Each of the seven painting in an art gallery has a different price, is

Question

Each of the seven painting in an art gallery has a different price, is it possible to purchase at least 3 paintings for no more than $1800 in total?

1) The Median price of seven paintings is $550.

2) It is possible to purchase four  more  paintings at the gallery for a total of $2300.

Source: GMAT Advanced Quant: 250+ Practice Problems by Manhattan Prep (2020)

stne · Answer

1) The Median price of seven paintings is $550.

If the median is 550 then the 4th painting is 550 which means that three paintings are less  \leq   550. also since all are differently priced hence 3 paintings cost < 1650 (550*3). Hence it is possible to buy 3 paintings for no more than 1800.  SUFF

2) It is possible to purchase four more paintings at the gallery for a total of $2300.

It won't be possible to buy 3 paintings for \leq  1800 if all four painting are more than 600
Now if 4 paintings cost 2300 that means all cannot be more than 600 as then cost could be more than 2400

Worst case scenario 600 600 600 500 Which means it is always possible to select 3 paintings such that cost is  \leq  1800.

SUFF

Ans- D

Hope it's clear.

IanStewart · Answer

If the median of the seven prices is $550, and the prices are distinct, then three of the prices are less than $550. So you could buy those 3 paintings for less than $(3)(550) = $1650, and statement 1 is sufficient.

If you can buy four paintings for $2300, you're buying each of those paintings for an average of $2300/4 = $575. The largest of those four prices must then be greater than $575 (the four prices can't all be below average), so if we just buy the cheapest three of those four paintings, the cost must be less than 2300 - 575 = 1725 dollars. So Statement 2 is also sufficient and the answer is D.

unraveled · Answer

Although I answered correctly, Statement 2 seems bit off.
We need to have different prices. 
As per the question we can just validate by buying the 3 least valued paintings.

Case I: All the four more paintings are the highest tagged price.
By default we have other 3 being the lowest tagged price, if the 4 more ones are priced 573, 574, 575 and 577. 
Answer is YES.

Case II: All four more paintings are not highest tagged price.
If the 4 more ones are priced 1, 2, 3 and 2294, one among the remaining three must be at max. 1793 value. But we don't know the actual value.
So, the answer can be NO or YES.

Also, one possibility is that all the seven paintings total 2300, in which case we get a sure shot YES.

IanStewart  
Am I missing something. Please help!!

IanStewart · Answer

I expect that Statement 2 was not copied correctly from the book - in the original post above, Statement 2 reads:

"2) It is possible to purchase four  more  paintings at the gallery for a total of $2300."

That word "more" that I've highlighted makes no sense - "more" than what? There's no sensible way to interpret it. So I've interpreted Statement 2 to mean

"2) It is possible to purchase four (of the seven) paintings at the gallery for a total of $2300."

Then if we simply buy the cheapest three of those four paintings, we must spend less than the $1800 the question asks about.

I gather you're interpreting Statement 2 and the question to mean something like: "if we can buy four of the paintings for $2300, is it possible to buy the other three paintings for less than $1800?" If that's what Statement 2 meant, then yes, it is certainly not sufficient, since you have almost no information, under that interpretation, about the cost of the three paintings you're trying to buy.

If, on the other hand, the question has been faithfully transcribed from the source, then the source desperately needs editing. There are at least three other typos in it (there's a comma splice, 'painting' needs to be pluralized, and Statement 1 is missing a definite article) in addition to the problem I mention above. But I'd be surprised if the source contained that many errors, and I expect the interpretation I made above is either the one written in the book, or at least the one intended by the book.

unraveled · Answer

Thank you Ian.
This question is too open to be interpreted with a single conclusion.
Didn't expect Manhattan to write such open-ended questions, if poster has transcribed it properly.

Mio0821 · Answer

Hi,
I don't still understand the statement (2) part.

Because if, for example, the total $2,300 is allocated to 1, 2, 1148, 1149 respectively, it's not enough to say it's possible to purchase three paintings by $1800 only based on this statement.

I might missed anything, but can anyone explain this case?

Posted from my mobile device

bumpbot · Answer

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Each of the seven painting in an art gallery has a different price, is

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