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# p is 75% of q and p equals 2r.

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p is 75% of q and p equals 2r. [#permalink]  10 Jun 2018, 04:44
Expert's post
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Question Stats:

85% (00:41) correct 14% (01:28) wrong based on 102 sessions
p is 75% of q and p equals 2r.

 Quantity A Quantity B 0.375q r

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Sandy
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Manager
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Re: p is 75% of q and p equals 2r. [#permalink]  16 Jun 2018, 15:45
1
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p is 75% of q
$$p=.75q$$

p equals 2r
$$p=2r$$

Quantity A: $$0.375q$$
Quantity B: $$r$$

I manipulated the equation to make $$r=\frac{p}{2}$$
From here, we can substitute $$\frac{p}{2}$$ for r as Quantity B.

Quantity A: $$0.375q$$
Quantity B: $$\frac{p}{2}$$

Multiply both sides by 2.

Quantity A: $$0.75q$$
Quantity B: $$p$$

We see that the first equation given to us matches what we have in Quantity A and B.

Quantity A is equivalent to Quantity B.

Retired Moderator
Joined: 07 Jun 2014
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Re: p is 75% of q and p equals 2r. [#permalink]  11 Jul 2018, 15:53
1
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Expert's post
Explanation

Write an equation from the first part of the given information: p = 0.75q. Since p = 2r, substitute 2r for p in the first equation:

$$2r = 0.75q$$
$$r = 0.375q$$

The two quantities are equal.

Alternatively, use smart numbers. If q is 8, then p is (8)(0.75) = 6. (Note: because you have to multiply q by 0.75, or , try to pick something divisible by 4 for q, so that p will be an integer.)

Therefore, r is = 3.

Since 0.375q = (0.375)(8) = 3, the value for r is also 3. The two quantities are equal.
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Sandy
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Re: p is 75% of q and p equals 2r. [#permalink]  01 May 2020, 03:45
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I did this a little differently , but it's what works in my head.

If p=2r, then r=p/2.

Using the given equation p=.75q, you would then have r=.75q/2
r=.75q/2
r=q*(.75/2)
r=q*.375 , which equals A. Hence, the answer is C, both are equal.
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Re: p is 75% of q and p equals 2r. [#permalink]  04 Jun 2020, 06:24
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sandy wrote:
p is 75% of q and p equals 2r.

 Quantity A Quantity B 0.375q r

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Simply lets take:
Q=100
P=75
P=75=2r
r=37.5

Then
A: 0.375q -> 0.375*100 -> 37.5
B: r (37.5)

Intern
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Re: p is 75% of q and p equals 2r. [#permalink]  02 Jul 2020, 07:17
I solved it correctly. Can we consider negative values for "p" ?
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Re: p is 75% of q and p equals 2r. [#permalink]  02 Jul 2020, 09:33
1
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Expert's post
rust32627 wrote:
I solved it correctly. Can we consider negative values for "p" ?

Yes, it's perfectly acceptable to have negative values for p (either way, the correct answer is still C).

Having said that, when it comes to questions involving percent, the test makers typically create questions where all of the values are positive.
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Re: p is 75% of q and p equals 2r.   [#permalink] 02 Jul 2020, 09:33
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