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# If 25% of p equals 65% of 80 and if q is 50% of p, which of the follow

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
If 25% of p equals 65% of 80 and if q is 50% of p, which of the follow  [#permalink]

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08 Feb 2019, 05:14
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45% (medium)

Question Stats:

55% (02:04) correct 45% (02:02) wrong based on 20 sessions

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If 25% of p equals 65% of 80 and if q is 50% of p, which of the following must be true?

I. q is 130% of 80
II. p is 200% of q
III. q/p = 50% of 1

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

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Location: India
Concentration: Sustainability, Marketing
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Re: If 25% of p equals 65% of 80 and if q is 50% of p, which of the follow  [#permalink]

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08 Feb 2019, 05:38
Bunuel wrote:
If 25% of p equals 65% of 80 and if q is 50% of p, which of the following must be true?

I. q is 130% of 80
II. p is 200% of q
III. q/p = 50% of 1

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

given info
.25*p=.65*.8
p= 208
and q = .5 * 208 = 104

so :
q is 130% of 80 ; true
p is 200% of q: true
q/p = 50% of 1; true
all true
IMO E
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Re: If 25% of p equals 65% of 80 and if q is 50% of p, which of the follow  [#permalink]

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08 Feb 2019, 06:24
Bunuel wrote:
If 25% of p equals 65% of 80 and if q is 50% of p, which of the following must be true?

I. q is 130% of 80
II. p is 200% of q
III. q/p = 50% of 1

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

25% of p equals 65% of 80 => $$5P=13*80$$
=>P= $$\frac{13}{5}*80$$

q is 50% of P => $$q= \frac{P}{2}$$
=> $$2q=P$$

So $$q= \frac{1}{2}*\frac{13}{5}*80$$
=> $$q=\frac{13}{10}*80$$

I. q is 130% of 80 => $$q=\frac{13}{10}*80$$ True

II. p is 200% of q => $$P=2q$$ True

III. q/p = 50% of 1 =>$$\frac{q}{P}=\frac{1}{2}$$ True
Re: If 25% of p equals 65% of 80 and if q is 50% of p, which of the follow   [#permalink] 08 Feb 2019, 06:24
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