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P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is [#permalink]
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19 Sep 2017, 23:02
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P, Q, R , S, T, U are positive integers, such that \(\frac{S}{P} + \frac{T}{Q} = \frac{U}{R}\), is P odd? (1) Q and R are odd (2) S is odd Kudos for correct solution
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Last edited by Bunuel on 20 Sep 2017, 00:30, edited 1 time in total.
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P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is [#permalink]
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19 Sep 2017, 23:40
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bkpolymers1617 wrote: P, Q, R , S, T, U are positive integers, such that \(S/P\) + \(T/Q\)= \(U/R\), is P odd?
a) Q and R are odd b) S is odd
Kudos for correct solution \(\frac{S}{P} = \frac{U}{R}\frac{T}{Q}\), Solve this to get \(P = \frac{QRS}{(QUTR)}\) Now \(P\) is a positive integer, so integer \(QRS\) is divisible by integer \((QUTR)\). We need to know whether \(QRS\) is odd or even to determine whether \(P\) is odd or even Statement 1: We know \(Q*R\) is odd but nothing is given about \(S\). So \(QRS\) can be odd or can be even. hence insufficientStatement 2: We know \(S\) is odd but know nothing about \(Q\) & \(R\). Hence insufficientCombining 1 & 2, we know \(Q*R*S\) is ODD, Hence \(P\) is ODD. SufficientOption C
Last edited by niks18 on 20 Sep 2017, 01:50, edited 1 time in total.



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Re: P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is [#permalink]
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20 Sep 2017, 00:00
niks18 wrote: bkpolymers1617 wrote: P, Q, R , S, T, U are positive integers, such that \(S/P\) + \(T/Q\)= \(U/R\), is P odd?
a) Q and R are odd b) S is odd
Kudos for correct solution \(\frac{S}{P} = \frac{U}{R}\frac{T}{Q}\), Solve this to get \(P = \frac{QRS}{(QUTU)}\) Now \(P\) is a positive integer, so integer \(QRS\) is divisible by integer \((QUTU)\). We need to know whether \(QRS\) is odd or even to determine whether \(P\) is odd or even Statement 1: We know \(Q*R\) is odd but nothing is given about \(S\). So \(QRS\) can be odd or can be even. hence insufficientStatement 2: We know \(S\) is odd but know nothing about \(Q\) & \(R\). Hence insufficientCombining 1 & 2, we know \(Q*R*S\) is ODD, Hence \(P\) is ODD. SufficientOption CThat is perfect. Thanks for posting
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Re: P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is [#permalink]
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20 Sep 2017, 02:59
bkpolymers1617 wrote: P, Q, R , S, T, U are positive integers, such that \(\frac{S}{P} + \frac{T}{Q} = \frac{U}{R}\), is P odd?
(1) Q and R are odd (2) S is odd
Kudos for correct solution What am I missing? \(\frac{U}{R} = \frac{(QS + PT)}{PQ}\) 1. Q and R are odd From the above equation PQ=R and if Q and R are odd so shouldn't P also be odd?



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Re: P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is [#permalink]
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20 Sep 2017, 04:43
ramalo wrote: bkpolymers1617 wrote: P, Q, R , S, T, U are positive integers, such that \(\frac{S}{P} + \frac{T}{Q} = \frac{U}{R}\), is P odd?
(1) Q and R are odd (2) S is odd
Kudos for correct solution What am I missing? \(\frac{U}{R} = \frac{(QS + PT)}{PQ}\) 1. Q and R are odd From the above equation PQ=R and if Q and R are odd so shouldn't P also be odd? Hi ramalowhat you have mentioned here is a ratio, so you cannot directly equate the denominators. Consider this: \(2*PQ = 2*R\), Now LHS and RHS are even and P may or may not be ODD despite Q & R being ODD



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Re: P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is [#permalink]
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20 Sep 2017, 05:48
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Hi Ramalo Here is an example to clarify your point. Check these 2 ratios: 8/6=4/3 check tge denominators. Are they of the same nature. See even though your fractions are the same, even then denominators are of opposite nature. So you simply cant equate the denominators. Hope this helps Posted from my mobile device
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Re: P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is [#permalink]
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26 Sep 2017, 03:16
bkpolymers1617 wrote: P, Q, R , S, T, U are positive integers, such that \(\frac{S}{P} + \frac{T}{Q} = \frac{U}{R}\), is P odd?
(1) Q and R are odd (2) S is odd
Kudos for correct solution Before we do anything we need to rewrite the statement and isolate that way we can simplify and find the true fundamental question s/p= (qutr)/(qr)  to rewrite in terms of p just flip the right handside and multiply the top by "s" p= qr*s/(qutr) Statement 1Too many possibilities insuff Statement 2Several possiblities insuff Statement 1 and 2If we know what QRS is then we know whether or not P is odd because any odd number that's an integer must be the product of two other odd integers C




Re: P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is
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