Yesterday each coat in a store was offered on sale price.

Question

Yesterday each coat in a store was offered on sale price. Did one of the coats have a sale price that was less than $40?

(1) Each coat had a regular price that was between $60 and $150
(2) Each coat had a sale price that was between 50 percent and 70 percent of its regular price.

edthehead7 · Answer

Hi there - any chance Bunuel or someone else can walk through step by step how to find the answer? thank you

Bunuel · Answer

Yesterday each coat in a store was offered on sale price. Did one of the coats have a sale price that was less than $40?

(1) Each coat had a regular price that was between $60 and $150

Not sufficient as we don't know anything about the discount.

(2) Each coat had a sale price that was between 50 percent and 70 percent of its regular price.

Not sufficient as we don't know anything about the price.

(1)+(2) If all coats cost $150 and the discount was 50% on each, then the sale price of each would be $75, which is greater than $40. However, if one coat cost $60 and the discount was 50% on it, then the sale price of that coat would be $30, which is less than $40. Not sufficient.

Answer: E.

Kinshook · Answer

Starburst10 
Given: Yesterday each coat in a store was offered on sale price.
Asked: Did one of the coats have a sale price that was less than $40?

(1) Each coat had a regular price that was between $60 and $150
Sale price may be different than regular price.
NOT SUFFICIENT

(2) Each coat had a sale price that was between 50 percent and 70 percent of its regular price.Since regular prices are unknown
NOT SUFFICIENT

(1) + (2) 
(1) Each coat had a regular price that was between $60 and $150
(2) Each coat had a sale price that was between 50 percent and 70 percent of its regular price.
Sales price may range between $60*50% = $30 to $150*70% = $105.
Sales price definitely range between $60*70% = $42 to $150*50% = $75.
But it may be possible that no coat is sold between $30 to $40.
NOT SUFFICIENT

IMO E

nijat00 · Answer

Hi Banuel,

But considering that the questions states "one of the coats", shouldn't we assume that both statements together are sufficient? My reasoning is that given the ranges stated in the question, at least one of the coats will have a sale price of $60* 0.5 = $30 which is less than $40. Please, tell me what I am missing here.

Bunuel · Answer

What if the coat, with a regular price of $60, if it were any, was sold at 70 percent of its regular price, so at $42?

Dbrunik · Answer

hi Bunuel, i assumed, via statement one that at least one coat had a price of 60 and one had a price of 150. why can we not assume this? if this is the case, then at a minimum, even if the lowest priced coat had the lowest discount, it would still be 30$, thus making C the correct answer .thanks,

Bunuel · Answer

Both statements only provide  ranges : statement (1) gives the price range for the coats, and statement (2) gives the discount range. The range for the coat prices ($60 to $150) does not mean there must be a coat priced exactly at $60 or $150—it only indicates that all coat prices lie somewhere within that range.

Nalapatricia · Answer

Yesterday each coat in a store was offered on sale price. Did one of the coats have a sale price that was less than $40?

(1) Each coat had a regular price that was between $60 and $150
 60< Prices < 150 without more info we cannot determine anything. 
INSUFFICIENT

(2) Each coat had a sale price that was between 50 percent and 70 percent of its regular price.

50< sale price < 70 without more info we cannot determine anything. 
INSUFFICIENT

(1) + (2) if 60< Prices < 150 and 50<percent of its regular price < 70

Could be possible:
All the coat were sold at

-$150*50% off = 75 sold price 
-$60*50% off = 30 sold price

But dont specify of provide any info to make sure that at least one was cheaper price with bigger discount, since we don ́t have more info, is 
INSUFFICIENT

Correct answer: Answer E

Juangui17 · Answer

So the catch here is that it's 70% of its regular price? So its a 30% discount of the 60 which gives a No answer to the question and a Yes to the 50% so we can be sure they applied the big discounts to the cheap ones.

lily123400 · Answer

I originally got this question wrong but re-read statement 2 again:
Each coat had a sale price that was between 50 percent and 70 percent of its regular price.

I took that originally to mean that each coat is between 50-70% off. However, it actually means that each coat's sale price is between 50-70% off (the discount varies from 30%-50%). So here, 30-50% of 60$ is 30$ - 42$ so it can be below and above 40$ thus insufficient.

bharathhr · Answer

Also It doesnt say that the price was between 60-150 $, including the ranges right , If they told that then we might think that there was definately a coat that was 60 $ .

egmat · Answer

Hi bharathhr,

Good instinct to check the wording, and you're right that "between $60 and $150" doesn't nail down whether the endpoints are included. But here's the key point:  even if the range were inclusive, it still wouldn't guarantee a coat priced at exactly $60.

A range tells you where every coat's price  could  fall - not that any coat actually sits at a specific value. "Each coat had a regular price between $60 and $150" just means no coat is below  $60  or above  $150 . Every single coat could be priced at  $150 , or  $99 , or  $73 . Nothing forces one of them to land on  $60 .

So the endpoint question is a bit of a red herring: inclusive or not, you can't conclude a  $60  coat exists.

Why it still fails even if a $60 coat existed

Suppose we  grant  you a coat at exactly  $60 . Statement 2 says its sale price is between  50%  and  70%  of regular:

- At  50%  off-base - sale price =  $30  (under  $40  - answer "yes")
- At  70%  - sale price =  $42  (over  $40  - answer "no")

Same coat, same statements, two different answers. That's exactly why the combination is  not sufficient  and the answer is  E .

This is the DS habit to lock in: a statement that only gives a  range  almost never pins down a specific value. Ask "does any allowed scenario give a different answer?" - and here, both a "yes" and a "no" fit comfortably.

Answer: E

Yesterday each coat in a store was offered on sale price.

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Yesterday each coat in a store was offered on sale price.

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