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If Randy has twice as many coins as Alice, and if Maria has 7 times as many coins as Alice, what is the combined number

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by Gmat_mission » Sat Oct 31, 2020 6:44 am

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If Randy has twice as many coins as Alice, and if Maria has 7 times as many coins as Alice, what is the combined number of coins that all three of them have?

(1) Alice has 4 fewer coins than Randy.
(2) Maria has 20 more coins than Randy.

Answer: D

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Re: If Randy has twice as many coins as Alice, and if Maria has 7 times as many coins as Alice, what is the combined num

by Brent@GMATPrepNow » Thu Nov 05, 2020 8:18 am
Gmat_mission wrote: ↑
Sat Oct 31, 2020 6:44 am
 If Randy has twice as many coins as Alice, and if Maria has 7 times as many coins as Alice, what is the combined number of coins that all three of them have?

(1) Alice has 4 fewer coins than Randy.
(2) Maria has 20 more coins than Randy.

Answer: D

Source: GMAT Prep
Given: Randy has twice as many coins as Alice, and if Maria has 7 times as many coins as Alice

Target question: What is the combined number of coins that all three of them have?
This is a good candidate for rephrasing the target question.

Let A = the number of coins Alice has
So 2A = the number of coins Randy has
And 7A = the number of coins Maria has
So, the COMBINED number of coins they have = A + 2A + 7A = 10A

REPHRASED target question: What is the value of 10A?

Aside: the video below has tips on rephrasing the target question

Statement 1: Alice has 4 fewer coins than Randy.
In other words: (the number of coins Alice has) = (the number of coins Randy has) - 4
Substitute to get: A = 2A - 4
Solve to get: A = 4, which means 10A = 40
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: Maria has 20 more coins than Randy.
In other words: (the number of coins Maria has) = (the number of coins Randy has) + 20
Substitute to get: 7A = 2A + 20
Solve to get: A = 4, which means 10A = 40
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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