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

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Retired Moderator
Joined: 22 Aug 2013
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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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13 Aug 2018, 23:08
1
6
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Difficulty:

95% (hard)

Question Stats:

43% (01:57) correct 57% (02:22) wrong based on 66 sessions

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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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Joined: 02 Aug 2009
Posts: 7986
P and Q are two positive numbers. Is P = Q ? (1) P is K% less than  [#permalink]

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14 Aug 2018, 01:07
1
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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14 Aug 2018, 02:11
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.

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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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25 Aug 2018, 18:47
1
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.

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Re: P and Q are two positive numbers. Is P = Q ? (1) P is K% less than   [#permalink] 25 Aug 2018, 18:47
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