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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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Manager
Joined: 01 Sep 2016
Posts: 194
GMAT 1: 690 Q49 V35
P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is  [#permalink]

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Updated on: 20 Sep 2017, 00:30
2
9
00:00

Difficulty:

95% (hard)

Question Stats:

36% (02:18) correct 64% (02:01) wrong based on 99 sessions

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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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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!

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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Updated on: 20 Sep 2017, 01:50
5
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.
##### General Discussion
Manager
Joined: 01 Sep 2016
Posts: 194
GMAT 1: 690 Q49 V35
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
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
_________________

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!

Manager
Joined: 30 Jul 2013
Posts: 125
Concentration: Strategy, Sustainability
GMAT 1: 710 Q49 V39
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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Posts: 1217
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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 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
Manager
Joined: 01 Sep 2016
Posts: 194
GMAT 1: 690 Q49 V35
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
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

Posted from my mobile device
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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!

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Joined: 12 Nov 2016
Posts: 733
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
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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
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

C
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Posts: 9149
Re: P, Q, R , S, T, U are positive integers, such that S/P + T/Q = U/R, is  [#permalink]

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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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