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Math Expert V
Joined: 02 Sep 2009
Posts: 58347
Mark has twice as many oranges as George. Tony has 10 less than twice  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 77% (02:49) correct 23% (03:01) wrong based on 31 sessions

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Mark has twice as many oranges as George. Tony has 10 less than twice the sum of George and Marks 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

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Senior PS Moderator D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: Mark has twice as many oranges as George. Tony has 10 less than twice  [#permalink]

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Bunuel wrote:
Mark has twice as many oranges as George. Tony has 10 less than twice the sum of George and Marks 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

We have been given a lot of information. Let us denote the # of oranges with Mark etc. by the first letter of the name. Also, the final ask is How many oranges did George have originally? or in our notation G=?

$$M = 2G$$
$$T = 2(G+M) -10$$
$$T/2 = G+15$$
$$T/2 = M+5$$

No we clearly have more equations than the number of unknowns, and the fastest way to solve would be to keep in mind what is being asked ( G=?)

$$M=2G$$
$$T = 2G+2M -10$$ Lets substitute from the first equation into this one to get rid of M.

$$T = 2G + 2(2G) -10$$
$$T = 6G -10$$

Second question : $$T = 2G + 30$$

$$2G + 30 = 6G - 10$$
$$4G = 40$$
$$G = 10$$

Hence option (A) is our choice.

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Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: Mark has twice as many oranges as George. Tony has 10 less than twice  [#permalink]

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Bunuel wrote:
Mark has twice as many oranges as George. Tony has 10 less than twice the sum of George and Marks 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

"Mark has twice as many oranges as George."
M = 2*G

"Tony has 10 less than twice the sum of George and Marks oranges."
T = 2*(G + M) - 10 = 2*(G + 2G) - 10 = 6G - 10

"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."
(6G - 10)/2 = G + 15 = 2G + 5

G = 10

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Intern  B
Joined: 27 Feb 2018
Posts: 11
Re: Mark has twice as many oranges as George. Tony has 10 less than twice  [#permalink]

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my approach
M=2G
T=2(G+M)-10

M+5+G+15=2(G+M)-10
M+G+20=2G+2M-10
M+G=2G+2M-30
0=G+M-30
G+M=30

M=2G
3G=30
G=10 Re: Mark has twice as many oranges as George. Tony has 10 less than twice   [#permalink] 03 Nov 2018, 01:23
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