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: GMATPrep
If Randy has twice as many coins as Alice, and
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Let the number of coins that Alice has \(= x\).BTGModeratorVI wrote: ↑Mon May 25, 2020 7:28 amIf 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: GMATPrep
\(\Rightarrow\) Randy has \(2x\) coins and Maria has \(7x\) coins.
Total number of coins \(= x + 2x + 7x = 10x\)
Statement 1: Alice has \(4\) fewer coins than Randy.
\(2x- x = 4\)
\( x = 3.\)
\(\Rightarrow 10x = 30\) coins in total.
Thus we are able to obtain the value of the total no. of coins that all 3 of them have. So, sufficient. \(\Large{\color{green}\checkmark}\)
Statement 2: Maria has \(20\) more coins than Randy.
\(7x = 2x + 20\)
\(5x = 20\)
\( x = 4 \Rightarrow 10x = 40.\)
Again we have the total number of coins all \(3\) of them have. So, sufficient. \(\Large{\color{green}\checkmark}\)
Therefore, D
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Given: Randy has twice as many coins as Alice, and if Maria has 7 times as many coins as AliceBTGModeratorVI wrote: ↑Mon May 25, 2020 7:28 amIf 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: GMATPrep
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: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
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