself. This can be expressed by the formula Tₙ₊₁ = Tₙ - ⌊ Tₙ / 10 ⌋, where Tₙ is the current term.

Starting with the first term: 3917 - 391 = 3526

Applying the same rule to the second term to find the missing value: 3526 - 352 = 3174

To verify the pattern with the final term: 3174 - 317 = 2857

The calculation confirms that 3174 is the correct missing number in the series.

Explanation

The series follows a pattern where each subsequent number is obtained by multiplying the previous number by 2 and then adding a progressively increasing integer starting from 1. The steps are: 5 × 2 + 1 = 11 11 × 2 + 2 = 24 24 × 2 + 3 = 51 51 × 2 + 4 = 106 Following this logic, the missing number is calculated by multiplying the last term by 2 and adding the next integer in the sequence, which is 5: 106 × 2 + 5 = 212 + 5 = 217

Explanation

The rate of pipe A is 1/5 of the tank per hour. When the leak is active, the time taken to fill the tank increases to 5 + 3 = 8 hours, making the net filling rate 1/8 of the tank per hour. The rate of the leak can be found using the relation:

Leak Rate = Rate of Pipe A - Net Rate

Substituting the values: Leak Rate = ⅕ - ⅛ = (8 - 5)/(40) = ³⁄₄₀ tank per hour

The time taken by the leak to empty the full tank is the reciprocal of its rate: Time = ⁴⁰⁄₃ hours = 13⅓ hours

To convert the fractional part into minutes: ⅓ × 60 = 20 minutes

Thus, the leak will take 13 hours 20 minutes to empty the full tank.

Explanation

Point X serves as the starting reference for both individuals. A initially walks 3 m away from X and then moves an additional 4 m in the North direction. This results in A being at a total distance of 3 m + 4 m = 7 m North from point X.

B initially walks 4 m away from point X in the opposite direction (South) and then travels another 5 m further South. This results in B being at a total distance of 4 m + 5 m = 9 m South from point X.

Because A is 7 m to the North of point X and B is 9 m to the South of point X, they are positioned on a straight line on opposite sides of the starting point. The total distance between them is the sum of their displacements from X: Distance = 7 m + 9 m = 16 m

Explanation

Based on Statement (I), the set of all cities is contained within the set of towns (C ⊆ T). Statement (II) establishes that there is an overlap between the set of cities and the set of villages (C ∩ V ≠ ∅). Because every city is also a town, any element that exists in the intersection of cities and villages must also belong to the set of towns. This confirms that the intersection of villages and towns is not empty (V ∩ T ≠ ∅), which logically validates the conclusion that some villages are towns.

Explanation

In logical reasoning, a conclusion is valid only if it is a necessary and direct consequence of the given statement. The statement Sun is the source of light identifies the Sun as a source but does not include restrictive qualifiers such as only, sole, or exclusive. Without such qualifiers, the statement does not imply that the Sun is the only source of light, making Conclusion II logically unsustainable. Similarly, the statement provides information exclusively about the Sun and contains no data regarding the Moon. Therefore, Conclusion I cannot be derived because the premise does not provide a basis to confirm or deny the light-emitting properties of any other object. Since neither conclusion is supported by the specific scope of the premise, neither follows.

Explanation

The relationship in the analogy is between an alcoholic beverage and its primary raw material. Wine is produced through the fermentation of grapes. Similarly, whiskey is a distilled spirit manufactured from a fermented mash of cereal grains. Among the given choices, oats are a specific type of grain historically and traditionally used in the production of various styles of whiskey.

Explanation

The relationship between the terms in each pair is defined by the product of two numbers with a difference of 10, where the factors of the second term are each 20 units greater than the factors of the first term. This can be expressed by the pattern n(n + 10) : (n + 20)(n + 30).

For the first pair, 600 is the product of 20 and 30. Following the pattern, the second term is calculated by adding 20 to each factor: (20 + 20) × (30 + 20) = 40 × 50 = 2000.

Applying this logic to the second pair, we analyze the term 9000. It is the product of two factors with a difference of 10, namely 90 and 100. To find the preceding term in the analogy, we subtract 20 from each of these factors. The first factor becomes 90 - 20 = 70 and the second factor becomes 100 - 20 = 80. The product of these adjusted factors is 70 × 80 = 5600.

