Logical Reasoning

1. A. B, A, D, C
2. B. B, A, C, D
3. C. A, A, C, D
4. D. A, A, D, C

Answer: C

Explanation

Let’s analyze the given sequence: A_BCD_BBCDABC_DABC_D. The pattern appears to be a repeating block where one letter is duplicated in each subsequent block. Let’s assume the base block is ABCD. The pattern seems to be:
1. A A BCD (A is duplicated)
2. A B BCD (B is duplicated)
3. A B C C D (C is duplicated)
4. A B C D D (D is duplicated)
Applying this pattern to the given sequence:
– For A_BCD, the first block should be A A BCD. So, the first blank is A.
– For _BBCD, the second block should be A B BCD. So, the second blank is A.
– For ABC_D, the third block should be A B C C D. So, the third blank is C.
– For ABC_D, the fourth block should be A B C D D. So, the fourth blank is D.
Therefore, the missing letters are A, A, C, D. This is a complex series completion problem requiring careful pattern recognition.

1. A. 3 times
2. B. 4 times
3. C. 5 times
4. D. 6 times

Answer: A

Explanation

The hour and minute hands coincide 11 times in every 12-hour period (or 22 times in 24 hours). This is because they coincide once every hour, except for the period between 11 and 1 o’clock, where they coincide only once, exactly at 12 o’clock. Let’s count the coincidences in the given time frame: 10:00 a.m. to 2:00 p.m. (a 4-hour period).
1. Between 10:00 a.m. and 11:00 a.m.: The hands coincide once (around 10:55 a.m.).
2. Between 11:00 a.m. and 12:00 p.m.: The hands coincide exactly at 12:00 p.m. (noon).
3. Between 12:00 p.m. and 1:00 p.m.: The hands coincide only at 12:00 p.m., which has already been counted. There is no other coincidence in this hour.
4. Between 1:00 p.m. and 2:00 p.m.: The hands coincide once (around 1:05 p.m.).
Total coincidences = 1 (10-11) + 1 (at 12:00) + 1 (1-2) = 3 times. This question tests knowledge of clock problems, specifically the relative movement and coincidences of the hands.

1. A. 2029
2. B. 2030
3. C. 2031
4. D. 2033

Answer: C

Explanation

A calendar repeats when the total number of odd days accumulated from the given year to the repeating year becomes a multiple of 7 (i.e., 0 odd days). A normal year has 1 odd day, and a leap year has 2 odd days. We start counting from the year after the given year (2025).
– 2025: 1 odd day
– 2026: 1 odd day (Cumulative: 2)
– 2027: 1 odd day (Cumulative: 3)
– 2028: 2 odd days (Leap year) (Cumulative: 5)
– 2029: 1 odd day (Cumulative: 6)
– 2030: 1 odd day (Cumulative: 7)
Since the cumulative sum of odd days reaches 7 (which is 0 mod 7) at the end of 2030, the calendar for 2025 will repeat in the year immediately following 2030, which is 2031. This question tests knowledge of calendar concepts and the calculation of odd days.

1. A. 12.5°
2. B. 15°
3. C. 17.5°
4. D. 20°

Answer: C

Explanation

To find the angle between the minute hand and hour hand, we can use the formula: Angle = |30H – (11/2)M|, where H is the hour and M is the minutes. Here, H = 4 and M = 25. Angle = |30 × 4 – (11/2) × 25| = |120 – (275/2)| = |120 – 137.5| = |-17.5| = 17.5°. Alternatively, we can calculate the position of each hand from the 12 o’clock mark. The minute hand moves 6° per minute, so at 25 minutes, it is at 25 × 6° = 150°. The hour hand moves 30° per hour and 0.5° per minute. At 4:25, its position is 4 × 30° + 25 × 0.5° = 120° + 12.5° = 132.5°. The angle between the hands is the absolute difference: |150° – 132.5°| = 17.5°. This question tests knowledge of clock problems and angle calculations.

1. A. North-West
2. B. West
3. C. South
4. D. South-West

Answer: C

Explanation

Let’s assume the person initially walks North and trace the path:
1. Starts at (0,0), walks 100m North: (0, 100).
2. Turns left (now facing West), walks 100m: (-100, 100).
3. Turns left (now facing South), walks 300m: (-100, 100 – 300) = (-100, -200).
4. Turns right (now facing West), walks 100m: (-100 – 100, -200) = (-200, -200).
In this hypothetical scenario, the office is at (-200, -200) relative to the house (0,0), which is in the South-West direction.

