The total price of a basic TV and a TV stand was $1,500. If

I also solved it using three equations formed by the three pieces of information provided here with the answer B. The only problem with this question is I think there is no shortcut and it takes almost three minutes to solve it.

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

TV+TVs=1500
[TV+TV+2000(which is 3d)]/8=TVs
2TV+2000=8(1500-TV)
10TV=10000
TV=1000

Basic TV + Stand = 1500

3DTV = 2000 + Basic TV

(1/8)(Basic TV + 3DTV) = Stand
i.e. Stand = (2*Basic TV+2000) / 8

i.e. Basic TV + Stand = 1500
i.e. Basic TV + (2*Basic TV+2000) / 8 = 1500
i.e. 10*Basic TV+2000 = 1500*7 = 12000
i.e. 10*Basic TV = 12000 - 2000
i.e. Basic TV = 10000 / 10 = $1000

Answer: Option B

let the price of basic TV be x, 3D TV be 2000+x and TV stand be y

x +y = 1500 (1)
final price = x +x +2000 +y
y/2x +2000 +y = 1/8
or 8y = 2x +y +2000
or 8y = x +3500
or x = 8y -3500 (2)

solving these two equation we get x = 1000 and y = 500

Option B

if basic tv costs 1000 then 3d tv cost will 3000 and 1/8 of 3000 will be the cost of tv stand
tv stand = 375
1000+375=1375 but cost of basic TV and tv stand =1500
I think values does not add up
Please help mikemcgarry Bunuel gmatophobia

lovesuit There is a minor error in your understanding of the highlighted portion. Happy to help you here -



"that total" refers to the cost of basic TV + cost of 3D TV

Cost of TV Stand = 1/8 (Cost of Basic TV + Cost of 3D TV)

Cost of Basic TV = 1000
Cost of 3D TV = 1000 + 2000 = 3000

Cost of TV Stand = 1/8 * (1000 + 3000)

= 1/8 * 4000 = 500

Therefore Cost of Basic TV + Cost of Stand = 1000 + 500 = 1500

Hope this helps !

thanks for your help,
is it an efficient way to approach this question? it took me around 1.30 sec to check out all the options but because of a misunderstanding answer did not match.

You can use the options efficiently to solve this word problem.
The first option to try is of course 1000 because of how easy the numbers will be.
If Basic TV cost is 1000, that of the stand will be 500 and that of 3D TV will be 3000.
Cost of basic TV + 3D TV = 4000 and 500 is 1/8th of it so it works.

Answer (B)

But what if it hadn't worked? Say 500 was smaller than 1/8th of the total. We would have then decreased the cost of basic TV.
Had 500 been more than 1/8th of the total, we would have increased the cost of the basic TV. This way, we would require at most two iterations.

Say we tried with 1200 as the cost of basic TV first.
Then cost of stand is 300 and cost of 3D TV is 3200.
Total cost of both TVs is 4400 and 300 is less than 1/10th of it so we need to increase the cost of stand and hence reduce the cost of basic TV. So out of options (A), (B) and (C), next we would pick option (B). Either it will be correct or it will tell us what the correct answer is.