GMAT DS Problem: Dilemma whether to solve it or not?

Don't get carried away with solving a DS problem, all the times. The main point here is, in most of the cases, we need not really solve the problem. “Checking that whether the given statements are enough to solve the problem” is only required than actually solving the problem.

For example, see this one:

Q1)What percent of 10 is 'x':

(1) x is 50 percent of 12

(2) 10 is 5 percent of x

Here note that each statement is individually sufficient to solve the problem. We can find the value of ‘x’ from each statement independently and then get the required answer ie., “what percent of 10 is x”. But don't get carried away with solving. Just by seeing each of the statements, we can say that we can solve the problem with the help of it. That’s all, that’s enough. The answer option is "D"

Let us see one more example here:

Q2)Find the value of y:

(1) 3x-7y = 20

(2) x+y = 2+y

Here the ace is statement(2). It directly gives the value of x (of course, it is 2). But is it sufficient to answer the Q'? It is asked to find the value of 'y', not 'x'. Hence by using the value of 'x' from statement(2) and substituting it in statement(1), we can get the value of 'y'. As both the statements are required to solve this one, the answer option is "C".

But suppose that it is asked for the value of 'x' in the main stem of the problem. In that case, irrespective of statement(1), statement(2) alone is sufficient to answer the Q’. And also, as statement(1) alone is not sufficient to answer the Q’, the answer option is "B".

But in some cases, it is required to solve the problem. This arises in cases where the given statements seem to be enough to answer the Q’ but if we really solve, it may result in "ambiguous" or "not defined" or no answers. This is where GMAC can really trick us. For a given DS problem, “the clarity on whether to go for solving or not” will come only through practicing different types of problems and a careful noting of the special cases there on.

For example, see this one:

Q3)What is the value of 'x":

(1) x-2y = 7

(2) 3x-5 = 6y

We know that two unknowns (in this case x and y) can be solved by using at least two equations. And hence we conclude that, both the given conditions are required together to find the value of x. That’s where we commit mistake.

See the second statement carefully. 3x-5 = 6y => 3x-6y = 5 => 3(x-2y) = 5 => “x-2y = 5/3”, which is inconsistent with the first statement "x-2y = 7". Hence, this Q’ cannot be answered even if we consider both the given statements together. To get this clarity, as just now done on the second statement, we need to shed a little on solving the given statements. I think we have no doubts to mark the answer option as "E" for the above Q’.

Finally, we will see one more example, where we need to really work on the given statements to get answer for the Q’.

Q4) Find the value of “5x-8y+z”:

(1) 2x+y-2z = 9

(2) 5x-y-3z = 6

A little brainstorming is required here whether we can find two numbers with which if we respectively multiply the two statements and do some manipulation to finally yield the value of “5x-8y+z”. In the case, where we can find those two numbers, we can select the answer option “C”. But, there is a possibility that we cannot find those two numbers ultimately and may land to the answer option “E” as well. Try this out…