Explanation

The relationship between the sets of letters is based on the concept of opposite letters in the alphabet, where the sum of the positions of two corresponding letters is always 27. In the first pair XZG : CAT, X is the 24th letter and C is the 3rd letter (24 + 3 = 27), Z is the 26th letter and A is the 1st letter (26 + 1 = 27), and G is the 7th letter and T is the 20th letter (7 + 20 = 27). Following this pattern for DOG, D is the 4th letter, so its opposite is the 23rd letter W (27 - 4 = 23). O is the 15th letter, making its opposite the 12th letter L (27 - 15 = 12). G is the 7th letter, making its opposite the 20th letter T (27 - 7 = 20). Thus, DOG relates to WLT.

Explanation

The series consists of 16 positions in total. By dividing the sequence into four equal groups of four letters each, the pattern becomes _aab | ab_a | b_ab | _bba. Substituting the letters b, b, a, and a from the first option into the respective gaps creates the sequence baab | abba | baab | abba. This demonstrates a logical repeating pattern where the first and third blocks are identical (baab) and the second and fourth blocks are identical (abba), with each block forming a palindrome.

Explanation

The letter series follows a pattern where a block of four letters is repeated, with the letter b shifting its position one place to the left in each successive block. The four-block cycle is as follows:

Block 1: aaab (b is in the 4th position) Block 2: aaba (b is in the 3rd position) Block 3: abaa (b is in the 2nd position) Block 4: baaa (b is in the 1st position)

By sequentially placing the letters from option a) abba into the gaps, we complete this logical sequence:

aa(a)b / aa(b)a / a(b)aa / (a)baa

In this arrangement: The first gap is filled by a to complete the first block: aaab. The second gap is filled by b to complete the second block: aaba. The third gap is filled by b to complete the third block: abaa. The fourth gap is filled by a to complete the fourth block: baaa.

This cyclic shifting of the letter b within the four-letter groups correctly completes the series.

Explanation

The first letter of each term follows an alphabetical increment of 2. C is the 3rd letter, E is the 5th, G is the 7th, and I is the 9th. Following this sequence, the next letter is the 11th letter of the alphabet, which is K.

The middle numerical sequence follows the rule xₙ = (xₙ₋₁ × 2) + k, where k is an increasing integer starting from 1. The sequence progresses as (2 × 2) + 1 = 5, then (5 × 2) + 2 = 12, and (12 × 2) + 3 = 27. Applying the next step in the pattern, the missing number is (27 × 2) + 4 = 58.

The last letter of each term follows an alphabetical increment of 3. E is the 5th letter, H is the 8th, K is the 11th, and N is the 14th. Following this +3 pattern, the next letter is the 17th letter of the alphabet, which is Q. Combining the first letter K, the middle number 58, and the last letter Q yields the term K58Q.

Explanation

Each term in the series consists of three letters where the position of each subsequent letter is determined by adding 3 to the alphabetical position of the preceding letter. In the first term BEH, the numerical positions are B(2) +3 E(5) +3 H(8). In the second term DGJ, the positions are D(4) +3 G(7) +3 J(10). In the third term NQT, the positions are N(14) +3 Q(17) +3 T(20).

The missing term JMP follows this identical internal logic, as the alphabetical positions of the letters J, M, and P are 10, 13, and 16 respectively, maintaining the constant +3 interval (10 +3 13 +3 16).

Explanation

The series consists of three patterns involving two letters and a number in each term. The first letters follow a reverse alphabetical order: Z → Y → X → W, leading to V as the next letter. The second alphabetical sequence follows a forward order: A → B → C → D, leading to E as the next letter.

The numerical part follows an alternating sequence where the difference increases by one each time: 5 - 1 = 4, 4 + 2 = 6, and 6 - 3 = 3. Following this pattern of -1, +2, -3, the next operation is +4, resulting in 3 + 4 = 7. Additionally, the position of the number alternates between the third and second spots in each term. In ZA5 the number is third, in Y4B it is second, in XC6 it is third, and in W3D it is second. Therefore, in the fifth term, the number 7 must occupy the third position. Combining the first letter V, the second letter E, and the number 7 at the end gives VE7.

Explanation

The series follows a consistent pattern where each corresponding letter in a term is shifted forward by five positions in the English alphabet to form the next term.

