|
Author |
Message |
|
TAGS:
|
|
|
Senior Manager
Joined: 22 Dec 2011
Posts: 298
Followers: 2
Kudos [?]:
42
[0], given: 32
|
A store sells a certain product at a fixed price per unit. A [#permalink]
 04 Oct 2012, 11:35
Question Stats:
56% (04:10) correct
43% (02:46) wrong based on 48 sessions
A store sells a certain product at a fixed price per unit. At the product's current price, q units cost a total of exactly $300. If the price were lowered by $5 from its current value, then q + 2n units would cost exactly $300; if the price were raised by $5, then q – n units would cost exactly $300. What is the value of q? A. 10 B. 15 C. 20 D. 25 E. 30 Is there any easy way to solve this problem? Ans is the real exam going to have these sort of problems? Cheers
Last edited by Bunuel on 04 Oct 2012, 12:27, edited 1 time in total.
RENAMED THE TOPIC.
|
|
|
|
|
|
|
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 858
Followers: 222
Kudos [?]:
618
[2] , given: 14
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
04 Oct 2012, 14:52
2
This post received
KUDOS
Jp27 wrote: A store sells a certain product at a fixed price per unit. At the product's current price, q units cost a total of exactly $300. If the price were lowered by $5 from its current value, then q + 2n units would cost exactly $300; if the price were raised by $5, then q – n units would cost exactly $300. What is the value of q?
A. 10
B. 15
C. 20
D. 25
E. 30
Is there any easy way to solve this problem? And is the real exam going to have these sort of problems? Dear Jp27, I'm happy to help with this.  This problem is very hard --- definitely an upper 700 level question. If you are doing very well on the Quant section, the CAT could feed you a question like this. This question is a very challenging if you take an algebraic approach, but it's remarkably simple if you backsolve. Let's start with (C). Assume q = 20 units If we can buy 20 units, they must cost a price of 300/20 = $15 Lower the price $5 to a new price of $10 --- then we could buy 300/10 = 30 units (10 more than the original case) Raise the price $5 to a new price of $20 ---- then we could buy 300/20 = 15 units (5 fewer than the original case) This is the case for which we are looking ----- the increase in units from a $5 decrease in price is twice as much as the decrease in units from a $5 increase in price. Does this make sense? Mike
_________________
Mike McGarry
Magoosh Test Prep
|
|
|
|
|
|
Senior Manager
Joined: 28 Jun 2009
Posts: 457
Location: United States (MA)
Followers: 14
Kudos [?]:
84
[1] , given: 46
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
04 Oct 2012, 15:09
1
This post received
KUDOS
It got too complicated when I used algebra. Using plugging in, it was quite fast.
Price Quantity total value
p q pq = 300
p-5 q+2n (p-5)(q+2n) = 300
p+5 q-n (p+5)(q-n) = 300
Solving three equations for three unknowns. Tough!!
Plugging in, I always start with C. C was the answer here, so saved calculation!
Putting values in above equations:
Price Quantity total value
15 20 300
10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5
20 15 300
So q = 20 satisfies all equations!!
What is the source?
|
|
|
|
|
|
Manager
Joined: 26 Jul 2011
Posts: 122
Location: India
WE: Marketing (Manufacturing)
Followers: 1
Kudos [?]:
15
[0], given: 15
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
05 Oct 2012, 00:02
As it is said for GMAT "whenever you see yourself dealing with some extra long equations or calculations trust!! there is an easy way out" here in this case back solving makes this question way too easy.
B is the answer
|
|
|
|
|
|
Senior Manager
Joined: 22 Dec 2011
Posts: 298
Followers: 2
Kudos [?]:
42
[0], given: 32
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
06 Oct 2012, 21:52
mikemcgarry wrote: Jp27 wrote: A store sells a certain product at a fixed price per unit. At the product's current price, q units cost a total of exactly $300. If the price were lowered by $5 from its current value, then q + 2n units would cost exactly $300; if the price were raised by $5, then q – n units would cost exactly $300. What is the value of q?
A. 10
B. 15
C. 20
D. 25
E. 30
Is there any easy way to solve this problem? And is the real exam going to have these sort of problems? Dear Jp27, I'm happy to help with this. This problem is very hard --- definitely an upper 700 level question. If you are doing very well on the Quant section, the CAT could feed you a question like this. This question is a very challenging if you take an algebraic approach, but it's remarkably simple if you backsolve. Let's start with (C). Assume q = 20 units If we can buy 20 units, they must cost a price of 300/20 = $15 Lower the price $5 to a new price of $10 --- then we could buy 300/10 = 30 units (10 more than the original case) Raise the price $5 to a new price of $20 ---- then we could buy 300/20 = 15 units (5 fewer than the original case) This is the case for which we are looking ----- the increase in units from a $5 decrease in price is twice as much as the decrease in units from a $5 increase in price. Does this make sense? Mike Thanks Mike. It does, especially the way you have circumvented calculating the variable N. I guess all the thinking goes before even touching the pen! cheers
|
|
|
|
|
|
Intern
Status: Fighting to kill GMAT
Joined: 23 Sep 2012
Posts: 35
Location: United States
Concentration: International Business, General Management
GPA: 3.8
WE: General Management (Other)
Followers: 0
Kudos [?]:
8
[0], given: 38
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
07 Oct 2012, 08:57
piyatiwari wrote: It got too complicated when I used algebra. Using plugging in, it was quite fast.
