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Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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p is 75% of q and p equals 2r. [#permalink]
Expert's post 00:00

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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Re: p is 75% of q and p equals 2r. [#permalink]
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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
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3036  , given: 394

Re: p is 75% of q and p equals 2r. [#permalink]
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]
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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. Intern  Joined: 07 May 2020
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Re: p is 75% of q and p equals 2r. [#permalink]
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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 Joined: 27 Jun 2020
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Re: p is 75% of q and p equals 2r. [#permalink]
I solved it correctly. Can we consider negative values for "p" ? GRE Instructor Joined: 10 Apr 2015
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Re: p is 75% of q and p equals 2r. [#permalink]
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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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Brent Hanneson – Creator of greenlighttestprep.com  Re: p is 75% of q and p equals 2r.   [#permalink] 02 Jul 2020, 09:33
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