For the first letter of each term, the progression is d (4) to i (9), i (9) to n (14), and n (14) to the next letter. Adding 5 to n (14) results in 19, which is the letter s. Verifying the final step, s (19) plus 5 yields x (24).

For the second letter, the progression is e (5) to j (10), j (10) to o (15), and o (15) to the next letter. Adding 5 to o (15) results in 20, which is the letter t. Verifying the final step, t (20) plus 5 yields y (25).

For the third letter, the progression is b (2) to g (7), g (7) to l (12), and l (12) to the next letter. Adding 5 to l (12) results in 17, which is the letter q. Verifying the final step, q (17) plus 5 yields v (22).

By combining these results, the missing term in the sequence is identified as stq.

Explanation

The pair 543 and 453 is the odd one out because the second number is not a left cyclic permutation of the first. In a left cyclic shift, the first digit of a number is moved to the last position, as seen in the transformation abc → bca. Applying this operation to the number 543 would result in 435 (543 → 435). Since the provided second number is 453, it does not follow this specific positional digit-rotation logic.

Explanation

Thekkady is the name of a town in Kerala that serves as the gateway to the Periyar National Park and Wildlife Sanctuary. In contrast, Vedanthangal, Bandipur, and Mudumalai are the actual names of the wildlife sanctuaries and national parks themselves. While the first three terms refer directly to the specific protected biological reserves, Thekkady refers to the geographic location or settlement adjacent to the Periyar reserve.

Explanation

Google is a search engine and a web-based service provider, which differentiates it from the software applications known as web browsers. A search engine is a tool used to index and retrieve information from the internet, whereas a web browser is the interface used to access such platforms and other online content. While browsers are locally installed software programs, a search engine is an online service accessed through them.

Explanation

An ally is a person, group, or nation that cooperates with or supports another for a common purpose. This term signifies partnership and mutual assistance, which is the opposite of the other three words that all describe a person who competes with, opposes, or acts as a rival or enemy toward someone else.

Explanation

Diagonal is the odd word because it represents a line segment connecting two non-adjacent vertices within a polygon, rather than being a complete geometric shape or figure itself. It is a structural component of a polygon, whereas the others are names of specific two-dimensional closed figures.

Explanation

The sequence follows a pattern where each element in a given set is the square of the corresponding element in the immediately preceding set. If we represent the sets as (xₙ, yₙ, zₙ), the relationship is defined by xₙ₊₁ = xₙ², yₙ₊₁ = yₙ², and zₙ₊₁ = zₙ².

Applying this to the second elements of the sets, the sequence is 3, 9, 81, and the next term is 81² = 6561. Applying this to the third elements, the sequence is 2, 4, 16, and the next term is 16² = 256. The pattern is consistent with the first elements as well, where 4, 16, 256, and 256² = 65536. Therefore, the missing numbers in the fourth set are 6561 and 256.

Explanation

The sequence follows a pattern where each term is divided into two parts: the first two digits and the last two digits.

For the first two digits, the sequence is 23, 45, ?, 89. Each term in this sub-sequence increases by a constant value of 22: 23 + 22 = 45 45 + 22 = 67 67 + 22 = 89 Thus, the first two digits of the missing number are 67.

For the last two digits, the sequence is 11, 29, ?, 89. The differences between these terms increase by 8 each time: 29 - 11 = 18 55 - 29 = 26 (where 26 = 18 + 8) 89 - 55 = 34 (where 34 = 26 + 8) Thus, the last two digits of the missing number are 55.

Alternatively, the pattern can be observed by looking at the difference between the full four-digit numbers. The difference between 4529 and 2311 is 2218. The difference between the next two terms increases by 8, making it 2218 + 8 = 2226. Adding this to the second term gives 4529 + 2226 = 6755. Verifying with the final term, 6755 + (2226 + 8) = 6755 + 2234 = 8989. Combining these observations confirms the missing number is 6755.

Explanation

The series follows a pattern where each subsequent number is obtained by adding a decreasing integer to the previous term. Calculating the differences between the known consecutive terms reveals the logic: 30 - 21 = 9 38 - 30 = 8

Following this descending sequence of differences (9, 8, 7, 6, 5, 4), the next increment must be 7. Adding this to the preceding term results in 38 + 7 = 45. This value is confirmed by checking the subsequent terms in the provided sequence: 45 + 6 = 51 51 + 5 = 56 56 + 4 = 60

The pattern of additions +9, +8, +7, +6, +5, +4 is consistent throughout the entire series.

Explanation

The series is based on the addition of increasing multiples of 8 to each preceding term. The difference between the first and second terms is 14 - 6 = 8. The difference between the second and third terms is 30 - 14 = 16. These differences form an arithmetic progression where each step increases the difference by 8 (8, 16, 24, …). To find the missing number, the next difference of 16 + 8 = 24 is added to the third term, resulting in 30 + 24 = 54.

Explanation

The arrangement of the six girls in a circle facing the centre is directly established by the conditions given in the problem. The statement explicitly mentions that Subbu is positioned to the left of Pappu. By placing Pappu at a fixed point, Subbu is located at the immediate next position in the clockwise direction. Revathi is placed between Subbu and Nisha, which completes one side of the circle. On the other side, Aruna is placed between Pappu and Keerthana. This specific circular sequence—Pappu, Subbu, Revathi, Nisha, Keerthana, Aruna—satisfies all the positional constraints provided. Since the question asks for the person to the left of Pappu, the answer is directly found in the initial premise of the arrangement.

Explanation

Naseebah begins at a starting point and travels 10km East. Her first left turn moves her 6km North. The second left turn changes her direction to West, and she travels 6km in this direction. At this stage, her horizontal distance from the starting point is 10km - 6km = 4km, and she is still 6km North of the original line of travel. Her final left turn directs her South for 6km, which brings her back exactly to the East-West line of her starting point. Consequently, she is located 10km - 6km = 4km away from the starting point along the original eastern path.

Explanation

The provided mapping of symbols is: = stands for ÷, + stands for -, × stands for =, - stands for >, > stands for +, < stands for ×, and ÷ stands for <.

Substituting these symbols into the expression in option a: 4 < 2 + 5 + 8 × 5 4 × 2 - 5 - 8 = 5

Following the order of operations, first perform the multiplication: 8 - 5 - 8 = 5

Then perform the subtractions from left to right: 3 - 8 = 5 -5 = 5

The resulting statement is mathematically incorrect, identifying this option as the wrong one among the choices.

Explanation

The word TENDENTIOUS contains the following letter frequencies: T appears twice, E appears twice, N appears twice, D appears once, I appears once, O appears once, U appears once, and S appears once. To form the word INTENTION, one requires three instances of the letter N and two instances of the letter I. Since the source word TENDENTIOUS only provides two Ns and a single I, it is impossible to construct the word INTENTION using only the letters available.

Explanation

The word TERMINAL cannot be formed from the letters of the word INTERNATIONAL because the letter M is not present in the source word. While all other letters in TERMINAL can be found within INTERNATIONAL, the absence of the letter M makes it impossible to construct this specific alternative.

Explanation

The word REPRIEVE requires the letter V, which is entirely absent from the source word DEPRECIATE. In addition to the missing letter V, REPRIEVE also requires two instances of the letter R, whereas the word DEPRECIATE contains only one R. This makes the word impossible to form because the necessary character V and the required quantity of the character R are not available in the original set of letters.

Explanation

Substituting the signs ×, -, and ÷ in the given equation 8 6 96 * 2 = 0, we get the expression 8 × 6 - 96 ÷ 2 = 0. Following the BODMAS rule, the division operation is performed first, where 96 ÷ 2 = 48. This simplifies the equation to 8 × 6 - 48 = 0. Next, the multiplication operation is carried out, giving 8 × 6 = 48. Finally, subtracting the values results in 48 - 48 = 0. This satisfies the equation as both sides equal zero.

Explanation

The expression 12Q15P3R4S6 is evaluated by substituting the letter symbols with their corresponding mathematical operators and following the BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) rule. Based on the operations required to reach the result, Q denotes multiplication (×), P denotes division (÷), R denotes addition (+), and S denotes subtraction (-).

Substituting these operators into the expression, we get: 12 × 15 ÷ 3 + 4 - 6

Following the order of operations, we first perform the division: 15 ÷ 3 = 5

The expression now becomes: 12 × 5 + 4 - 6

Next, we perform the multiplication: 12 × 5 = 60

Then, we perform the addition: 60 + 4 = 64

Finally, we perform the subtraction: 64 - 6 = 58

Explanation

To find the value of the given expression, substitute the provided alphabetical symbols with their corresponding mathematical operators. Replacing R with division, A with addition, Q with subtraction, and V with multiplication, the expression 225 R 5 A 64 Q 13 V 6 is rewritten as: 225 ÷ 5 + 64 - 13 × 6

According to the BODMAS rule, operations must be performed in the sequence of Division, Multiplication, Addition, and Subtraction.