The problem states that the office is actually in the North-East direction. South-West is exactly opposite to North-East (180 degrees apart).
This means our initial assumption for the starting direction was 180 degrees off. If assuming North led to South-West, then the actual starting direction must be 180 degrees opposite to North, which is South.

Let’s verify with an initial South direction:
1. Starts at (0,0), walks 100m South: (0, -100).
2. Turns left (now facing East), walks 100m: (100, -100).
3. Turns left (now facing North), walks 300m: (100, -100 + 300) = (100, 200).
4. Turns right (now facing East), walks 100m: (100 + 100, 200) = (200, 200).
The office is at (200, 200) relative to the house (0,0), which is indeed in the North-East direction. Thus, he initially walked South. This question tests direction sense and spatial reasoning.

1. A. South-West
2. B. South-East
3. C. North-West
4. D. North-East

Answer: D

Explanation

Let’s trace the person’s direction:
1. **Walks 100 m Westward**: The person is facing West.
2. **Turns left**: If facing West, a left turn means turning 90 degrees counter-clockwise. This changes the direction to South. The person is now facing South.
3. **Takes a 225-degree turn clockwise**: From facing South:
– A 90-degree clockwise turn from South leads to West.
– Another 90-degree clockwise turn from West leads to North. (Total 180 degrees clockwise).
– Remaining turn: 225 – 180 = 45 degrees clockwise.
– A 45-degree clockwise turn from North leads to North-East.

Alternatively, using degrees (North = 0°, East = 90°, South = 180°, West = 270°):
1. Starts facing West (270°).
2. Turns left (90° counter-clockwise): 270° – 90° = 180° (South).
3. Takes a 225° turn clockwise: 180° + 225° = 405°.
4. To find the final direction, subtract 360° (a full circle): 405° – 360° = 45°.
5. 45° corresponds to the North-East direction. This question tests direction sense and angular turns.

1. A. Only Conclusion-I follows
2. B. Only Conclusion-II follows
3. C. Both Conclusion-I and Conclusion-II follow
4. D. Neither Conclusion-I nor Conclusion-II follows

Answer: D

Explanation

The statement only provides information about India being the largest *producer* of milk. It does not offer any details regarding domestic consumption, demand, or international trade (exports or imports).

– **Conclusion I: India is the world’s largest exporter of milk.** Being the largest producer does not automatically imply being the largest exporter. A country might have high domestic consumption, leaving little surplus for export, or its milk might not be competitive in international markets. Thus, this conclusion does not necessarily follow.
– **Conclusion II: India does not import milk.** Similarly, high production does not guarantee zero imports. If domestic demand exceeds production, or if specific types of milk or dairy products are imported to meet niche demands, India could still be an importer. Thus, this conclusion also does not necessarily follow.

Without additional information on domestic consumption, export policies, or trade balances, neither conclusion can be logically derived from the given statement. This question assesses the ability to draw conclusions strictly based on provided information, avoiding external knowledge or assumptions.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: C

Explanation

We need to find unique natural numbers m and n.

**Statement I: m + n > mn and m > n.**
Let’s test some natural number pairs where m > n:
– If m=2, n=1: 2+1 = 3, 2*1 = 2. Since 3 > 2, (2,1) is a possible pair.
– If m=3, n=1: 3+1 = 4, 3*1 = 3. Since 4 > 3, (3,1) is a possible pair.
Since there are multiple possibilities, Statement I alone is insufficient.

**Statement II: The product of m and n is 24 (mn = 24).**
Possible pairs of natural numbers (m,n):
– (1,24), (2,12), (3,8), (4,6), (6,4), (8,3), (12,2), (24,1).
Since there are multiple possibilities, Statement II alone is insufficient.

