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P and Q are two positive numbers. Is P = Q ? (1) P is K% less than

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P and Q are two positive numbers. Is P = Q ? (1) P is K% less than  [#permalink]

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New post 13 Aug 2018, 22:08
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Question Stats:

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P and Q are two positive numbers. Is P = Q ?

(1) P is K% less than the sum (P+Q), where K is a positive number and K < 30.

(2) Q is Z% less than the sum (P+Q), where Z is a positive number and Z < 80.
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P and Q are two positive numbers. Is P = Q ? (1) P is K% less than  [#permalink]

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New post 14 Aug 2018, 00:07
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P and Q are two positive numbers. Is P = Q ?

(1) P is K% less than the sum (P+Q), where K is a positive number and K < 30.
\(P=(1-\frac{k}{100})(P+Q).......\)
Let us take P=Q..
So \(1=(1-\frac{k}{100})2...........50=100-k.........k=50......\)
But k<30, so \(P\neq{Q}\)
Sufficient

(2) Q is Z% less than the sum (P+Q), where Z is a positive number and Z < 80.
Here too z=50 as in statement I..
If z=50, Ans is YES otherwise NO
Insufficient

A
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Re: P and Q are two positive numbers. Is P = Q ? (1) P is K% less than  [#permalink]

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New post 14 Aug 2018, 01:11
Question: Is P = Q?

Let P = Q = 1

Then, P +Q = 2

Hence P = Q = 50% of (P+Q) or P is 50% less than (P+Q)

So, the Question reduces to “ IS P 50% less than (P+Q)” or, “ IS Q 50% less than (P+Q)”



Statement 1: P is K% less than (P+Q) and K<30.

Here. K cannot be equal to 50, P is NOT 50% less than (P+Q)

So, P is not equal to Q.

SUFFICIENT



Statement2: Q is Z% less than (P+Q) and Z<80

Here, If, Z = 50 , P=Q = 50% of (P+Q).

Hence P = Q

if Z = 60, P is not equal to Q.

NOT SUFFICIENT.



Answer A
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Re: P and Q are two positive numbers. Is P = Q ? (1) P is K% less than  [#permalink]

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New post 25 Aug 2018, 17:47
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amanvermagmat wrote:
P and Q are two positive numbers. Is P = Q ?

(1) P is K% less than the sum (P+Q), where K is a positive number and K < 30.

(2) Q is Z% less than the sum (P+Q), where Z is a positive number and Z < 80.

Question: is P = Q ? --> is \(P = Q = \frac{P+Q}{2}\) ? --> is \(P = Q = (P+Q)*(1-\frac{50}{100})\) ?

(1) \(P = (P+Q)*(1-\frac{K}{100})\). Since K < 30, we can conclude that \(K≠50\), thus \(P≠Q\) -> NO -> Sufficient.
(2) \(Q = (P+Q)*(1-\frac{Z}{100})\). Since Z < 80, if Z = 50 then YES, if \(Z≠50\) then NO. -> Not Sufficient.

Answer A.
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