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Question 1 of 5
1. Question
Consider the following including the Question and the Statements:
There are 5 persons: P, Q, R, S, and T.
Question: How is R related to S?
Statements:
- P is the father of R.
- Q is the brother of P and S is the daughter of Q.
- T is the mother of Q.
Which one of the following is correct in respect of the above Question and Statements?
Correct
Answer: (a)
Explanation:
- From (1):
- P is the father of R ⇒ R is the child of P.
- From (2):
- Q is the brother of P ⇒ Q is R’s paternal uncle.
- S is the daughter of Q ⇒ S is the daughter of R’s uncle.
So, using (1) and (2) together:
- R is the child of P.
- S is the child of R’s uncle (Q).
⇒ R and S are first cousins.
The relation “cousin” does not depend on the gender of R or S, so it is fully determined. - Statement (3) only tells us T is the mother of Q, i.e., grandmother of S and aunt/grandmother relation chain, but this is not needed to determine how R is related to S.
- (1) and (3) together: link P, Q, T but no information about S.
- (2) and (3) together: link Q, S, T, but nothing about R.
Hence, Statement-1 and Statement-2 are sufficient, so option (a) is correct.
Incorrect
Answer: (a)
Explanation:
- From (1):
- P is the father of R ⇒ R is the child of P.
- From (2):
- Q is the brother of P ⇒ Q is R’s paternal uncle.
- S is the daughter of Q ⇒ S is the daughter of R’s uncle.
So, using (1) and (2) together:
- R is the child of P.
- S is the child of R’s uncle (Q).
⇒ R and S are first cousins.
The relation “cousin” does not depend on the gender of R or S, so it is fully determined. - Statement (3) only tells us T is the mother of Q, i.e., grandmother of S and aunt/grandmother relation chain, but this is not needed to determine how R is related to S.
- (1) and (3) together: link P, Q, T but no information about S.
- (2) and (3) together: link Q, S, T, but nothing about R.
Hence, Statement-1 and Statement-2 are sufficient, so option (a) is correct.
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Question 2 of 5
2. Question
A train leaves a station every 20 minutes at a uniform speed of 54 km/h. A jeep starting from the same station and moving in the same direction meets a train every 30 minutes. Find the speed of the jeep.
Correct
Incorrect
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Question 3 of 5
3. Question
Find the maximum value of ‘n’ such that 120 × 90 × 25 × 6 is perfectly divisible by 30ⁿ.
Correct
Answer: (d)
Solution:
We need 120 × 90 × 25 × 6 to be divisible by 30ⁿ.
30 = 2 × 3 × 5 ⇒ 30ⁿ = 2ⁿ × 3ⁿ × 5ⁿ.Prime factorisation of each term:
120 = 2³ × 3 × 5
90 = 2 × 3² × 5
25 = 5²
6 = 2 × 3Now count powers:
2’s: 120 (3) + 90 (1) + 6 (1) = 3 + 1 + 1 = 5
3’s: 120 (1) + 90 (2) + 6 (1) = 1 + 2 + 1 = 4
5’s: 120 (1) + 90 (1) + 25 (2) = 1 + 1 + 2 = 4
So the product = 2⁵ × 3⁴ × 5⁴ × (other primes if any).
Write in terms of 30:
= (2⁴ × 3⁴ × 5⁴) × 2¹
= 30⁴ × 2The maximum power of 30 that divides this expression is therefore 30⁴.
So the maximum value of ‘n’ is 4.
Hence, option (d) is correct.
Incorrect
Answer: (d)
Solution:
We need 120 × 90 × 25 × 6 to be divisible by 30ⁿ.
30 = 2 × 3 × 5 ⇒ 30ⁿ = 2ⁿ × 3ⁿ × 5ⁿ.Prime factorisation of each term:
120 = 2³ × 3 × 5
90 = 2 × 3² × 5
25 = 5²
6 = 2 × 3Now count powers:
2’s: 120 (3) + 90 (1) + 6 (1) = 3 + 1 + 1 = 5
3’s: 120 (1) + 90 (2) + 6 (1) = 1 + 2 + 1 = 4
5’s: 120 (1) + 90 (1) + 25 (2) = 1 + 1 + 2 = 4
So the product = 2⁵ × 3⁴ × 5⁴ × (other primes if any).
Write in terms of 30:
= (2⁴ × 3⁴ × 5⁴) × 2¹
= 30⁴ × 2The maximum power of 30 that divides this expression is therefore 30⁴.
So the maximum value of ‘n’ is 4.
Hence, option (d) is correct.
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Question 4 of 5
4. Question
An amount of ₹72 was spent on notebooks and pens. A notebook costs ₹8 and a pen costs ₹4.
Which one of the following statements is correct?Correct
Answer: (d)
Solution:
Equation: 8n + 4p = 72
Divide by 4:
2n + p = 18Try values:
Case 1: n = 5 → p = 8
→ More pensCase 2: n = 6 → p = 6
→ EqualCase 3: n = 7 → p = 4
→ More notebooksSince all three outcomes are possible, we cannot determine which one is more.
Hence, option (d) is correct.
Incorrect
Answer: (d)
Solution:
Equation: 8n + 4p = 72
Divide by 4:
2n + p = 18Try values:
Case 1: n = 5 → p = 8
→ More pensCase 2: n = 6 → p = 6
→ EqualCase 3: n = 7 → p = 4
→ More notebooksSince all three outcomes are possible, we cannot determine which one is more.
Hence, option (d) is correct.
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Question 5 of 5
5. Question
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
A and B together can complete a job.
Question: In how many days can A alone complete the job?
Statement I: A and B together can complete the job in 6 days, and B alone can complete it in 9 days.
Statement II: A is 50% more efficient than B.Which one of the following is correct in respect of the above Question and the Statements?
Correct
Answer: (a)
Explanation:
From Statement I:
Let total work = 1 unit.
A + B together = 1/6 per day, B = 1/9 per day
So A = 1/6 − 1/9 = (3 − 2)/18 = 1/18 per day
⇒ A alone takes 18 days.
So Statement I alone is sufficient.From Statement II:
Let B’s work rate = r. Then A’s rate = 1.5r.
Total rate A + B = 2.5r, but we do not know how long they take together or alone, so we cannot find A’s exact days.
So Statement II alone is not sufficient.Hence, the Question can be answered by using one of the Statements alone (Statement I), but not by using Statement II alone.
So option (a) is correct.Incorrect
Answer: (a)
Explanation:
From Statement I:
Let total work = 1 unit.
A + B together = 1/6 per day, B = 1/9 per day
So A = 1/6 − 1/9 = (3 − 2)/18 = 1/18 per day
⇒ A alone takes 18 days.
So Statement I alone is sufficient.From Statement II:
Let B’s work rate = r. Then A’s rate = 1.5r.
Total rate A + B = 2.5r, but we do not know how long they take together or alone, so we cannot find A’s exact days.
So Statement II alone is not sufficient.Hence, the Question can be answered by using one of the Statements alone (Statement I), but not by using Statement II alone.
So option (a) is correct.
