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Mr.John used to purchase certain number of mangoes for $360.

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Mr.John used to purchase certain number of mangoes for $360.  [#permalink]

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New post Updated on: 13 Feb 2014, 07:15
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Question Stats:

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Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.

A. 360
B. 380
C. 400
D. 406
E. 412

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Originally posted by rxs0005 on 28 Jul 2010, 06:55.
Last edited by Bunuel on 13 Feb 2014, 07:15, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Percent  [#permalink]

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New post 28 Jul 2010, 07:57
C - no of mangoes

(360/0.9C)-(360/C)=12
C=10/3

120 mangoes should cost 400
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Re: Percent  [#permalink]

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New post 28 Jul 2010, 09:22
1
x = price per mango
y = number of mangoes

Equation 1:
x*y = 360 => y = 360/x

Equation 2:
x*0.9*(y+12) = 360

Replace y in equation with 360/x (obtained from Equation 1 and solve for x)

=> x = 10/3

Multiplying with 120 (number of mangoes the question asks for) yields (10/3)*120 = 400
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Re: Percent  [#permalink]

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New post 13 Feb 2014, 06:53
1
Im trying to answer this another way but I can't seem to think what I'm doing wrong

So we have

PQ = 360
(0.9P)(Q+12) = 360

We need to find 120P

Now if we reduce 10% on P and still get the same result then Q increases 10%
So Q + 12 = 11/10 Q --> Q = 120

Therefore P is equal to 3.

And we have that 120P = 360.

I don't quite know what I can't get the answer 400 following this approach, could any expert please advise

Thanks a lot!
Cheers
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Re: Percent  [#permalink]

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New post 13 Feb 2014, 07:38
1
jlgdr wrote:
Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.

A. 360
B. 380
C. 400
D. 406
E. 412

Im trying to answer this another way but I can't seem to think what I'm doing wrong

So we have

PQ = 360
(0.9P)(Q+12) = 360

We need to find 120P

Now if we reduce 10% on P and still get the same result then Q increases 10%
So Q + 12 = 11/10 Q --> Q = 120

Therefore P is equal to 3.

And we have that 120P = 360.

I don't quite know what I can't get the answer 400 following this approach, could any expert please advise

Thanks a lot!
Cheers
J


P reduces 9/10 times, thus Q increases 10/9 times: Q + 12 = 10/9*Q --> Q = 108.

Alternatively you could solve the system of equations: PQ = 360 and (0.9P)(Q+12) = 360 to get the same result.
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Re: Percent  [#permalink]

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New post 13 Feb 2014, 09:02
Bunuel wrote:
jlgdr wrote:
Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.

A. 360
B. 380
C. 400
D. 406
E. 412

Im trying to answer this another way but I can't seem to think what I'm doing wrong

So we have

PQ = 360
(0.9P)(Q+12) = 360

We need to find 120P

Now if we reduce 10% on P and still get the same result then Q increases 10%
So Q + 12 = 11/10 Q --> Q = 120

Therefore P is equal to 3.

And we have that 120P = 360.

I don't quite know what I can't get the answer 400 following this approach, could any expert please advise

Thanks a lot!
Cheers
J


P reduces 9/10 times, thus Q increases 10/9 times: Q + 12 = 10/9*Q --> Q = 108.

Alternatively you could solve the system of equations: PQ = 360 and (0.9P)(Q+12) = 360 to get the same result.


I see were my mistake was. Well but replacing and all into (2) is too much work. Once with Q then you can solve much easier in my opinion

Thanks again buddy
Cheers
J
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Re: Percent  [#permalink]

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New post 13 Feb 2014, 10:16
jlgdr wrote:
Bunuel wrote:
jlgdr wrote:
Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.

A. 360
B. 380
C. 400
D. 406
E. 412

Im trying to answer this another way but I can't seem to think what I'm doing wrong

So we have

PQ = 360
(0.9P)(Q+12) = 360

We need to find 120P

Now if we reduce 10% on P and still get the same result then Q increases 10%
So Q + 12 = 11/10 Q --> Q = 120

Therefore P is equal to 3.

And we have that 120P = 360.

I don't quite know what I can't get the answer 400 following this approach, could any expert please advise

Thanks a lot!
Cheers
J


P reduces 9/10 times, thus Q increases 10/9 times: Q + 12 = 10/9*Q --> Q = 108.

Alternatively you could solve the system of equations: PQ = 360 and (0.9P)(Q+12) = 360 to get the same result.


I see were my mistake was. Well but replacing and all into (2) is too much work. Once with Q then you can solve much easier in my opinion

Thanks again buddy
Cheers
J


Actually you can get \(Q + 12 = \frac{10}{9}*Q\) from the system of equations we have quite easily. Divide \((0.9P)(Q+12) = 360\) by \(PQ = 360\):

\(\frac{0.9(Q+12)}{Q} = 1\) --> \(0.9(Q+12) = Q\) --> \(Q + 12 = \frac{10}{9}*Q\).

Hope it helps.
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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Mr.John used to purchase certain number of mangoes for $360.  [#permalink]

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New post 13 Feb 2014, 10:55
Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.

Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 120 mangoes = 120*3.33 = 400.

Method 2:
Let price per mango be x. Then, 360/(0.9x) - 360/x = 12
=> 400/x - 360/x = 12 => 40/x = 12 => x = 40/12.
Price of 120 mangoes = 120 x = 120 *40/12 = 400
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Re: Mr.John used to purchase certain number of mangoes for $360.  [#permalink]

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New post 26 Jun 2014, 03:13
Price ................ Qty .............. Total

p ........................ \(\frac{360}{p}\) ................ 360
(Assume)

Price reduction = 10%; Qty increase = 12

\(\frac{90p}{100}\) ............... \(\frac{360}{p} + 12\) ............. 360

Setting up the equation

\(\frac{90p}{100} * (\frac{360}{p} + 12) = 360\)

\(p = \frac{40}{12}\)

Price for 120 Mangoes

\(= \frac{40}{12} * 120 = 400\)

Answer = C
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Re: Mr.John used to purchase certain number of mangoes for $360.  [#permalink]

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