# How Approximation Can Answer Unanswerable Questions:

Many students are very rigid in their approach to answering Problem Solving questions. If confronted with a quadratic equation, for example, we were originally taught to move all the terms to one side, factor and solve for both solutions. This strategy usually takes too long on the GMAT. More advanced students should be comfortable with adjusting, estimating and approximating the given information to accurately come close to the correct answer and orient their focus on the most feasible options. See my previous article about some of these techniques.

In many situations, the question stimulus will ask for a definitive answer and provide information that is not the most straightforward or simple. In these cases, alter the information slightly to make the calculations easier for yourself. Change 24.8 to 25 or make ^{29}/_{14} = 2, for example.

In other scenarios, certain key words should serve as a clue that approximation is necessary. These terms include, but are not limited to: “approximately,” “about,” “nearest to,” “closest to,” “best,” “most likely,” etc.

A detailed explanation of the following question will be provided in a separate article tomorrow. Note that while many of the answer choices may be “close” to the given ratio, one is clearly the “best” answer.

The ratio of 2 + √6 to 3 is approximately equal to which of the following ratios?

A. 2:1

B. 3:2

C. 4:3

D. 7:6

E. 13:12

## 6 comments

Prabhu on December 6th, 2009 at 10:47 am

I think the answer is B

Raghav on December 7th, 2009 at 1:11 am

(2+Root(6))/3 = 2/3 + Root(6)/3 = 2/3 + 6/9 = 2/3 + 2/3 = 4/3

Ans : C

Sid on December 7th, 2009 at 5:43 am

Since we are dealing with approximation, we can solve for root(6) as, root(2)*root(3), which is 1.4*1.7 or 1*2=2, therefore the equation becomes 2+2/3=4/3, C.

sowmya on December 7th, 2009 at 10:55 pm

the answer is B

(2+ root(6))/3 = 2/3 + root(2)*root(3))/3=2/3 + root(2)/root(3) = 2/3 + 14/17=(34+42)/51=76/51=1.45 approx equal to 3:2

Pankaj on December 12th, 2009 at 5:22 pm

the answer is (B) 3:2

jeremy8 on July 3rd, 2010 at 7:09 pm

I think the answer is B as well.

25*25 is 625, so sq root of 6 ~ 2.5 with only a deviation of 1/24th, and 4.5/3 is equivalent to 3/2.