Price Quantity total value
p q pq = 300
p-5 q+2n (p-5)(q+2n) = 300
p+5 q-n (p+5)(q-n) = 300
Solving three equations for three unknowns. Tough!!
Plugging in, I always start with C. C was the answer here, so saved calculation!
Putting values in above equations:
Price Quantity total value
15 20 300
10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5
20 15 300
So q = 20 satisfies all equations!!
What is the source? Is there any reason why you start with C while using POE? What if the numbers are not given in a particular order (ascending here)? Do you use the same strategy in other question types?
_________________
Kudos is the currency of appreciation.
You can have anything you want if you want it badly enough. You can be anything you want to be and do anything you set out to accomplish, if you hold to that desire with the singleness of purpose. ~William Adams
Many of life's failures are people who did not realize how close to success they were when they gave up. ~Thomas A. Edison
Wir müssen wissen, Wir werden wissen. (We must know, we will know.) ~Hilbert
|
|
|
|
|
|
Senior Manager
Joined: 28 Jun 2009
Posts: 457
Location: United States (MA)
Followers: 14
Kudos [?]:
84
[0], given: 46
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
07 Oct 2012, 09:53
closed271 wrote: Is there any reason why you start with C while using POE? What if the numbers are not given in a particular order (ascending here)? Do you use the same strategy in other question types? No reason. I always start with option C while using plugging in. MGMAT advanced math book has some nice techniques about ruling out option choices. But here, I didn't use any of those.
|
|
|
|
|
|
Manager
Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 74
Location: India
Concentration: Leadership, Entrepreneurship
GMAT 1: Q33 V27
GPA: 2.92
WE: Analyst (Computer Software)
Followers: 0
Kudos [?]:
9
[0], given: 52
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
08 Oct 2012, 07:43
Jp27 wrote: A store sells a certain product at a fixed price per unit. At the product's current price, q units cost a total of exactly $300. If the price were lowered by $5 from its current value, then q + 2n units would cost exactly $300; if the price were raised by $5, then q – n units would cost exactly $300. What is the value of q?
A. 10
B. 15
C. 20
D. 25
E. 30
Is there any easy way to solve this problem? Ans is the real exam going to have these sort of problems?
Cheers Since from the options is of pure chance, one would end up losing lots of time. Any other solution for this question?
|
|
|
|
|
|
Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)
Followers: 46
Kudos [?]:
278
[0], given: 43
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
08 Oct 2012, 09:46
navigator123 wrote: Jp27 wrote: A store sells a certain product at a fixed price per unit. At the product's current price, q units cost a total of exactly $300. If the price were lowered by $5 from its current value, then q + 2n units would cost exactly $300; if the price were raised by $5, then q – n units would cost exactly $300. What is the value of q?
A. 10
B. 15
C. 20
D. 25
E. 30
Is there any easy way to solve this problem? Ans is the real exam going to have these sort of problems?
Cheers Since from the options is of pure chance, one would end up losing lots of time. Any other solution for this question? Back to the basics. Write down the prices and corresponding quantities using the given answers. You will get a small table: (Q, P) (10, 30) (15, 20) (20, 15) (25, 12) (30, 10) From the given information, about raising/reducing the price, you can conclude the following about the prices and corresponding quantities: Q+2N P-5 Q P Q-N P+5 The corresponding prices for the quantities Q+2N, Q, and Q-N are three consecutive multiples of 5: P-5, P, and P+5. From the table, the prices should be 10, 15, and 20, and thus the quantity should be 20. Answer C. Remark: this is my corrected post, as in my previous one, I mixed up prices and quantities. If somebody saw it, please, just forget about it.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
|
|
|
|
|
|
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 858
Followers: 222
Kudos [?]:
618
[0], given: 14
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
08 Oct 2012, 13:00
closed271 wrote: Is there any reason why you start with C while using POE? What if the numbers are not given in a particular order (ascending here)? Do you use the same strategy in other question types? On official GMAT problems, if the answer choices are all single numbers, those numbers will be in numerical order. This is true on all official material and all high quality material, and therefore it's an excellent test of how authentic a given prep source is --- if you see a number of questions with the answers out of order, that's a red flag --- you should question whether that source is trustworthy. Some GMAT prep sources are excellent, and some are not worth the paper on which they are printed. The reason we start with the middle answer (i.e. (C) on official material) is so that we know which way to go if our first choice is not right. Consider this hypothetical question: Frank started with X money. He bought blah blah, blah blah, blah % of blah, etc etc and was left with $41.50 in cash after those purchases. What was Frank's original starting amount?
