GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 May 2019, 04:34

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Did the seller earn a profit?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Senior Manager
Senior Manager
User avatar
P
Status: Manager
Joined: 27 Oct 2018
Posts: 300
Location: India
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
GMAT ToolKit User
Did the seller earn a profit?  [#permalink]

Show Tags

New post 16 Apr 2019, 04:29
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

52% (01:31) correct 48% (01:44) wrong based on 33 sessions

HideShow timer Statistics

Did the seller earn a profit?

(1) The selling price of 20 items equals the cost of 15 items.

(2) The cost of 10 items is $55 greater than the selling price of 8 items.

Source: GMAT Math BIBLE, p.444, q.152

Explanation from the source:

Let c and s be the cost and the selling price, respectively, for the seller on each item.

From Statement (1) alone, we have that the selling price of 20 items equals the cost of 15 items.
Hence, we have 20s = 15c, or s = (\(\frac{15}{20}\))c = \(\frac{3c}{4}\).
Now, profit = selling price – cost = s – c = \(\frac{3c}{4}\) – c = \(\frac{–c}{4}\), a negative value (c is price and therefore is positive. Hence, –c/4 is negative).
A negative profit should be considered a loss. Hence, Statement (1) alone is sufficient to determine that the seller did not earn a profit.

From Statement (2) alone, we have that the cost of 10 items is $55 more than the selling price of 8 items.
The cost of 10 items is 10c and the selling price of 8 items is 8s.
Hence, we have 10c – 8s = 55.
Subtracting 2s from both sides yields 10c – 10s = 55 – 2s; 10(c – s) = 55 – 2s; c – s = \(\frac{(55 – 2s)}{10}\).
Now, if 55 – 2s is positive, c – s, which equals \(\frac{(55 – 2s)}{10}\), is positive. Here, Cost > Selling Price, and seller made a profit.
Otherwise, he did not make a profit. 55 – 2s is not positive if s < 55/2.
Hence, we have a double case and Statement (2) alone is not sufficient.

_________________
..Thanks for KUDOS
Image
Senior Manager
Senior Manager
User avatar
G
Joined: 13 Feb 2018
Posts: 270
GMAT 1: 640 Q48 V28
Premium Member
Re: Did the seller earn a profit?  [#permalink]

Show Tags

New post 16 Apr 2019, 05:00
1
Honestly, I don't like the wording of the question, but who cares :)

1 stm - it's clear that our selling price is less than the cost, as selling 20 items will cover the costs only for 15 items. We will lose if we sell any. Suff
2 stm - 10*cost-8*price=55 We can manipulate a lot with two variables. Not suff

IMO
Ans: A
Manager
Manager
avatar
B
Joined: 11 Jun 2018
Posts: 83
GMAT 1: 500 Q39 V21
Re: Did the seller earn a profit?  [#permalink]

Show Tags

New post 21 Apr 2019, 02:28
chetan2u :-how is statement 2 not sufficient. Please explain, i can't find a scenario where it will lead to a profit for the seller.
Senior Manager
Senior Manager
User avatar
P
Status: Manager
Joined: 27 Oct 2018
Posts: 300
Location: India
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)
GMAT ToolKit User
Re: Did the seller earn a profit?  [#permalink]

Show Tags

New post 21 Apr 2019, 02:55
hi Manat

for statement 2:
\(10c = 8p + 55\), \(c =\) \(\frac{8p + 55}{10}\)


if \(p\leq{27}\), then \(c\geq{27.1}\) --> loss
if \(p = 27.5\), then \(c = 27.5\) --> break even (when \(p = c\), \(10c = 8c + 55\), \(2c = 55\), \(c = p = 27.5\))
if \(p\geq{28}\) , then \(c\leq{27.9}\) --> profit

while in statement 1, it is locked ratio and c is always greater as long as we are dealing with positive numbers.
\(20s = 15c\), \(\frac{c}{s} = \frac{20}{15}\) ---> (we can never assume that c = p as in statement 2)
_________________
..Thanks for KUDOS
Image
Senior Manager
Senior Manager
User avatar
P
Joined: 25 Dec 2018
Posts: 299
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
Re: Did the seller earn a profit?  [#permalink]

Show Tags

New post 21 Apr 2019, 03:19
how statement 1 is sufficient?
Manager
Manager
avatar
B
Joined: 05 Oct 2017
Posts: 64
Did the seller earn a profit?  [#permalink]

Show Tags

New post 21 Apr 2019, 03:26
1
mangamma wrote:
how statement 1 is sufficient?


Statement 1 :
20s=15c

\(\frac{s}{c}= \frac{15}{20}\)

which means selling price is less than cost price, hence the seller went in loss.
Question - "Did the seller earn a profit?" -- Answer - No
So, statement 1 is sufficient.
_________________
Press Kudos if you liked my response!!!
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7682
Did the seller earn a profit?  [#permalink]

Show Tags

New post 21 Apr 2019, 06:21
1
Manat wrote:
chetan2u :-how is statement 2 not sufficient. Please explain, i can't find a scenario where it will lead to a profit for the seller.


Hi Manat
The difference 55 holds the key..

If the cost of two items is more than 55, then profit..
Say each costs 50, so cost of 10 items is 50*10=500.
But 500-55=445 is the selling price of 8 items.. so each item is sold for 445/8=~55
So profit of 5 per piece.


If the cost of two items is less than 55, then loss..
Say each costs 10, so cost of 10 items is 10*10=100.
But 100-55=45 is the selling price of 8 items.. so each item is sold for 45/8=~5.5
So loss of 5 per piece.
_________________
Intern
Intern
avatar
B
Joined: 15 Nov 2017
Posts: 11
Re: Did the seller earn a profit?  [#permalink]

Show Tags

New post 24 Apr 2019, 14:28
chetan2u wrote:
Manat wrote:
chetan2u :-how is statement 2 not sufficient. Please explain, i can't find a scenario where it will lead to a profit for the seller.


Hi Manat
The difference 55 holds the key..

If the cost of two items is more than 55, then profit..
Say each costs 50, so cost of 10 items is 50*10=500.
But 500-55=445 is the selling price of 8 items.. so each item is sold for 445/8=~55
So profit of 5 per piece.


If the cost of two items is less than 55, then loss..
Say each costs 10, so cost of 10 items is 10*10=100.
But 100-55=45 is the selling price of 8 items.. so each item is sold for 45/8=~5.5

So loss of 5 per piece.





what if I solve the question with Option II in the following manner :-

let assume the S.P. of 8 items are $X
the S.P. of 1 item is $X/8

C.P of 10 items are $55
C.P of 1 items $5.5

now based on 1 item (S.P - C.P) will give us a negative value which implies the seller did loss by selling the product.

Please let me know where I am thinking wrong with this procedure.
GMAT Club Bot
Re: Did the seller earn a profit?   [#permalink] 24 Apr 2019, 14:28
Display posts from previous: Sort by

Did the seller earn a profit?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.