First, perform the division: 225 ÷ 5 = 45

Next, perform the multiplication: 13 × 6 = 78

The expression now simplifies to: 45 + 64 - 78

Now, perform the addition: 45 + 64 = 109

Finally, perform the subtraction: 109 - 78 = 31

Explanation

The numerical value assigned to each letter follows the formula V = 2n, where n is the standard rank of the letter in the English alphabet (A=1, B=2, …, Z=26). For the word INDIA, the standard positions are I = 9, N = 14, D = 4, I = 9, and A = 1. The total value is calculated by substituting these positions into the formula and summing the results: Total Value = (2 × 9) + (2 × 14) + (2 × 4) + (2 × 9) + (2 × 1) Total Value = 18 + 28 + 8 + 18 + 2 = 74 Alternatively, the sum of the alphabetical ranks can be multiplied by the factor of 2: Total Value = 2 × (9 + 14 + 4 + 9 + 1) = 2 × 37 = 74

Explanation

The coding logic involves shifting each letter of the word backward by three positions in the alphabetical order. In the word STYLE, the transformations are S (19) to P (16), T (20) to Q (17), Y (25) to V (22), L (12) to I (9), and E (5) to B (2).

Applying the same subtraction of 3 to the word SMELL: S (19 - 3 = 16) results in P. M (13 - 3 = 10) results in J. E (5 - 3 = 2) results in B. L (12 - 3 = 9) results in I. L (12 - 3 = 9) results in I.

Following this pattern, SMELL is encoded as PJBII.

Explanation

Let the starting point (Ram's house) be the origin (0, 0) on a Cartesian plane where the y-axis represents North-South and the x-axis represents East-West. Ram walks 10 m South to (0, -10). Turning left from South means he moves East; walking 25 m East brings him to (25, -10). Turning left from East means he moves North; walking 40 m North brings him to (25, 30) since -10 + 40 = 30. Finally, turning right from North means he moves East again; walking 5 m East brings him to (30, 30). The final coordinates (30, 30) are positive for both the North and East axes, placing the school in the North-East direction relative to his house.

Explanation

Let the starting point, the school, be at the origin (0, 0). The boy first moves 3 km South, which corresponds to the coordinates (0, -3). From this position, he turns left. Since he was facing South, a left turn directs him towards the East. Moving 2 km East brings his position to (2, -3).

Next, he turns left again. While facing East, a left turn directs him towards the North. Walking 3 km North changes his coordinates to (2, 0). Finally, he turns left one last time. While facing North, a left turn directs him towards the West. Moving 1 km West results in the final coordinates (1, 0). Because the point (1, 0) is located to the right of the origin (0, 0) along the horizontal axis, the home is in the East direction from the school.

Explanation

By comparing the given words and their respective codes, we can identify the specific symbol assigned to each letter through direct substitution.

In the word ANT, which is coded as "x-, the letter A corresponds to ", N corresponds to x, and T corresponds to -.

In the word SENT, which is coded as +ˣ-, the letter S corresponds to +, E corresponds to ^, N corresponds to x, and T corresponds to -.

To determine the code for the word TEN, we extract the symbols for each letter: The symbol for T is -. The symbol for E is ^. The symbol for N is x.

Arranging these symbols in the order T-E-N results in the code -ˣ.

Explanation

The statement establishes a conditional relationship where intelligence is expected to lead to creativity. Assumption I is valid because any proposition that links two distinct attributes, such as intelligence and creativity, must be based on the underlying premise that these traits are related. Without the assumption of an inherent connection, the if-then statement would lack a logical basis. Assumption II is invalid because the statement specifies a directional expectation from intelligence to creativity but does not provide grounds to assume the reverse. In formal logic, the premise if P then Q implies that P leads to Q, but it does not necessitate that all instances of Q must have originated from P. Therefore, while intelligence is linked to creativity here, the statement does not support the assumption that all creative individuals are necessarily intelligent.