**Combining Statement I and Statement II:**
We need to find a pair (m,n) from the list in Statement II that satisfies m + n > mn and m > n.
From Statement II, mn = 24. So the condition m + n > mn becomes m + n > 24.
Let’s check the pairs from Statement II that also satisfy m > n:
1. (24,1): m+n = 25. Is 25 > 24? Yes. So (24,1) is a solution.
2. (12,2): m+n = 14. Is 14 > 24? No.
3. (8,3): m+n = 11. Is 11 > 24? No.
4. (6,4): m+n = 10. Is 10 > 24? No.
Only the pair (24,1) satisfies both conditions. Thus, m=24 and n=1 are uniquely determined.
Therefore, both statements together are sufficient to answer the question. This question tests data sufficiency and number properties.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: C

Explanation

To calculate the time required to download software, we need two pieces of information: the total size of the software and the rate at which it can be transferred.

– **Statement I alone**: Provides only the size of the software (12 megabytes). Without knowing the transfer rate, we cannot determine the time. Thus, Statement I alone is insufficient.
– **Statement II alone**: Provides only the transfer rate (2.4 kilobytes per second). Without knowing the size of the software, we cannot determine the time. Thus, Statement II alone is insufficient.

– **Combining both statements**: We have the software size (12 megabytes) and the transfer rate (2.4 kilobytes per second). To calculate the time, we need to convert units to be consistent. Assuming 1 megabyte = 1000 kilobytes (a common simplification in CSAT, though technically 1024 KB):
Software size = 12 MB = 12 * 1000 KB = 12000 KB.
Transfer rate = 2.4 KB/s.
Time = Total Size / Transfer Rate = 12000 KB / 2.4 KB/s = 5000 seconds.

Since a unique time can be calculated using both statements together, but not individually, option (C) is correct. This question tests data sufficiency in a practical context.

1. A. The question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: C

Explanation

We need to find unique distinct natural numbers x and y.

**Statement I: x/y is odd.**
Possible pairs (x,y) where x/y is an odd natural number:
– If y=1, x can be 3, 5, 7, … (e.g., (3,1), (5,1))
– If y=2, x can be 6, 10, 14, … (e.g., (6,2), (10,2))
Since there are multiple possibilities, Statement I alone is insufficient.

**Statement II: xy = 12.**
Possible pairs (x,y) of distinct natural numbers:
– (1,12), (2,6), (3,4), (4,3), (6,2), (12,1).
Since there are multiple possibilities, Statement II alone is insufficient.

**Combining Statement I and Statement II:**
We need a pair (x,y) from the list in Statement II where x/y is an odd natural number.
– (1,12): x/y = 1/12 (not an integer, so not odd)
– (2,6): x/y = 2/6 = 1/3 (not an integer)
– (3,4): x/y = 3/4 (not an integer)
– (4,3): x/y = 4/3 (not an integer)
– (6,2): x/y = 6/2 = 3 (which is an odd natural number). This gives (x=6, y=2).
– (12,1): x/y = 12/1 = 12 (which is an even natural number, not odd).

The only pair that satisfies both conditions is (6,2). Thus, x=6 and y=2 are uniquely determined.
Therefore, both statements together are sufficient. This question tests data sufficiency and number properties.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: C

Explanation

Let the total amount distributed be T = X + Y + Z.

**Statement I: X received 4/5 of what Y and Z together received.**
X = (4/5)(Y + Z)
Since Y + Z = T – X, we have X = (4/5)(T – X)
5X = 4T – 4X => 9X = 4T => X = 4T/9.
This statement tells us X’s share relative to the total, but we cannot compare X, Y, and Z individually. So, Statement I alone is insufficient.

**Statement II: Y received 2/7 of what X and Z together received.**
Y = (2/7)(X + Z)
Since X + Z = T – Y, we have Y = (2/7)(T – Y)
7Y = 2T – 2Y => 9Y = 2T => Y = 2T/9.
This statement tells us Y’s share relative to the total, but we cannot compare X, Y, and Z individually. So, Statement II alone is insufficient.

**Combining Statement I and Statement II:**
From Statement I, X = 4T/9.
From Statement II, Y = 2T/9.
Since X + Y + Z = T, we can find Z:
(4T/9) + (2T/9) + Z = T
6T/9 + Z = T
2T/3 + Z = T
Z = T – 2T/3 = T/3 = 3T/9.

Now we have the shares:
X = 4T/9
Y = 2T/9
Z = 3T/9
Comparing these values, Y (2T/9) received the least amount. Thus, both statements together are sufficient to answer the question. This question tests data sufficiency and algebraic reasoning with ratios.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: D

Explanation

We need to find the number of students (N) in the class, given that the average marks are 60.

