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PQP is a three-digit number having digits P and Q; and RQS5 is a four-

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PQP is a three-digit number having digits P and Q; and RQS5 is a four-  [#permalink]

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New post 28 Jul 2017, 00:22
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Question Stats:

58% (02:15) correct 42% (02:19) wrong based on 93 sessions

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PQP is a three-digit number having digits P and Q; and RQS5 is a four-digit number having digits R, Q, S and 5. What is the value of R?

(1) PQP × P = RQS5
(2) P, Q, R and S are distinct non-zero digits.

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Re: PQP is a three-digit number having digits P and Q; and RQS5 is a four-  [#permalink]

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New post 28 Jul 2017, 00:45
Bunuel wrote:
PQP is a three-digit number having digits P and Q; and RQS5 is a four-digit number having digits R, Q, S and 5. What is the value of R?

(1) PQP × P = RQS5
(2) P, Q, R and S are distinct non-zero digits.


(1) Since P*P = 5, P can only take 5
PQP × P = RQS5
505 * 5 = 2525 (Q not matching)
515 * 5 = 2575 (Q not matching)
595 * 5 = 2975 Yes (BTW in all cases value of R will remain as 2)
R = 2
Sufficient

(2) Not Sufficient

A
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Re: PQP is a three-digit number having digits P and Q; and RQS5 is a four-  [#permalink]

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New post 29 Jul 2017, 01:28
For Statement A:

Given PQP*P = RQS5,
Units digit is 5 on RHS, its only possible in case 5*5 (i.e. 25)
So, P=5
Now, Irrespective of the Q value 5Q5*5 will always have 2 in thousands place
Example: 515*5= 2575
525*5= 2625
595*5= 2975
Therefore, R = 2 and Statement 1 is sufficient

For Statement B:

Its given all the digits P, Q, R, S are distinct and we cannot infer R value from this statement alone

Answer: A
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Re: PQP is a three-digit number having digits P and Q; and RQS5 is a four-  [#permalink]

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New post 13 Sep 2018, 05:29
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Re: PQP is a three-digit number having digits P and Q; and RQS5 is a four- &nbs [#permalink] 13 Sep 2018, 05:29
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