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Mark has twice as many oranges as George. Tony has 10 fewer
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23 Apr 2020, 10:18
23 Apr 2020, 10:18
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Question Stats:
56% (02:21) correct
44% (02:30) wrong based on 25 sessions
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Mark has twice as many oranges as George. Tony has 10 fewer than twice the sum of George and Mark’s oranges. If Tony were to give 15 oranges to George and 5 oranges to Mark, George and Mark would each have half the number of oranges Tony had originally. How many oranges did George have originally?
A. 10
B. 15
C. 20
D. 25
E. 50
A. 10
B. 15
C. 20
D. 25
E. 50
Re: Mark has twice as many oranges as George. Tony has 10 fewer
[#permalink]
17 Aug 2020, 16:50
17 Aug 2020, 16:50
1
First thing we want to do is find out how many oranges Tony has in terms of George's oranges.
We'll have \(T\) = Tony's oranges, \(G\) = George's oranges, and \(M\) = Mark's oranges.
We have:
\(M = 2G\)
\(T = 2(G+M) - 10\)
Substituting in \(2G\) for \(M\), we have:
\(T = 2(G+2G) - 10\)
\(T = 2(3G) - 10\)
\(T = 6G - 10\) [1]
At this point we can completely ignore Mark, as we're interested in George. This is what trapped me initially.
"When Tony gives 15 oranges to George, George has half the number of oranges that Tony had originally"
This means the following:
\(G + 15 = \frac{T}{2}\)
Or:
\(2G + 30 = T\)
From above, we can substitute in Equation [1] for \(T\) into this equation:
\(2G + 30 = 6G - 10\)
\(40 = 4G\)
\(10 = G\)
And there's our answer, Choice A
We'll have \(T\) = Tony's oranges, \(G\) = George's oranges, and \(M\) = Mark's oranges.
We have:
\(M = 2G\)
\(T = 2(G+M) - 10\)
Substituting in \(2G\) for \(M\), we have:
\(T = 2(G+2G) - 10\)
\(T = 2(3G) - 10\)
\(T = 6G - 10\) [1]
At this point we can completely ignore Mark, as we're interested in George. This is what trapped me initially.
"When Tony gives 15 oranges to George, George has half the number of oranges that Tony had originally"
This means the following:
\(G + 15 = \frac{T}{2}\)
Or:
\(2G + 30 = T\)
From above, we can substitute in Equation [1] for \(T\) into this equation:
\(2G + 30 = 6G - 10\)
\(40 = 4G\)
\(10 = G\)
And there's our answer, Choice A
gmatclubot
Re: Mark has twice as many oranges as George. Tony has 10 fewer [#permalink]
17 Aug 2020, 16:50
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