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

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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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:

80% (00:45) correct 20% (01:36) wrong based on 25 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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Intern
Joined: 02 May 2018
Posts: 45
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Kudos [?]: 28 [0], given: 17

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

GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

Re: p is 75% of q and p equals 2r. [#permalink]  11 Jul 2018, 15:53
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.
_________________

Sandy
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Re: p is 75% of q and p equals 2r.   [#permalink] 11 Jul 2018, 15:53
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