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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Archie, Betty and Coach bought a radio. Archie paid the leas ##### This topic has 4 expert replies and 2 member replies ## Archie, Betty and Coach bought a radio. Archie paid the leas Archie, Betty and Coach bought a radio. Archie paid the least amount of money, Coach paid twice as much as Archie, and Betty paid the most. Archie paid seventy dollars less than the difference between what Betty and Coach paid. If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less. Which of the following equals the amount Betty paid? A. 40 B. 90 C. 130 D. 140 E. 150 OA C ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 vinni.k wrote: Archie, Betty and Coach bought a radio. Archie paid the least amount of money, Coach paid twice as much as Archie, and Betty paid the most. Archie paid seventy dollars less than the difference between what Betty and Coach paid. If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less. Which of the following equals the amount Betty paid? A. 40 B. 90 C. 130 D. 140 E. 150 OA C If Coach paid twice as much as Archie, and we designate Archie as 'A' then Coach is '2A.' We know that Archie paid 70 less than the difference between Betty and Coach, so we know that A = Betty - 2A - 70 Or Betty = 3A + 70 Now we have everyone in terms of 'A.' Archie: A Betty: 3A + 70 Coach: 2A Total: 6A + 70 If Archie paid twice as much, or 2A, then Betty and Coach would have paid$10 less. (Presumably, the total would remain the same.) This yields the following

Archie: 2A
Betty: 3A + 60
Coach: 2A - 10
Total: 6A + 70

Now we have: 2A + 3A + 60 + 2A - 10 = 6A + 70
7A + 50 = 6A + 70
A = 20

We want the amount Betty paid, or 3A + 70. So we get 3*20 + 70 = 60 + 70 = 130. The answer is C

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### GMAT/MBA Expert

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vinni.k wrote:
Archie, Betty and Coach bought a radio. Archie paid the least amount of money, Coach paid twice as much as Archie, and Betty paid the most. Archie paid seventy dollars less than the difference between what Betty and Coach paid. If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less. Which of the following equals the amount Betty paid?

A. 40
B. 90
C. 130
D. 140
E. 150
Since A, B and C each contribute to the total cost, we get:
T = A + B + C.

If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less.
Thus:
T = 2A + (B-10) + (C-10)
T = 2A + B + C - 20.

Since the blue expressions above both represent the total cost, they must be equal:
2A + B + C - 20 = A + B + C
A = 20.

Coach paid twice as much as Archie.
Thus, C = 2A = 2*20 = 40.

Archie paid seventy dollars less than the difference between what Betty and Coach paid.
Thus:
A = (B-C) - 70.
Substituting A=20 and C=40 into A = (B-C) - 70, we get:
20 = B - 40 - 70
130 = B.

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Master | Next Rank: 500 Posts
Joined
17 Apr 2011
Posted:
421 messages
Followed by:
2 members
6
Test Date:
2016
Target GMAT Score:
700+
GMAT Score:
620
Mitch and David,
Thank you for your solutions... really appreciate it

### GMAT/MBA Expert

GMAT Instructor
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vinni.k wrote:
Archie, Betty and Coach bought a radio. Archie paid the least amount of money, Coach paid twice as much as Archie, and Betty paid the most. Archie paid seventy dollars less than the difference between what Betty and Coach paid. If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less. Which of the following equals the amount Betty paid?

A. 40
B. 90
C. 130
D. 140
E. 150
The key to solving this problem is this sentence: “If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less.” This means that Betty and Coach together would have paid 20 dollars less, which means that Archie would have paid 20 dollars more than he paid. Since the extra 20 dollars would have resulted in Archie’s paying twice as much, he must have paid 20 dollars originally (so that the doubled amount would be 40 dollars).

Since Archie paid 20 dollars and Coach paid twice as much, Coach paid 40 dollars.

Since Betty paid the most and Archie paid seventy dollars less than the difference between what Betty and Coach paid, if we let x = the amount Betty paid, we have:

20 = x - 40 - 70

130 = x

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scott@targettestprep.com

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