# GMAT Data Sufficiency Problem: A Tricky Trap to Avoid

We always hope to solve GMAT Data Sufficiency problems as quickly and efficiently as possible.  But look out for hidden traps which try to lure you into making unwarranted assumptions.

To point out one such trap, we’ll look at two sample GMAT Data Sufficiency problems.

Here’s the first problem:

Does x = 3 ?

1)  3x + 2y =  24

2)  5x  -  y  =  14

A.  Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.

B.  Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.

C.  Both statements 1 and 2 together are sufficient to answer the question asked, but neither statement alone is sufficient.

E.  Statements 1 and 2 are not sufficient to answer the question asked and additional data would be needed to answer the question.

A statement is sufficient if it allows us to answer either “definitely yes” or “definitely no” to the question, “does x = 3?”.  Otherwise, if we can only answer “definitely maybe”, the statement is not sufficient.

Another way to think of it:  Here a statement is sufficient if it allows us to solve for a UNIQUE value of x, even if that value is not 3.

We can analyze this problem rather quickly.  Each equation contains two unknowns, x and y.  In general, we need two different equations to solve for 2 unknowns.  So neither equation (statement) is sufficient by itself.  However, together they should be sufficient, since we can (in general) solve the system of 2 equations for both unknowns.  Therefore, Choice C is the correct answer.

Since this is Data Sufficiency rather than Problem Solving, we didn’t even have to actually solve the system, although if we had, we would have found that x = 4 and y = 6.

Smooth sailing so far.  But let’s look at a very similar problem which contains a trap.

Here it is:

Does x = 5 ?

1)  14x - 8y =  22

2)   7x - 4y =  11

(Data Sufficiency answer choices are always the same.)

At first glance, this looks like the same situation we met with in the first problem.  Neither statement is sufficient alone, but together they form a system of equations that can be solved for x and y.  So Choice C is again the correct answer, right?  Actually, in this case, wrong.

Why?  Well, it turns out that the two equations are really the same equation.  If we divide the first equation by “2” on both sides, we get the second equation.  So we actually only have one equation with 2 unknowns, which we cannot solve for a UNIQUE solution.

Another example of a system which could not be solved would be one in which the two equations represent parallel lines.   Always keep in mind possible “exceptions to the rule” when dealing with systems of equations and other types of subject matter found in Data Sufficiency problems.

Good luck on the GMAT!

#### More Data Sufficiency Posts

1. Siddhartha says

Well lets redo the logic in a different manner:

Statement #1:
3x + 2y = 24 =>

3x = 24 -2y = > 3x = 2( 12-y)

3x = 2( 12-y) now the RHS side has at at least one even number i.e 2. So 3x can't be an odd number, in other words x can not be 3.

It will be applicable for all values of y : y as integer or friction

Suppose to refute it, we take y=1/2. It will make the RHS = 23 then also it proves that x can not be 3.

However, statement #2 can't prove this. It might be the reason for why test Makers missed 2 in #2.