Question 1

Statements:
1. Some athletes are strong.
2. All strong people are healthy.

Conclusion: Some athletes are healthy.

Is the conclusion valid?

Accepted Answer

The conclusion is VALID. From Premise 1, some athletes are strong. From Premise 2, all strong people are healthy. Therefore, those athletes who are strong must also be healthy. Hence, some athletes are healthy.

Question 2

A residential colony experiences frequent power cuts lasting 4-6 hours daily. Residents are unable to work from home and children cannot study. What should the local authority do first?

Accepted Answer

This tests the ability to identify the most urgent and foundational course of action.

Question 3

Statements:
1. All teachers are educated.
2. Some educated people are doctors.

Conclusion: Some doctors are teachers.

Is the conclusion valid?

Accepted Answer

The conclusion is INVALID. From the premises, we know all teachers are educated, and some educated people are doctors. However, this does not guarantee that the doctors who are educated are the same as the teachers. The educated doctors could be a completely different group from the teachers.

Question 4

Statements:
1. All birds can fly.
2. Penguins are birds.

Conclusion: Penguins can fly.

Is the conclusion valid according to the premises?

Accepted Answer

The conclusion is VALID according to the premises. Premise 1 states all birds can fly. Premise 2 states penguins are birds. Therefore, by logical deduction, penguins can fly. (Note: In reality, penguins cannot fly, but we evaluate validity based on the given premises, not real-world facts.)

Question 5

Statements:
1. No reptiles are mammals.
2. All snakes are reptiles.

Conclusion: No snakes are mammals.

Is the conclusion valid?

Accepted Answer

The conclusion is VALID. From Premise 2, all snakes are reptiles. From Premise 1, no reptiles are mammals. Therefore, no snakes can be mammals. This follows the valid syllogistic form: No B are C; All A are B; therefore No A are C.

Question 6

A company notices that its customer service response time has increased from 2 hours to 8 hours over the last quarter. Customer complaints have risen by 30%. Which course of action should be prioritized?

Accepted Answer

This tests the ability to link a problem to its likely cause and identify the most direct solution.

Question 7

Given: M < N, N ≤ O, O > P, P ≥ Q, Q = R. Which conclusion is definitely TRUE?

Accepted Answer

From the given: M < N ≤ O > P ≥ Q = R. Let's check: (a) M < O: M < N and N ≤ O, so M < O is TRUE. (b) O > Q: O > P and P ≥ Q, so O > Q is TRUE. (c) N > P: N ≤ O and O > P, but this doesn't directly tell us if N > P. N could be less than, equal to, or greater than P. This is INDETERMINATE. (d) R ≥ M: R = Q and Q ≤ P and P < O and O ≥ N > M. We cannot determine if R ≥ M.

Question 8

Given: J ≤ K, K < L, L ≥ M, M > N, N ≤ O. Which conclusion is INDETERMINATE?

Accepted Answer

From the given: J ≤ K < L ≥ M > N ≤ O. Let's check: (a) J < L: J ≤ K < L, so J < L is TRUE. (b) L > N: L ≥ M > N, so L > N is TRUE. (c) K > M: K < L and L ≥ M, but this doesn't tell us if K > M. K could be less than, equal to, or greater than M. This is INDETERMINATE. (d) O ≥ N: N ≤ O is given, so O ≥ N is TRUE.

Question 9

Statements:
1. No criminals are honest.
2. All dishonest people are criminals.

Conclusion: All dishonest people are criminals.

Is the conclusion valid?

Accepted Answer

The conclusion is VALID. Premise 2 directly states 'All dishonest people are criminals,' which is exactly the conclusion. This is a straightforward application of the given statement.

Question 10

Statements:
1. All fruits are healthy.
2. Some healthy things are expensive.

Conclusion: Either all fruits are expensive OR some fruits are not expensive.

Is the conclusion valid?

Accepted Answer

The conclusion is VALID. From the premises, we cannot determine whether fruits are expensive or not. Therefore, the 'Either/Or' statement—which covers both possibilities—must be true. At least one of the two parts must hold.

Question 11

A government school has a 50% dropout rate among girls. Teachers report that many girls leave school to help with household chores and childcare. What should the school administration prioritize?

Accepted Answer

This tests the ability to identify a course of action that addresses a social barrier to education.

Question 12

Given: P ≤ Q, Q < R, R ≥ S, S > T, T ≤ U. Which conclusion is DEFINITELY FALSE?

Accepted Answer

From the given: P ≤ Q < R ≥ S > T ≤ U. Let's check each option: (a) P < R: P ≤ Q < R, so P < R is TRUE. (b) S ≥ T: We have S > T, so S ≥ T is TRUE. (c) T > U: We have T ≤ U, which means T is less than or equal to U, so T > U is FALSE. (d) Q ≤ R: We have Q < R, so Q ≤ R is TRUE.

Question 13

A city is facing a severe water shortage. The municipal corporation has identified that 40% of water is lost due to leaking pipes. Which of the following is the most appropriate course of action?

Accepted Answer

The question tests the ability to identify the most logical and immediate action to address a stated problem.

Question 14

A school observes that student attendance has dropped to 60% in the past month. Teachers report that many students are absent due to illness. What should the school do?

Accepted Answer

This tests the ability to identify appropriate follow-up actions when a problem has a known cause.

Question 15

Given: A > B, B ≥ C, C > D, D = E, E < F. Which of the following conclusions is definitely TRUE?

Accepted Answer

From the given inequalities: A > B ≥ C > D = E < F. We can deduce A > C (transitive), A > D (transitive), B > D (transitive), and D = E. However, we cannot determine the relationship between A and F, or between C and F, because F's position relative to the chain is only constrained by E < F, and E is the smallest in the A-B-C-D-E chain.

Question 16

Given: X ≥ Y, Y > Z, Z ≤ W, W < V, V ≤ X. Which of the following is INDETERMINATE (cannot be determined)?

Accepted Answer

From the given: X ≥ Y > Z ≤ W < V ≤ X. Let's analyze: (a) X > Z: X ≥ Y > Z, so X > Z is TRUE. (b) W ≥ Z: W ≥ Z is given (Z ≤ W), so this is TRUE. (c) V > Y: V ≤ X and X ≥ Y, but this doesn't tell us if V > Y. V could be less than, equal to, or greater than Y. This is INDETERMINATE. (d) Z < X: Z < Y and Y ≤ X, so Z < X is TRUE.

Question 17

Given: A ≥ B, B > C, C ≤ D, D < E, E ≥ F. Which of the following is definitely FALSE?

Accepted Answer

From the given: A ≥ B > C ≤ D < E ≥ F. Let's check: (a) A > C: A ≥ B > C, so A > C is TRUE. (b) D ≥ C: C ≤ D is given, so D ≥ C is TRUE. (c) E > C: E > D and D ≥ C, so E > C is TRUE. (d) F > E: E ≥ F means F ≤ E, so F > E is FALSE.

Question 18

A machine processes input numbers through the following steps:
Step 1: Multiply the input by 2
Step 2: Add 5 to the result
Step 3: Divide by 3

If the input is 10, what is the final output?

Accepted Answer

Following the three-step process sequentially: Step 1: 10 × 2 = 20. Step 2: 20 + 5 = 25. Step 3: 25 ÷ 3 = 8.33 (or 8⅓). The final output is 8.33.

Question 19

A hospital reports that patient waiting time in the emergency department has increased to 3 hours, and patient satisfaction scores have dropped significantly. The hospital has adequate staff and equipment. What is the most logical course of action?

Accepted Answer

This tests the ability to identify the cause when resources are not the constraint, and choose an appropriate action.

Question 20

A word-processing system transforms words as follows:
Step 1: Count the number of vowels
Step 2: Multiply this count by 2
Step 3: Add the number of consonants

Apply this to the word 'MACHINE'. What is the final output?

Accepted Answer

MACHINE has vowels: A, I, E (3 vowels) and consonants: M, C, H, N (4 consonants). Step 1: 3 vowels. Step 2: 3 × 2 = 6. Step 3: 6 + 4 = 10. Final output is 10.

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