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Last edited by Bunuel on 20 Sep 2017, 01:30, edited 1 time in total.

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, 00:40

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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

\(P = \frac{QRS}{(QU-TR)}\) 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

Last edited by niks18 on 20 Sep 2017, 02:50, edited 1 time in total.

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, 01:00

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

\(P = \frac{QRS}{(QU-TU)}\) 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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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!

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, 06:48

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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

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we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!