Hi, I had a general math theory question, and one regarding some wording on GMAT questions.

First in regards to math theory, I still constantly mess up questions that are in regards to square roots. I was under the impression that if we get to something like x^2=16, then x could be +-4, and thus a statement would be insufficient, unless there is something in the question that excludes the negative root (an explicit statement, geometry problem, etc). But then I was doing a gmat prep question which ended with exactly the above x^2=16, but it was sufficient that x=4. The explanation I read elsewhere was that the root is always positive, so even though both -4 and +4 could result in 16, when we do square root +16 (since a -ve number does not have a square root), it is sufficient to say that the answer is +4. I can think of many exception in questions to this, such as questions with even or odd numbered exponents, or other DS questions where the answer would not be sufficient. Can someone please clarify the rules here.

Would the same rule apply if we have something like x^2=y^2? So x=y. Or because we have variables here, we cannot assume that x=y, unlike the case where x^2=16, 16 is not a variable.

My other question is in regards to the wording x is BETWEEN 6 and 16. I recall from the course that BETWEEN means 6<x<16, thus 7<=x<=15. Is this always the case? I came across a question where they had taken between to mean inclusive of the end numbers. Can someone please clarify.

For your first question, the general rule is that if YOU draw the square root sign yourself you must allow for both the positive and negative possibilities. If the GMAT gives you the square root sign (the radical symbol is actually physically displayed on the problem), you are to take only the positive root. Without seeing the actual problem you are referring to, it’s difficult to know whether this was the source of your confusion. It is also possible since this appears to have been a DS problem that there may have been an issue regarding which direction you were going in determining sufficiency. Can you post the actual problem?

For the second problem, 6 < x < 16 means literally between, i.e. not sitting on an endpoint. Thus x cannot be 6. However this DEFINITELY does not mean 7 <= x !!! x could be 6.5; please please remember this, because this is one of the easiest ways for the GMAT to steal points from you. BTW if you came across a problem that used ”between” inclusively, please let us know where it can be found. My guess is that it did not come from GMAT or MGMAT..

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Tim Sanders
Manhattan GMAT Instructor