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

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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p is 75% of q and p equals 2r. [#permalink] New post 10 Jun 2018, 04:44
Expert's post
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Question Stats:

77% (00:44) correct 22% (01:36) wrong based on 22 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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Re: p is 75% of q and p equals 2r. [#permalink] New post 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.

The answer is C.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1664 [0], given: 396

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

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