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 lies between:
  • a)
    4 & 5
  • b)
    5 & 6
  • c)
    6 & 7
  • d)
    7 & 8
  • e)
    8 & 9
Correct answer is option 'D'. Can you explain this answer?

Answers

In order to rid the expression of square roots, let's first square the entire expression. We are allowed to do this as long as we remember to "unsquare" whatever solution we get at that end. 

Notice that the new expression is of the form where

Recall that  This is one of the GMAT's favorite expressions.
Returning to our expression: 
 
Notice that x2 + y2  neatly simplifies to 48. This leaves only the 2xy expression left to simplify.
In order to simplify   recall that  
Thus, 
Notice that the expression under the square root sign is of the form  And recall that   This is another one of the GMAT's favorite expressions. Returning to our expression: 


Finally then:

But now we must remember to "unsquare" (or take the square root of) our answer:

 

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lies between:a)4 & 5b)5 & 6c)6 & 7d)7 & 8e)8 & 9Correct answer is option 'D'. Can you explain this answer?
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In order to rid the expression of square roots, lets first square the entire expression. We are allowed to do this as long as we remember to "unsquare" whatever solution we get at that end.Notice that the new expression is of the formwhereRecall thatThis is one of the GMATs favorite expressions.Returning to our expression:Notice that x2 + y2neatly simplifies to 48. This leaves only the 2xyexpression left to simplify.In order to simplifyrecall thatThus,Notice that the expression under the square root sign is of the formAnd recall thatThis is another one of the GMATs favorite expressions. Returning to our expression:Finally then:But now we must remember to "unsquare" (or take the square root of) our answer: