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Board of Directors P
Joined: 17 Jul 2014
Posts: 2540
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: A store sells a certain product at a fixed price per unit. A  [#permalink]

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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

my approach:
pq=300
(p-5)(q+2n)=300
pq+2pn-5q-10n=300
now we know that pq=300, deduct from both sides:
2n-5q-10n=0

second equation
(p+5)(q-n)=300
pq-pn+5q-5n=300 - same thing - deduct 300
5q-pn-5n=0

now..take both new equations and add them:
2n-5q-10n + 5q-pn-5n= 0
we get np-15n=0
factor n:
n(p-15)=0
either n=0, or p=15
but n can't be 0, because otherwise (P-5)*Q or (P+5)*Q would not be the same as PQ, so it MUST be true that P=15
in this case Q=20.
Manager  S
Joined: 03 Jan 2017
Posts: 139
Re: A store sells a certain product at a fixed price per unit. A  [#permalink]

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first I jot down the equations:
x=price

x*q=300
(x-5)(q+2n)=300
(x+5)(q-n)=300

MNGMT advises to start from B and based on the move
B wasn't fine
so I tried C=>ok
Director  S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 542
Location: India
Re: A store sells a certain product at a fixed price per unit. A  [#permalink]

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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

price per unit = 300/q

300/q - 5 = 300/(q+2n) ... (1)

300/q + 5 = 300/(q-n) .... (2)

solving (1) and (2), we get
q = 20 n = 5

Option C
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GMAT Mentors Manager  B
Joined: 23 Dec 2013
Posts: 142
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44 GPA: 3.76
Re: A store sells a certain product at a fixed price per unit. A  [#permalink]

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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

This problem requires a great deal of space on a yellow pad. So it's going to likely need two quadrants on a GMAT folio. That said, the best approach is to set up a table with the values P | PQ = 300 | Q | (P-5)(Q+2N) = 300 | (P+5)(Q-N) = 300

Then at this point it's about plugging and chugging through the answers. The criterion by which to eliminate is the variable N which should be consistent within a given row in your table (e.g., for the correct answer, it's equal to 5).

Q = 20, P = 15.
(10)*(Q+2N) = 300
Q + 2N = 30
2N = 30 - Q = 30 -20
2N = 10
N = 5

(20)*(20-5) = 20*15 = 300
Director  D
Joined: 13 Mar 2017
Posts: 729
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A store sells a certain product at a fixed price per unit. A  [#permalink]

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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

A very simple solution to this question can be framed which will take approx 2 minutes by following method.
1st case : price is lowered by \$5
So Total price lowered = 5q
This lead to increase in number of units by 2n
So, 5q = 2n(300/q - 5)
5q/2n = 300/q - 5 ...........................(i)

2nd case : price is increased by \$5
So, total price increased = 5q
This lead to decrease in number of units by n.
So, 5q = n(300/q +5)
5q/n = 300/q + 5.............................(ii)

From (i) * 2 - (ii), we get
0 = 600/q - 10 - 300/q - 5
15 = 300/q
q = 20

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Re: A store sells a certain product at a fixed price per unit. A  [#permalink]

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_________________ Re: A store sells a certain product at a fixed price per unit. A   [#permalink] 10 Sep 2018, 14:52

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