**Statement I: The highest marks in the class are 70 and the lowest marks are 50.**
This statement provides the range of marks but gives no information about the number of students. Thus, Statement I alone is insufficient.

**Statement II: Exclusion of highest and lowest marks from the class does not change the average.**
Let S be the sum of marks of N students. So, S/N = 60 => S = 60N.
Let H be the highest marks and L be the lowest marks. After excluding them, the new sum is S – H – L, and the new number of students is N – 2.
The statement says the new average is still 60: (S – H – L) / (N – 2) = 60.
Substitute S = 60N: (60N – H – L) / (N – 2) = 60.
60N – H – L = 60(N – 2)
60N – H – L = 60N – 120
-H – L = -120 => H + L = 120.
This statement alone tells us that the sum of the highest and lowest marks is 120. It does not provide the number of students (N). Thus, Statement II alone is insufficient.

**Combining Statement I and Statement II:**
From Statement I, H = 70 and L = 50. Their sum is H + L = 70 + 50 = 120.
This value (120) is consistent with the condition derived from Statement II (H + L = 120). However, this consistency does not introduce any new information that allows us to determine N. The equation H + L = 120 does not contain N, so N cannot be found. Therefore, even both statements together are insufficient. This question tests data sufficiency and understanding of averages.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: A

Explanation

We need to find three distinct prime numbers (p1, p2, p3) whose sum (S) is also a prime number.
First, consider the prime number 2. If 2 is one of the three distinct primes, say p1=2, then p2 and p3 must be odd primes. The sum of two odd primes is always an even number. So, S = 2 + (odd + odd) = 2 + even = even. For S to be a prime number, it must be 2. However, the sum of three distinct positive primes cannot be 2. Therefore, 2 cannot be one of the three distinct prime numbers. This means all three primes (p1, p2, p3) must be odd primes, and their sum (S) will also be an odd prime.

**Statement I: Their sum is less than 23.**
Since S must be an odd prime and S < 23, possible values for S are 3, 5, 7, 11, 13, 17, 19.
The smallest sum of three distinct odd primes is 3 + 5 + 7 = 15.
So, S must be either 17 or 19.
– If S = 17: We need three distinct odd primes that sum to 17. Possible combinations: (3, 5, 9 – 9 is not prime), (3, 7, 7 – not distinct). No valid triplet sums to 17.
– If S = 19: We need three distinct odd primes that sum to 19. The only combination is (3, 5, 11). (3+5+11=19, and 19 is prime). This is a unique triplet.
Thus, Statement I alone is sufficient to determine the three numbers as (3, 5, 11).

**Statement II: One of the numbers is 5.**
Let the three primes be 5, p2, p3.
– If (3, 5, 11), sum = 19 (prime). This is a valid triplet.
– If (5, 7, 11), sum = 23 (prime). This is also a valid triplet.
Since there are multiple possible triplets, Statement II alone is insufficient.

Therefore, the question can be answered by using Statement I alone, but not Statement II alone. This question tests data sufficiency and number theory, specifically properties of prime numbers.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: D

Explanation

We need to determine if (x+y) is an integer.

**Statement I: (2x+y) is an integer.**
– Let x = 0.5, y = 1. Then 2x+y = 2(0.5)+1 = 1+1 = 2 (integer). But x+y = 0.5+1 = 1.5 (not an integer).
– Let x = 1, y = 1. Then 2x+y = 2(1)+1 = 3 (integer). And x+y = 1+1 = 2 (integer).
Since (x+y) can be an integer or not, Statement I alone is insufficient.

**Statement II: (x+2y) is an integer.**
– Let x = 1, y = 0.5. Then x+2y = 1+2(0.5) = 1+1 = 2 (integer). But x+y = 1+0.5 = 1.5 (not an integer).
– Let x = 1, y = 1. Then x+2y = 1+2(1) = 3 (integer). And x+y = 1+1 = 2 (integer).
Since (x+y) can be an integer or not, Statement II alone is insufficient.

