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1.	II. The ratio of P and Q is less than 2.1). The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.2). The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.3). The data in statement I alone or in statement II alone is sufficient to answer the question.4). The data in both the statements I and II is not sufficient to answer the question.
Answer» From statement I: Difference between P and Q is 29. To find what percentage of P and Q, ratio of P and Q is REQUIRED. It cannot be found with this information. ∴ Statement I alone is not sufficient to answer the question. From statement II: Ratio of P and Q is less than 2. To find what percentage of P and Q, ratio of P and Q is required. It can be found that ratio is less than 2 but exact ratio cannot be found with this information. ∴ Statement II alone is not sufficient to answer the question. From STATEMENTS I and II together: Difference between P and Q is 29. Ratio of P and Q is less than 2. So, P - Q = 29 and P < 2Q or Q - P = 29 and P < 2Q. To find what percentage of P and Q, ratio of P and Q is required. The exact ratio cannot be found with this information. ∴ Using EVEN both the statements together, we cannot answer the given question.

II. The ratio of P and Q is less than 2.1). The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.2). The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.3). The data in statement I alone or in statement II alone is sufficient to answer the question.4). The data in both the statements I and II is not sufficient to answer the question.

Answer»

From statement I:

Difference between P and Q is 29. To find what percentage of P and Q, ratio of P and Q is REQUIRED. It cannot be found with this information.

∴ Statement I alone is not sufficient to answer the question.

From statement II:

Ratio of P and Q is less than 2. To find what percentage of P and Q, ratio of P and Q is required. It can be found that ratio is less than 2 but exact ratio cannot be found with this information.

∴ Statement II alone is not sufficient to answer the question.

From STATEMENTS I and II together:

Difference between P and Q is 29. Ratio of P and Q is less than 2.

So, P - Q = 29 and P < 2Q or Q - P = 29 and P < 2Q. To find what percentage of P and Q, ratio of P and Q is required. The exact ratio cannot be found with this information.

∴ Using EVEN both the statements together, we cannot answer the given question.

Discussion

2.	1). Statement I and II together are sufficient.2). Statement I alone or statement II alone is sufficient.3). Statement II alone is sufficient.4). Statement I and II together are not sufficient.
Answer» Seven businessmen: A, B, C, D, E, F and G. Different lucky numbers: 1, 2, 3, 6, 7, 8 and 9. From STATEMENT I: C has second HIGHEST amount and his lucky number is neither 2 nor 8. E has least amount and his lucky number is neither 3 nor 8. D’s lucky number is 6 and he has more amount than B and G but less than A. From the given information, C has HIGHER amount than E, i.e. C > E. C’s lucky number could be 1, 3, 6, 7 or 9. D’s lucky number is 6 and he has more amount than B and G but less than A. Since E has least amount, therefore D must have more amount than E, i.e. A > D(6) > B,G, E. A or F could have highest amount and E’s lucky number could be 1, 2, 6, 7 or 9. So, statement I alone is not sufficient. From statement II: B’s lucky number is 7 and his amount is more than the amount of E but less than the amount of G. A’s lucky number is 1. The person, whose lucky number is 9, has the highest amount. From the given information, B’s lucky number is 7 and his amount is more than the amount of E but less than the amount of G, i.e. G > B(7) > E. A’s lucky number is 1. The person whose lucky number is 9 has the highest amount. A, C, D or F could have highest amount and E’s lucky number could be 2, 3, 6 and 8. So, statement II alone is not sufficient. On combining I and II, C has second highest amount and his lucky number is neither 2 nor 8. So, C’s lucky number could be 1, 3, 6, 7 or 9. E has least amount and his lucky number is neither 3 nor 8. So, E’s lucky number could be 1, 2, 6, 7 or 9. D’s lucky number is 6 and he has more amount than B and G but less than A. B’s lucky number is 7 and his amount is more than the amount of E but less than the amount of G. A’s lucky number is 1. The person, whose lucky number is 9, has the highest amount. Combining all together we get: (9) > C > A(1) > D(6) > G > B(7) > E Clearly, only one businessman is left, i.e. F. So, F has the highest amount. F(9) > C > A(1) > D(6) > G > B(7) > E Clearly, only option left for C’s lucky number is 3 and for E is 2. F(9) > C(3) > A(1) > D(6) > G(8) > B(7) > E(2) So, F has the highest amount and E’s lucky number is 2. Hence, the data in statement I and II together are required to answer the question.

1). Statement I and II together are sufficient.2). Statement I alone or statement II alone is sufficient.3). Statement II alone is sufficient.4). Statement I and II together are not sufficient.

Answer»

Seven businessmen: A, B, C, D, E, F and G.

Different lucky numbers: 1, 2, 3, 6, 7, 8 and 9.

From STATEMENT I: C has second HIGHEST amount and his lucky number is neither 2 nor 8. E has least amount and his lucky number is neither 3 nor 8. D’s lucky number is 6 and he has more amount than B and G but less than A.

From the given information,

C has HIGHER amount than E, i.e. C > E.

C’s lucky number could be 1, 3, 6, 7 or 9.

D’s lucky number is 6 and he has more amount than B and G but less than A.

Since E has least amount, therefore D must have more amount than E, i.e. A > D(6) > B,G, E.

A or F could have highest amount and E’s lucky number could be 1, 2, 6, 7 or 9.

So, statement I alone is not sufficient.

From statement II: B’s lucky number is 7 and his amount is more than the amount of E but less than the amount of G. A’s lucky number is 1. The person, whose lucky number is 9, has the highest amount.

From the given information,

B’s lucky number is 7 and his amount is more than the amount of E but less than the amount of G, i.e. G > B(7) > E.

A’s lucky number is 1.

The person whose lucky number is 9 has the highest amount.

A, C, D or F could have highest amount and E’s lucky number could be 2, 3, 6 and 8.

So, statement II alone is not sufficient.

On combining I and II,

C has second highest amount and his lucky number is neither 2 nor 8. So, C’s lucky number could be 1, 3, 6, 7 or 9.

E has least amount and his lucky number is neither 3 nor 8. So, E’s lucky number could be 1, 2, 6, 7 or 9.

D’s lucky number is 6 and he has more amount than B and G but less than A.

B’s lucky number is 7 and his amount is more than the amount of E but less than the amount of G.

A’s lucky number is 1.

The person, whose lucky number is 9, has the highest amount.

Combining all together we get:

(9) > C > A(1) > D(6) > G > B(7) > E

Clearly, only one businessman is left, i.e. F. So, F has the highest amount.

F(9) > C > A(1) > D(6) > G > B(7) > E

Clearly, only option left for C’s lucky number is 3 and for E is 2.

F(9) > C(3) > A(1) > D(6) > G(8) > B(7) > E(2)

So, F has the highest amount and E’s lucky number is 2.

Hence, the data in statement I and II together are required to answer the question.

Discussion