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Cindy bought 48 containers of soda, all either 12-ounce cans

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1652 [0], given: 396

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Cindy bought 48 containers of soda, all either 12-ounce cans [#permalink] New post 14 Jun 2018, 14:12
Expert's post
00:00

Question Stats:

62% (01:06) correct 37% (02:44) wrong based on 8 sessions
Cindy bought 48 containers of soda, all either 12-ounce cans or 20-ounce bottles. If the number of ounces she purchased in cans was equal to the number of ounces she purchased in bottles, how many bottles of soda did Cindy buy?

(A) 18
(B) 21
(C) 24
(D) 27
(E) 30
[Reveal] Spoiler: OA

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Sandy
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Intern
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Joined: 02 May 2018
Posts: 45
Followers: 0

Kudos [?]: 27 [0], given: 17

Re: Cindy bought 48 containers of soda, all either 12-ounce cans [#permalink] New post 16 Jun 2018, 13:50
We are given two equations in the question.

Cindy bought 48 containers of soda, all either 12-ounce cans or 20-ounce bottles.
\((C+B)=48\)

the number of ounces she purchased in cans was equal to the number of ounces she purchased in bottles
\(12(c)=20(b)\)

Since we want to know how many bottles are needed, we can manipulate the first equation and then plug it into the second.
\(C=48-b\)

\(12(48-b)=20(b)\)
\(576-12b=20b\)
\(576=32b\)
\(18=b\)

The answer is A.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1652 [0], given: 396

CAT Tests
Re: Cindy bought 48 containers of soda, all either 12-ounce cans [#permalink] New post 05 Jul 2018, 01:46
Expert's post
Explanation

Define variables and translate equations from the given information:

Number of bottles = b
Number of cans = c

\(b + c = 48\) (Number of containers purchased)

\(12c = 20b\) (Equal number of ounces in bottles purchased and cans purchased)

The question asks for b, so isolate c in the first equation and substitute into the second equation:

\(c = 48 - b\)

\(12(48 - b) = 20b\)

\(576 - 12b = 20b\)

\(576 = 32b\)

\(b = 18\)

Check the answer. If Cindy bought 18 bottles, she bought 30 cans. The number of ounces in the bottles was 18 × 20 = 360. The number of ounces in the cans was 30 × 12 = 360.

Hence option A is correct!
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Sandy
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Re: Cindy bought 48 containers of soda, all either 12-ounce cans   [#permalink] 05 Jul 2018, 01:46
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Cindy bought 48 containers of soda, all either 12-ounce cans

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