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What is the value of k?

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GMATH Teacher
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What is the value of k?  [#permalink]

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New post 28 Feb 2019, 09:09
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (02:00) correct 30% (01:54) wrong based on 20 sessions

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GMATH practice exercise (Quant Class 15)

Image

What is the value of \(k\) ?

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

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

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Re: What is the value of k?  [#permalink]

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New post 28 Feb 2019, 14:33
From the value of x we cannot come to any point(insufficient). Hence A and D option eliminated.

From the value of y, we can find smaller triangle hypotenuse which will be 2. But still alone we cannot tell the value of k. (insufficient). Hence B and D eliminated.

Thus Options can be then either C or E.

Combining both statements, we see that the other triangle has two sides of length 2 and one angle is 120 , hence other two angles should be 30 each (being isosceles)...

Hence together they are sufficient. Hence C is the option.

Give kudos if you like my comment. Cheers!!! Happy Learning!!!
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Re: What is the value of k?  [#permalink]

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New post 28 Feb 2019, 17:43
fskilnik wrote:
GMATH practice exercise (Quant Class 15)

Image

What is the value of \(k\) ?

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


I like to approach problems like this by imagining 'stretching' and 'squishing' the diagram. If I can draw the diagram in two different ways, the statement I'm working with is insufficient.

Here's statement 1:

Image

If y is small, k could be somewhere around 30 degrees. And if y is much bigger than 2 (notice how in the second drawing, x looks a lot smaller than y), k could be much smaller than 30 degrees. Not sufficient.

statement 2:

Image

(I used the 30-60-90 rule to fill out the remaining sides of the bottom triangle, just for clarity.)

[b]Combining the statements[b]:

Image

Fill in all of the known lengths. Then, notice that you have an isosceles triangle on top, with two sides that equal 2. So, you could split it into two identical right triangles with the red dotted line. The angle that's split in half by the red dotted line measures 180-60=120, so half of that angle is 60. Therefore, the missing angle is 30, which is the value of k.

(Also, you might notice that having two sides of 2+1 = 3 and sqrt(3) makes the larger triangle a 30-60-90.)
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What is the value of k?  [#permalink]

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New post 01 Mar 2019, 06:38
fskilnik wrote:
GMATH practice exercise (Quant Class 15)

Image

What is the value of \(k\) ?

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


Image


\(? = k\,\,\,\left[ {{\rm{degrees}}} \right]\)

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


The correct answer is (C).


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

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

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What is the value of k?   [#permalink] 01 Mar 2019, 06:38
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