In the diagram above, what is the length of MP if LNOQ is a

Question

https://img.photobucket.com/albums/v322/shanewyatt/KaplanDSSquareandangles-1.jpg 
In the diagram above, what is the length of MP if LNOQ is a square with an area of 64?

(1) a - b= 0
(2) OP = 1/2 OQ

OA is E but I disagree.
(1) I agree is INSUFF
(2) I think is SUFF because that the area is 64 tells us that each side is 8. If each side is 8 then the line from M to OQ is 8 and since OP = 1/2OQ then OP should be 4. Since this is a right angled triangle we can use Pythagorean theorem to tell us the length of MP. Am I correct?

KapTeacherEli · Answer

Hi shanewyatt,

We're missing the height of M. Without the height of M, we cannot determine the difference in height between M and P. Without that difference, we cannot determine the height of the triangle--and without only one side triangle, we cannot use the pythagorean theorem to determine the hypotenuse.

Bunuel · Answer

In the diagram above, what is the length of MP if LNOQ is a square with an area of 64?

I guess that  a  and  b  on the diagram refer to the angle measurement.

(1) a - b= 0 -->  a=b . This is unnecessary info. We could derive this info from the fact that  NL||OQ .

(2) OP = 1/2 OQ -->  OP=\frac{1}{2}OQ .  OP=PQ=4 , in other words point  P  is fixed, but no info about point  M . Insufficient.

(1)+(2) Zero info from (1) and insufficient info from (2). So taken together still insufficient.

Answer: E.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In the diagram above, what is the length of MP if LNOQ is a square with an area of 64?

(1) a - b= 0
(2) OP = 1/2 OQ

There are 5 variables (2 triangles are side by side), one equation (LQ=8) and only 2 more equations are given from the 2 conditions, so there is high chance (E) will be our answer.
Looking at the conditions together, 
a=b, 
even if OP is half of OQ, we cannot obtain values for PM, so the answer becomes (E).

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

bumpbot · Answer

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In the diagram above, what is the length of MP if LNOQ is a

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In the diagram above, what is the length of MP if LNOQ is a

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