**Combining Statement I and Statement II:**
We have: (2x+y) = K (an integer) and (x+2y) = M (an integer).
Adding these two equations: (2x+y) + (x+2y) = K + M
3x + 3y = K + M
3(x+y) = K + M.
Since K and M are integers, K+M is also an integer. So, 3(x+y) is an integer.
However, if 3(x+y) is an integer, (x+y) itself is not necessarily an integer. For example, if x=1/3 and y=1/3:
– 2x+y = 2/3 + 1/3 = 1 (integer).
– x+2y = 1/3 + 2/3 = 1 (integer).
– But x+y = 1/3 + 1/3 = 2/3 (not an integer).
Therefore, even with both statements combined, we cannot definitively say if (x+y) is an integer. This question tests data sufficiency and properties of integers and rational numbers.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: C

Explanation

We are given: p + q + r = ₹50 and q = ₹16. We also know that q is the least price, so p ≥ 16 and r ≥ 16.
Substituting q=16 into the total cost equation: p + 16 + r = 50 => p + r = 34.

**Statement I: The cost of p is not more than that of r.** This means p ≤ r.
Given p+r=34 and p,r ≥ 16:
– If p=16, then r=18. This satisfies p ≤ r (16 ≤ 18).
– If p=17, then r=17. This satisfies p ≤ r (17 ≤ 17).
Since p could be 16 or 17, Statement I alone is insufficient to find a unique value for p.

**Statement II: The cost of r is not more than that of p.** This means r ≤ p.
Given p+r=34 and p,r ≥ 16:
– If p=18, then r=16. This satisfies r ≤ p (16 ≤ 18).
– If p=17, then r=17. This satisfies r ≤ p (17 ≤ 17).
Since p could be 17 or 18, Statement II alone is insufficient to find a unique value for p.

**Combining Statement I and Statement II:**
From Statement I, p ≤ r.
From Statement II, r ≤ p.
The only way both conditions can be true simultaneously is if p = r.
Substitute p = r into the equation p + r = 34:
p + p = 34 => 2p = 34 => p = 17.
Since p=17, then r=17. Both are indeed greater than or equal to q=16. Thus, the price of article p is uniquely determined as ₹17.
Therefore, both statements together are sufficient. This question tests data sufficiency and basic algebraic problem-solving.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: D

Explanation

We need to determine if P > Q.

**Statement I: P + Q = R + S.**
This equation alone does not allow us to compare P and Q. For example:
– If P=10, Q=5, R=8, S=7 (P+Q=15, R+S=15). Here P > Q.
– If P=5, Q=10, R=7, S=8 (P+Q=15, R+S=15). Here P Q + R.**
This inequality alone does not allow us to compare P and Q. For example:
– If P=10, S=5, Q=8, R=2 (P+S=15, Q+R=10, so 15>10). Here P > Q.
– If P=8, S=5, Q=10, R=2 (P+S=13, Q+R=12, so 13>12). Here P R = P + Q – S
2. P + S > Q + R
Substitute R from (1) into (2):
P + S > Q + (P + Q – S)
P + S > P + 2Q – S
Subtract P from both sides:
S > 2Q – S
Add S to both sides:
2S > 2Q
S > Q.
This combined information tells us that S scored more marks than Q. However, it does not provide any definitive comparison between P and Q. Therefore, even both statements together are insufficient to answer whether P scored more marks than Q. This question tests data sufficiency and algebraic manipulation of inequalities.

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: A

Explanation

Let the age of P be 10x + y and the age of Q be 10y + x, where x and y are digits from 1 to 9 (since ages are >10 and Q).**
10x + y > 10y + x => 9x > 9y => x > y.
Possible pairs (x,y) satisfying x>y and x,y are digits (y cannot be 0 as Q would be a single digit):
– If x=2, y=1 => P=21, Q=12. Difference = 9.
– If x=3, y=1 => P=31, Q=13. Difference = 18.
– If x=3, y=2 => P=32, Q=23. Difference = 9.
Since the difference is not unique, Statement I alone is insufficient.

**Statement II: The sum of their ages is 11/6 times their difference.**
P + Q = (11/6) * |P – Q|
(10x + y) + (10y + x) = (11/6) * |(10x + y) – (10y + x)|
11x + 11y = (11/6) * |9x – 9y|
11(x + y) = (11/6) * 9 * |x – y|
x + y = (9/6) * |x – y|
x + y = (3/2) * |x – y|
Since x and y are positive digits, x+y is positive. For the equation to hold, |x-y| must also be positive, implying x ≠ y. Also, for x+y to be a multiple of 3/2, x-y must be even. This means x and y must have the same parity. If x-y is positive, then x > y.
2(x + y) = 3(x – y)
2x + 2y = 3x – 3y
5y = x.
Since x and y are single digits (1-9) and y cannot be 0:
– If y=1, then x=5. This gives P = 51 and Q = 15. (P>Q is satisfied, 51>15).
– If y=2, then x=10 (not a single digit). No other solutions.
So, the only unique pair is (x=5, y=1), which means P=51 and Q=15.
The difference in their ages = P – Q = 51 – 15 = 36.
This uniquely determines the ages and their difference. Thus, Statement II alone is sufficient.

Therefore, the question can be answered by using Statement II alone, but not Statement I alone.

1. A. SP only
2. B. RQ only
3. C. Both SP and RQ
4. D. Neither SP nor RQ

Answer: C

Explanation

The Main Statement, ‘Pradeep becomes either a Director or a Producer,’ implies an exclusive OR relationship: Pradeep must be one of the two, and cannot be both (or neither).

Let’s evaluate the given pairs:

1. **SP (S implies P):**
– Statement S: Pradeep is not a Producer.
– Given the Main Statement (either Director OR Producer), if Pradeep is not a Producer, he *must* be a Director.
– This implies Statement P: Pradeep is a Director. This deduction is consistent with the Main Statement.
Therefore, SP is a valid pair.

2. **RQ (R implies Q):**
– Statement R: Pradeep is not a Director.
– Given the Main Statement (either Director OR Producer), if Pradeep is not a Director, he *must* be a Producer.
– This implies Statement Q: Pradeep is a Producer. This deduction is consistent with the Main Statement.
Therefore, RQ is a valid pair.

Since both SP and RQ represent valid logical implications consistent with the Main Statement, the correct answer is (C). This question tests logical deduction and understanding of ‘either/or’ statements.

1. A. 15
2. C. –15
3. D. –25

Answer: D

Explanation

First, replace the mathematical operations in the given expression according to the provided rules:
Original expression: 10 + 30 – 100 x 50 ÷ 25

Applying the rules:
– ‘+’ becomes ‘–’
– ‘–’ becomes ‘x’
– ‘x’ becomes ‘÷’
– ‘÷’ becomes ‘+’

The transformed expression is: 10 – 30 x 100 ÷ 50 + 25

Now, follow the standard order of operations (BODMAS/PEMDAS):
1. **Division**: 100 ÷ 50 = 2
The expression becomes: 10 – 30 x 2 + 25
2. **Multiplication**: 30 x 2 = 60
The expression becomes: 10 – 60 + 25
3. **Addition and Subtraction** (from left to right):
10 – 60 = -50
-50 + 25 = -25

The value of the expression is -25. This question tests logical reasoning by reinterpreting mathematical operations.

1. A. 1 only
2. B. 2 only
3. C. Both 1 and 2
4. D. Neither 1 nor 2

Answer: D

Explanation

Let’s translate the given symbols:
P: >
Q: 8z.
From 3x = 4z, we can express x in terms of z: x = 4z/3.
Substitute this into the first inequality: 2(4z/3) ≥ 3y
8z/3 ≥ 3y
Multiply by 3: 8z ≥ 9y.
The conclusion given is 9y > 8z. This contradicts our derived inequality (8z ≥ 9y), as 9y cannot be strictly greater than 8z if 8z is greater than or equal to 9y. Thus, Statement 1 is incorrect.

**Statement 2: If x(Q)2y and y(R)z, then x(R)z.**
Translate: If x < 2y and y ≤ z, then x ≤ z.
From y ≤ z, we can infer that 2y ≤ 2z.
We have two inequalities: x < 2y and 2y ≤ 2z.
Combining these, we get x < 2z.
The conclusion given is x ≤ z. However, x < 2z does not necessarily imply x ≤ z. For example, if x=3 and z=2, then x < 2z (3 < 4) is true, but x ≤ z (3 ≤ 2) is false. Thus, Statement 2 is incorrect.

Therefore, neither Statement 1 nor Statement 2 is correct. This question tests logical reasoning with inequalities and symbolic representation.