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

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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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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

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Originally posted by bkpolymers1617 on 19 Sep 2017, 23:02.
Last edited by Bunuel on 20 Sep 2017, 00:30, edited 1 time in total.
Renamed the topic and edited the question.
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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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New post Updated on: 20 Sep 2017, 01:50
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3
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

\(P = \frac{QRS}{(QU-TR)}\)
Now \(P\) is a positive integer, so integer \(QRS\) is divisible by integer \((QU-TR)\).
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 insufficient

Statement 2: We know \(S\) is odd but know nothing about \(Q\) & \(R\). Hence insufficient

Combining 1 & 2, we know \(Q*R*S\) is ODD, Hence \(P\) is ODD. Sufficient

Option C

Originally posted by niks18 on 19 Sep 2017, 23:40.
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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New post 20 Sep 2017, 00:00
1
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

\(P = \frac{QRS}{(QU-TU)}\)
Now \(P\) is a positive integer, so integer \(QRS\) is divisible by integer \((QU-TU)\).

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 insufficient

Statement 2: We know \(S\) is odd but know nothing about \(Q\) & \(R\). Hence insufficient

Combining 1 & 2, we know \(Q*R*S\) is ODD, Hence \(P\) is ODD. Sufficient

Option C


That 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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New post 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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New post 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 ramalo

what 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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New post 20 Sep 2017, 05:48
1
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 :)

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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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New post 26 Sep 2017, 03:16
1
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= (qu-tr)/(qr) - to rewrite in terms of p just flip the right handside and multiply the top by "s"
p= qr*s/(qu-tr)

Statement 1


Too many possibilities

insuff

Statement 2

Several possiblities

insuff

Statement 1 and 2

If 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

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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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New post 04 Oct 2018, 05:27
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Re: P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is &nbs [#permalink] 04 Oct 2018, 05:27
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