Data Sufficiency

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 15)



What is the value of k?

(1) x = 2
(2) y^2 = 3

$$? = k\,\,\,\left[ {{\rm{degrees}}} \right]$$
$$\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,\Delta \,{\rm{below}}\,\,{\rm{unique}}\,\,\left( {{{30}^ \circ },{{60}^ \circ },{{90}^ \circ } + \,\,y\,\,{\rm{given}}} \right) \hfill \cr
\,\Delta \,{\rm{big}}\,\,{\rm{unique}}\,\,\left( {{\rm{legs}}\,\,{\rm{known + Pythagoras}}} \right)\,\, \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{30^ \circ } + {k^ \circ }\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$


The correct answer is (C).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Statement 1
x = 2
The value of x alone cannot provide the value of k because an increase or decrease in the value of y will definitely alter the value of , hence statement 1 is INSUFFICIENT.

Statement 2
$$y^2=3$$
$$y=\sqrt{3}$$
$$y=\sqrt{2+1}$$
This doesn't provide us with the value of k, hence statement 2 is INSUFFICIENT.

Combining statement 1 and 2 together.
The other triangle at the top now have 2 sides of length=2 and one of its angle =30 deg each
Hence k = 30 deg
both statements are INSUFFICIENT.

$$answer\ is\ Option\ C$$