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Jonathan buys c chairs and t tables for his newly set up restaurant, w

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Jonathan buys c chairs and t tables for his newly set up restaurant, w  [#permalink]

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New post 27 Jul 2017, 03:41
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Jonathan buys c chairs and t tables for his newly set up restaurant, where c and t are positive integers. The chairs regularly sell at $50 apiece and the tables regularly sell at $80 apiece. Jonathan gets a discount of 20 percent on the price of each chair and 15 percent on the price of each table that he buys. What percentage of the total amount spent by him in buying the chairs and the tables at discounted prices was spent in buying chairs?

(1) He saved a total of $100 by purchasing the chairs and the tables at their discounted prices instead of their regular prices
(2) Due to the discounts, he paid only five-sixths of the amount he would have paid in purchasing the chairs and the tables at their regular prices

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Jonathan buys c chairs and t tables for his newly set up restaurant, w  [#permalink]

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New post 27 Jul 2017, 06:23
duahsolo wrote:
Jonathan buys c chairs and t tables for his newly set up restaurant, where c and t are positive integers. The chairs regularly sell at $50 apiece and the tables regularly sell at $80 apiece. Jonathan gets a discount of 20 percent on the price of each chair and 15 percent on the price of each table that he buys. What percentage of the total amount spent by him in buying the chairs and the tables at discounted prices was spent in buying chairs?

(1) He saved a total of $100 by purchasing the chairs and the tables at their discounted prices instead of their regular prices
(2) Due to the discounts, he paid only five-sixths of the amount he would have paid in purchasing the chairs and the tables at their regular prices



HI..

we are given initial and discounted price of each chair.
we are looking for % of chairs, so a RATIO is also sufficient..

let's see the statements

(1) He saved a total of $100 by purchasing the chairs and the tables at their discounted prices instead of their regular prices


Discounted prices are 0.8*50 for chair and 0.85*80..
OR discounts are 10 for chair and 12 for table..

if c chair and t table are sold...
Discount = \(10c+12t=100....5c+6t=50\)...
SO t is multiple of 5.... and t can take only one value 5 as 10 will make c NEGATIVE..
so c=4 and t=5..
% can be found as \(\frac{4}{9}*100\)
sufficient

(2) Due to the discounts, he paid only five-sixths of the amount he would have paid in purchasing the chairs and the tables at their regular prices

initial amount = 50c+80t
discounted price = 40c+68t..
so \(\frac{5}{6}*(50c+80t)=40c+68t\)
here again you will get a ratio 5c=4t...or \(\frac{c}{t}=\frac{4}{5}\)..
\(\frac{c}{c+t}=\frac{4}{4+5}\)
%= \(\frac{4}{9}*100\)
sufficient


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Re: Jonathan buys c chairs and t tables for his newly set up restaurant, w  [#permalink]

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New post 27 Jul 2017, 06:48
duahsolo wrote:
Jonathan buys c chairs and t tables for his newly set up restaurant, where c and t are positive integers. The chairs regularly sell at $50 apiece and the tables regularly sell at $80 apiece. Jonathan gets a discount of 20 percent on the price of each chair and 15 percent on the price of each table that he buys. What percentage of the total amount spent by him in buying the chairs and the tables at discounted prices was spent in buying chairs?

(1) He saved a total of $100 by purchasing the chairs and the tables at their discounted prices instead of their regular prices
(2) Due to the discounts, he paid only five-sixths of the amount he would have paid in purchasing the chairs and the tables at their regular prices


C chairs - $50 each - $40 (After discount)
T tables - $80 each - $68 (After discount)
\(\frac{40C}{40C+68T}\)*100 = ?

So we need to find unique value for C and T.

1) 10C + 12T = 100
=> 5C + 6T = 50
C = 4, T = 5
Sufficient.

2) \(\frac{5}{6}\)*(50C + 80T) = 40C + 68T
=>\(\frac{C}{T}\) = \(\frac{4}{5}\)
=> C = 4, T = 5
Sufficient.

Answer is D

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: Jonathan buys c chairs and t tables for his newly set up restaurant, w   [#permalink] 27 Jul 2017, 06:48
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