(A) $100
(B) $120
(C) $150
(D) $180
(E) $200I will start with (C) 150 ----- if by chance I'm right, that's great. If I wind up with more leftover cash than $41.50, I know I started with too much --- I can eliminate (C) & (D) & (E). If I wind up with less leftover cash than $41.50, I know I started with too little --- I can eliminate (A) & (B) & (C). Does that make sense? Mike
_________________
Mike McGarry
Magoosh Test Prep
|
|
|
|
|
|
Intern
Joined: 26 Jul 2012
Posts: 35
Followers: 0
Kudos [?]:
0
[0], given: 6
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
10 Nov 2012, 15:00
Even with plugging in this is a humdinger problem!
I tried the algebraic approach first and got stuck. Finally, took a guess.
With plugging in, I will try to time myself but it will take exactly two minutes still.
Start with C (so we know which direction to go in)
Case 1:
(x) = Price of the unit
(q) = # of units
Let q = 20
Therefore, x = 15 because qx = 300
Case 2:
x-5 = 10
Given: q + 2n = 30; therefore:
20 + 2n = 30
2n = 10
n = 5
Case 3:
x+5 = 20
Given : q - n = 15
20 - 5 = 15
Done. D is the answer because the equation checks out!
|
|
|
|
|
|
Intern
Joined: 05 Dec 2012
Posts: 14
GMAT 1: 680 Q44 V38
Followers: 0
Kudos [?]:
2
[2] , given: 20
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
03 Mar 2013, 06:39
2
This post received
KUDOS
Hello !
I was reviewing some questions and I think this one is not as difficult as it seems. I solved it in less than 2 minutes using equations solving so I felt like it could be useful to other people :
We can write the following equations :
(1) pq = 300
(2) (q+2n)(p-5) = 300
(3) (q-n)(p+5) = 300
Distribute (2) and (3) :
(2) qp -5q +2np -10n = 300
(3) qp +5q -np - 5n = 300
Add them together :
(2) + (3) : 2qp +np -15n = 600
Thanks to (1) you get : np-15n = 0 or n(p-15) = 0
Since n can't be 0 ( it would mean that a lower or higher price doesn't affect the total price and quantities ) you have p-15 = 0 and p =15. With (1), you get q = 300/15 = 20
I know it seems time consuming but it worked for me. And I usually don't like picking numbers..
|
|
|
|
|
|
Senior Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 320
Location: Bangladesh
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Followers: 6
Kudos [?]:
35
[0], given: 46
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
28 Mar 2013, 04:56
pancakeFR wrote: Hello !
I was reviewing some questions and I think this one is not as difficult as it seems. I solved it in less than 2 minutes using equations solving so I felt like it could be useful to other people :
We can write the following equations :
(1) pq = 300
(2) (q+2n)(p-5) = 300
(3) (q-n)(p+5) = 300
Distribute (2) and (3) :
(2) qp -5q +2np -10n = 300
(3) qp +5q -np - 5n = 300
Add them together :
(2) + (3) : 2qp +np -15n = 600
Thanks to (1) you get : np-15n = 0 or n(p-15) = 0
Since n can't be 0 ( it would mean that a lower or higher price doesn't affect the total price and quantities ) you have p-15 = 0 and p =15. With (1), you get q = 300/15 = 20
I know it seems time consuming but it worked for me. And I usually don't like picking numbers.. Hi this also works for me.Most of the times i can`t pick the number.1 kudos for u
|
|
|
|
|
|
Intern
Joined: 22 Jan 2010
Posts: 25
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)
Followers: 0
Kudos [?]:
2
[1] , given: 3
|
Re: A store sells a certain product at a fixed price per unit. A [#permalink]
28 Mar 2013, 05:08
1
This post received
KUDOS
Let p be price per unit.
From the first condition we get pq = 300.
From the other conditions we get,
(p-5)(q+2n) = pq
=> pq -5q + 2pn - 10n = pq
=> 5q = 2pn - 10n
(p+5)(q-n) = pq
=> pq + 5q - pn -5n = pq
=> 5q = pn + 5n -------(3)
so, 2pn - 10n = pn + 5n
=> pn = 15n
=> p = 15
Then q = 300/15 = 20.
Answer : Option C.
-------------------------------------
Please press KUDOS if you like my post.
|
|
|
|
|
|
|
Re: A store sells a certain product at a fixed price per unit. A
[#permalink]
28 Mar 2013, 05:08
|
|
|
|
|
|
|
|
|
|
|
close
