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# P, Q, R are three distinct positive numbers. Which is the greatest

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Retired Moderator
Joined: 22 Aug 2013
Posts: 1443
Location: India
P, Q, R are three distinct positive numbers. Which is the greatest  [#permalink]

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17 Mar 2018, 00:25
3
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Difficulty:

75% (hard)

Question Stats:

37% (02:03) correct 63% (02:17) wrong based on 45 sessions

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P, Q, R are three distinct positive numbers. Which is the greatest number among P, Q, R?

(1) R - P < Q - P

(2) Q^2 * R > R^2 * P > P^2 * Q
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
P, Q, R are three distinct positive numbers. Which is the greatest  [#permalink]

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17 Mar 2018, 00:56
1
(1) R - P < Q - P
Rewriting this equation we will get R < Q
However, we don't have any information about P (Insufficient)

(2) Q^2 * R > R^2 * P > P^2 * Q

Case 1:
If Q = 4, R = 3, P = 2
Then 48 > 18 > 12

Case 2: If Q = 3, R = 3.1, P = 2
Then 27.3 > 19.22 > 12

Here, in case 1, Q > R > P whereas in case 2, Q < R > P (Insufficient)

Combining the information present in both the statements
Case 2 is not possible when Q > R and Q is the largest number among P,Q, and R.(Sufficient - Option C)

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P, Q, R are three distinct positive numbers. Which is the greatest  [#permalink]

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20 Mar 2018, 01:08
pushpitkc wrote:
(1) R - P < Q - P
Rewriting this equation we will get R < Q
However, we don't have any information about P (Insufficient)

(2) Q^2 * R > R^2 * P > P^2 * Q

Case 1: If Q = 4, R = 3, P = 2
Then 48 > 18 > 12

Case 2:If Q = 3, R = 3,P = 2
Then 27 > 18 > 12

Here, in case 1, Q > R > P whereas in case 2, Q=R > P (Insufficient)

Combining the information present in both the statements
Let test with another case where P > Q
Case 3 : Q = 5, R = 4, P = 6 Here, 100 > 96 < 180.
As Statement (2) becomes false, Case 3 is not possible.

Hence, Q is the largest number among P,Q, and R.(Sufficient - Option C)

pls look at the part highlighted by me in your explanation above...

Question States : P, Q, R are three distinct positivenumbers.

if three are distinctive number in such case.. case I only persists.

need guidance from expert.
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: P, Q, R are three distinct positive numbers. Which is the greatest  [#permalink]

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20 Mar 2018, 03:01
GMAT215 wrote:
pushpitkc wrote:
(1) R - P < Q - P
Rewriting this equation we will get R < Q
However, we don't have any information about P (Insufficient)

(2) Q^2 * R > R^2 * P > P^2 * Q

Case 1: If Q = 4, R = 3, P = 2
Then 48 > 18 > 12

Case 2:If Q = 3, R = 3,P = 2
Then 27 > 18 > 12

Here, in case 1, Q > R > P whereas in case 2, Q=R > P (Insufficient)

Combining the information present in both the statements

Let test with another case where P > Q
Case 3 : Q = 5, R = 4, P = 6 Here, 100 > 96 < 180.
As Statement (2) becomes false, Case 3 is not possible.

Hence, Q is the largest number among P,Q, and R.(Sufficient - Option C)

pls look at the part highlighted by me in your explanation above...

Question States : P, Q, R are three distinct positivenumbers.

if three are distinctive number in such case.. case I only persists.

need guidance from expert.

Thanks for noticing GMAT215
Have corrected my solution, the answer is still C(but the values of P,Q, and R change in the solution)

Hope it is clearer now!
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Re: P, Q, R are three distinct positive numbers. Which is the greatest   [#permalink] 20 Mar 2018, 03:01
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