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# If P, Q, R are positive numbers such that R = 100P + 20Q

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Re: If P, Q, R are positive numbers such that R = 100P + 20Q [#permalink]
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TomB wrote:
R=100(p) + 20(q), p+q=2,is R<120
after rephrasing:
R= 100(2-Q) +20(q)
R= 200-100(q)+20(q)
R= 200-80(q)
200-80(q)<120
200-120<80(q)
80<80(q)
Is 1<q or q>1

stmnt2) not sufficient

(1+2) p>1.1,p>q
minimum value of p= 1.2 then q maybe 1.1 ( q>1 yielding yes)
q may be .75 ( q<1, yielding no)

whats wrong with my answer , plz explain

(1) P > 1.1 --> since P=2-Q then 2-Q>1.1 --> Q<0.9. Sufficient.
(2) P>Q --> 2-Q>Q --> Q<1. Sufficient.

If P, Q, R are positive numbers such that R = 100P + 20Q, and P + Q = 2, is R < 120?

$$R=100P+20Q=80P+20(P+Q)=80P+40$$. The question asks: is $$80P+40<120$$ --> is $$P<1$$?

(1) P > 1.1. Sufficient.
(2) P > Q --> P>2-P --> P>1. Sufficient.

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Re: If P, Q, R are positive numbers such that R = 100P + 20Q [#permalink]
Could you explain why you tried to solve for Q instead of P?
I did it for P and worked out well, but is there a reason?
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Re: If P, Q, R are positive numbers such that R = 100P + 20Q [#permalink]
ronr34 wrote:
Could you explain why you tried to solve for Q instead of P?
I did it for P and worked out well, but is there a reason?

You can do either way.
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Re: If P, Q, R are positive numbers such that R = 100P + 20Q [#permalink]
is its definite NO answers with option A ?
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Re: If P, Q, R are positive numbers such that R = 100P + 20Q [#permalink]
mkumar26 wrote:
is its definite NO answers with option A ?

Yes, both statements give definite NO answer to the question.
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Re: If P, Q, R are positive numbers such that R = 100P + 20Q [#permalink]
mkumar26 wrote:
is its definite NO answers with option A ?

Simplify the question stem first. the question is R<120
or 100P+20Q<120. this implies - 5P+Q<6----(1)

Now P+Q=2 or Q=2-P. Putting the value of Q in equation (1) above, we get
5P+2-P<6 OR P<1 -----(2)

So the question reduces to is P<1

Statement 1: Directly provides the answer as P>1.1. Hence sufficient

Statement 2: P>Q, putting the value of Q we get

P>2-P OR P>1. Hence Sufficient.

So Option D
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Re: If P, Q, R are positive numbers such that R = 100P + 20Q [#permalink]
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Re: If P, Q, R are positive numbers such that R = 100P + 20Q [#permalink]
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