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Basic and 3D TVs

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Basic and 3D TVs

by EOV » Sun Dec 02, 2012 5:49 am
Hi everybody,

The total price of a basic TV and a TV stand was $1,500. If the same TV had been purchased with a next generation 3D TV whose price was $2,000 more than the price of the basic TV, then the price of the TV stand would have been one eighth of that total. What was the price of the basic TV?

(A) $900
(B) $1,000
(C) $1,100
(D) $1,200
(E) $1,300

Can you help me to find correct answer?
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by siddhantlife » Sun Dec 02, 2012 8:33 am
i am getting option b i.e. 1000$ as the answer? is it correct?
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by Brent@GMATPrepNow » Sun Dec 02, 2012 9:44 am
EOV wrote:Hi everybody,

The total price of a basic TV and a TV stand was $1,500. If the same TV had been purchased with a next generation 3D TV whose price was $2,000 more than the price of the basic TV, then the price of the TV stand would have been one eighth of that total. What was the price of the basic TV?

(A) $900
(B) $1,000
(C) $1,100
(D) $1,200
(E) $1,300

Can you help me to find correct answer?
I think the wording is somewhat confusing, but here it goes. . . .

Let T = cost of basic TV
Let S = cost of stand

The total price of a basic TV and a TV stand was $1,500.
T + S = 1500

If the same TV had been purchased with a next generation 3D TV whose price was $2,000 more than the price of the basic TV, then the price of the TV stand would have been one eighth of that total.

My interpretation: this new package consists of a basic TV and a 3D TV (but no TV stand).

T = cost of basic TV
T + 2000 = cost of 3D TV (since 3D TV's price is $2,000 more than price of basic TV)

Total cost = T + (T + 2000)
Simplify: total cost = 2T + 2000

The price of the TV stand would have been one eighth of that total.
We get: (1/8)(2T + 2000) = S

We now have 2 equations with 2 unknowns:
T + S = 1500
(1/8)(2T + 2000) = S

Multiply bottom equation by 8 to get:
T + S = 1500
2T + 2000 = 8S

If, T + S = 1500, then S = 1500 - T

Take bottom equation and replace S with 1500 - T to get:
2T + 2000 = 8(1500 - T)

Simplify: 2T + 2000 = 12,000 - 8T
Simplify: 10T = 10,000
Solve: T = 1000 = B

Cheers,
Brent
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by GMATGuruNY » Sun Dec 02, 2012 12:48 pm
EOV wrote:Hi everybody,

The total price of a basic TV and a TV stand was $1,500. If the same TV had been purchased with a next generation 3D TV whose price was $2,000 more than the price of the basic TV, then the price of the TV stand would have been one eighth of that total. What was the price of the basic TV?

(A) $900
(B) $1,000
(C) $1,100
(D) $1,200
(E) $1,300

Can you help me to find correct answer?
An alternate approach is to plug in the answers, which represent the price of the basic TV.

The price of the 3D TV is 2000 more than the price of the basic TV.
When the correct answer choice is plugged in, the price of the TV stand must be equal to 1/8 of the total cost of the two TVs.

Answer choice C: 1100
TV stand = 1500 - 1100 = 400.
Total cost of both TVs = 1100 + (2000+1100) = 4200.
1/8 * 4200 = 525.
Since 525>400, the total cost must decrease, implying that a smaller answer choice is needed.
Eliminate C, D and E.

Answer choice B: 1000
TV stand = 1500 - 1000 = 500.
Total cost of both TVs = 1000 + (2000+1000) = 4000.
1/8 * 4000 = 500.
Success!

The correct answer is B.
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