Length of diagonal

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Nov 23, 2013 11:13 am

Hello,

Can you please assist with this?

The four sides of quadrilateral JKLM have equal length. What is the length of
diagonal JL?

(1) JK = 2
(2) KM = 2

OA: C

When I tried to solve this problem I assumed that JKLM is a square but I guess it is a rhombus. I was wondering how can I decide whether it is a square or a rhombus given that the question says all sides are equal.

Thanks,
Sri

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Source: Beat The GMAT — Problem Solving | Sat Nov 23, 2013 11:13 am

riz_gmat: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Thu Sep 26, 2013 9:05 pm; Thanked: 5 times

by riz_gmat » Sat Nov 23, 2013 11:50 am

Hi Sri,

Diff between Square and Rhombus is ,
for Square , diagonals are equal
while for Rhombus - Diagonals are unequal!

Coming to question...
To find : Length of diagonal JL

Option 1 : JK = 2 ( ie, all sides = 2)
It can be a square or Rhombus .
Not sufficient !

Option 2 : KM = 2 ( One diagonal = 2)
Nothing mentioned about sides to calculate the diagonals and make sure they r equal or unequal.
Not sufficient !

Both Options combined:
Sides = 2 One diagonal = 2
It cannot be a square , since if sides = 2 ,then diagonals will be 2 root 2.
Hence it is rhombus and can find the length of other diagonal using formula
4 (side)^2 = (d1)^2 + (d2)^2.
Sufficient!
Hence C.

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by [email protected] » Sat Nov 23, 2013 2:47 pm

Hi Sri,

This DS question, while a bit complex, serves as a great lesson that you can apply to ALL DS questions: be CAREFUL about your assumptions.

If the prompt wanted you to know that you were dealing with a square, then it would have used the word "square." By using the word "quadrilateral", you have to ask yourself what THAT WORD means. I know that I'm dealing with a 4-sided shape, but I'm not sure what type. With the added information about how the four sides have equal length, that narrows it down to a square or a rhombus.

DS questions put an emphasis on your "thoroughness", so make sure that you are careful to consider more than just the obvious possibilities.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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