In the video below we discuss GMAT Test Questions and show you strategies to ace the concept of inequalities.
GMAT Test Questions on Inequalities [Transcript]
Please pause this video and answer the question before continuing. In this question, we want to determine whether 5-2x is greater than -1. Now at this point, our target question is somewhat cumbersome, so lets move it over here and see if we can rewrite it, so that it provides some insight into the question. First, if we subtract five from both sides, we get a new question. Is -2X greater than -6?
Next, if we divide both sides of the inequality by -2, we get another way to write the target question. Is x < 3? Please note, that since we divided both sides by a negative number, we have to reverse the direction of the inequality. As you can see, the new question, is X < 3, is much more manageable than the original question.
Now before we examine our statements, lets look at another way to rewrite our new target question. Notice if that x < 3, than x must lie somewhere to the left of three on the number line. So we can rephrase our question as, “On the number line, does x lie to the left of three?” Now that we have several ways to phrase our target question, lets examine the two statements. First, we have statement number one, x > 0. In other words, x is a positive number. Now if x is positive, can we determine whether or not x lies to the left of three on the number line? The answer is no. If x is positive, it could be here, in which it is less than three. However, x could also be here in which case it is greater than 3. Since we cannot answer the target question with any certainty, statement one is not sufficient.
Next we have statement two, x < 2. Does this provide enough information to determine whether or not x < 3? The answer here is yes. If x < 2, then x can be any point to the left of two on the number line. So x could be here, here, here and so on. If x is to the left of two on the number line, then we can conclude that it must also lie to the left of three on the number line. Since we can use statement two to definitively answer our target question, it must be sufficient. In which case the answer here is B.