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If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80.

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If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80. [#permalink]

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If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $70. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties?

A. $60
B. $64
C. $75
D. $96
E. Cannot be determined


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[Reveal] Spoiler: OA

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Re: If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80. [#permalink]

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New post 19 Aug 2015, 02:43
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Bunuel wrote:
If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $70. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties?

A. $60
B. $64
C. $75
D. $96
E. Cannot be determined


Ans: E

Solution: 3x+4y+rz=80 & 7x+2y+2z=70
adding both the equations= 10x+6y+4z=150
5x+3y+2z=75 ans
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If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80. [#permalink]

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New post 04 Jan 2018, 15:05
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Hi All,

This prompt gives us 3 variables, but only 2 equations to work with. While a typical 'system' question will have the same number of variables (2 variables and 2 equations, for example), if a PS question provides you with an unequal number of variables and equations, there is ALWAYS a pattern (in terms of how the two equations 'interact' with one another) that you can use to answer the given question that is asked.

To start, I'm going to call the variables:
S = number of shirts
T = number of trousers
V = number of ties

With the given information, we can create the following equations:
3S + 4T + 2V = 80
7S + 2T + 2V = 70

We're asked for the value of 5S + 3T + 2V....

Looking at the first variable in each equation, you should notice that 3S + 7S = 10S.... which is exactly DOUBLE the number of shirts we need. With the second variable, we have 4T+2T = 6T... which is exactly DOUBLE the number of shirts that we need. That is NOT a coincidence. If you add the two equations together, you get...

10S + 6T + 4V = 150

The question asks us for exactly HALF of that (5S + 3T + 2V), so we simply have to cut that equation 'in half':
5S + 3T + 2V = 75

Final Answer:
[Reveal] Spoiler:
C


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Last edited by EMPOWERgmatRichC on 08 Jan 2018, 11:49, edited 1 time in total.

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Re: If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80. [#permalink]

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New post 08 Jan 2018, 06:26
My first thought was to do ratios and find the unknown multiplier; however, that didn't work, but I am struggling to see why?

And I might have just answered my own question but I am not sure: Shirts, trousers, and ties are not worth the same so you have to solve for each variable?

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Re: If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80. [#permalink]

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New post 08 Jan 2018, 10:26
Bunuel wrote:
If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80. If Greg buys 7 shirts, 2 trousers and 2 ties, the total cost is $70. How much will it cost him to buy 3 trousers, 5 shirts and 2 ties?

A. $60
B. $64
C. $75
D. $96
E. Cannot be determined


Kudos for a correct solution.


3s + 4t + 2e = 80------------------> (I)
7s +2t + 2e = 70------------------> (II)

(I) + (II) = 10s + 6t + 4e = 150---------------------->(III)

We are asked to find : Price of 3 trousers, 5 shirts and 2 ties

So, the price of 3 trousers, 5 shirts and 2 ties will be (III)/2 = 75, answer will be (C)
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Re: If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80. [#permalink]

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New post 08 Jan 2018, 11:55
21savage21 wrote:
My first thought was to do ratios and find the unknown multiplier; however, that didn't work, but I am struggling to see why?

And I might have just answered my own question but I am not sure: Shirts, trousers, and ties are not worth the same so you have to solve for each variable?


Hi 21savage21,

You're correct - we don't know what the individual clothing items cost (and there's no way to actually determine any of those prices) - so you can't answer the question in that way. Beyond that point though, neither of the two equations can be individually manipulated to answer the question that is asked, so you can't take that approach either.

This question is a great example of how you should think critically about what you're specifically asked to solve for. If a question asks "what is the price of 1 shirt?", then the approach is likely fairly straight-forward (and there will likely be more than one way to get to the solution). Here though, the question asks for the "total price of 3 trousers, 5 shirts and 2 ties"... and that is a WEIRD thing to ask for. This implies that the solution is likely "pattern-based", so you really have to consider all of the information that you've been given (likely in ways that you wouldn't initially think of).

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Re: If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80.   [#permalink] 08 Jan 2018, 11:55
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If Greg buys 3 shirts, 4 trousers and 2 ties, the total cost is $80.

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