One Equation 2 Variables To Solve

[rickyishere]

Usually we need two equations to solve when looking to find the value of two unknowns. However, I have seen certain tough GMAT DS questions where by virtue of checking the possibe values of x and y, one equation is deemed appropriate to solve for x and y, hence one option is sufficient to solve the problem. I have attached an image of the problem. Can you guys let me know how in a matter of 2 minutes would you decide whether we can solve by using the traditional 2 eqn approach or choose based on certain values of x and y which will make the answer choice sufficient?

Your help is appreciated, because of questions like these I sometimes find myself in a quandry whether do i really need 2 equations or can i just look for various possible values of x & y which will make the single equation work.

Thanks
Ricky

[4GMAT_Mumbai]

Hi Ricky,

I shall try my best.

You are right - in the absence of additional information, one needs two equations to solve a linear equation in two unknowns.

However - there are some cases where additional information is given; in this case, the additional information is that x and y are integers. One has to buy either two stamps or three stamps. One cannot get 2.5 stamps.

Looking for such additional information which could be things like:

1. x and y are always integers, like in this case.

2. x could always be less than y, like in a question in which a kid eats y chocolates out of which x are pista chocolates.

3. one of either x or y could be an integer, like in a case where x refers to the number of kids in a competition

4. x is always a multiple of y, if the question states that y is the LCM of x

so on and so forth. I would be impossible to state an exhaustive list of possibilities.

The operative sentence is 'Look for additional information'.

Hope this helps.