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Math Expert V
Joined: 02 Sep 2009
Posts: 64248
Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for  [#permalink]

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Difficulty:   15% (low)

Question Stats: 85% (01:59) correct 15% (01:43) wrong based on 39 sessions

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Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs \$200 more than the size below it. Alan spends a total of \$3,400. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?

A. 850
B. 1,100
C. 1,700
D. 2,550
E. 3,400

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Manager  Joined: 25 Dec 2012
Posts: 114
Re: Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for  [#permalink]

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Bunuel wrote:
Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs \$200 more than the size below it. Alan spends a total of \$3,400. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?

A. 850
B. 1,100
C. 1,700
D. 2,550
E. 3,400

The problem stated is in AP.
Avg price = 3400/4 = 850

Since in AP , 850*2 = 1700 (Sum of 1st and 4th term or 2nd term and third term)
IMO C

1 + 2 + 3 + 4 + ....+98 + 99 + 100

100+1 = 99+2 = 98 + 3 = 97 + 4 and goes on till 51+50

This is how the formula N(N+1) divided by 2 got derived.
Senior Manager  Joined: 20 Aug 2015
Posts: 379
Location: India
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Re: Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for  [#permalink]

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Bunuel wrote:
Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs \$200 more than the size below it. Alan spends a total of \$3,400. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?

A. 850
B. 1,100
C. 1,700
D. 2,550
E. 3,400

Assume the cost of the least sized (26 Inch) TV = x
Cost of 28 inches TV = x + 200
Cost of 30 inches TV = x + 400
Cost of 32 inches TV = x + 600

Total cost = 4x + 1200 = 3400
Therefore x = 2200/4 = 550

Price of 28inch + 30 inch = 750 + 950 = 1700
Option C
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Re: Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for  [#permalink]

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Bunuel wrote:
Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs \$200 more than the size below it. Alan spends a total of \$3,400. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?

A. 850
B. 1,100
C. 1,700
D. 2,550
E. 3,400

We can let x = the cost of the 26-inch TV; thus, x + 200, x + 400 and x + 600 are the costs of the 28-inch, 30-inch and 32-in TVs, respectively. Since the total cost of the 28-inch and 30-inch TVs is 2x + 600, which is the same as the total cost of the 26-inch and 32-inch TVs, we see that the total cost of the 28-inch and 30-inch TVs must be half of the total cost of \$3,400, or \$1,700.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for   [#permalink] 06 Aug 2019, 17:01

# Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for  