Problem Solving

Hi swerve,

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 = 8T... 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: C

GMAT assassins aren't born, they're made,
Rich

swerve 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 is cost him to buy 3 trousers, 5 shirts and 2 ties?

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

The OA is C.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

We can create the equation:

3s + 4r + 2t = 80

and

7s + 2r + 2t = 70

If we add the two equations, we have:

10s + 6r + 4t = 150

Dividing the equation by 2, we have:

5s + 3r + 2t = 75

So the cost of 3 trousers, 5 shirts and 2 ties is $75.

Answer: C