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19 Aug 2015, 01:32
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C
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Difficulty:
75%
(hard)
Question Stats:
49% (01:53) correct
51%
(02:48)
wrong
based on 149
sessions
History
Date
Time
Result
Not Attempted Yet
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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A. $60
B. $64
C. $75
D. $96
E. Cannot be determined
Kudos for a correct solution.
19 Aug 2015, 03:43
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Bunuel
Ans: E
Solution: 3x+4y+rz=80 & 7x+2y+2z=70
adding both the equations= 10x+6y+4z=150
5x+3y+2z=75 ans
Updated on: 08 Jan 2018, 12:49
Originally posted by EMPOWERgmatRichC on 04 Jan 2018, 16:05.
Last edited by EMPOWERgmatRichC on 08 Jan 2018, 12:49, edited 1 time in total.
Last edited by EMPOWERgmatRichC on 08 Jan 2018, 12:49, edited 1 time in total.
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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:
GMAT assassins aren't born, they're made,
Rich
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:
GMAT assassins aren't born, they're made,
Rich
