Geometry

[papgust]

Is triangle ABC isosceles?

(1) x not equal to y
(2) AB / BC = 2

OA: C
Source: MGMAT

Please explain how the combined statement satisfies. Probably i'm missing a key concept.

[rohan_vus]

(1) x not equal to y
--->Its obviously insufficient..as you dont know about 3rd angle.
(2) AB / BC = 2
-->Assume AB = AC , this could be a possible is a isosceles triangle .
-->Also a triangle where,lets say AB = 2 unit , BC = 1 unit and AC = 1.5 unit is also possible .
So 2 different possibilities , hence insifficient

Combining , lets try to consider any case for isosceles and see if it works
.
Isosceles cases could 2 only , as AB = BC is ruled out based on stmnt (2) as AB = 2 BC
a) BC = AC
b) AB = AC ( This case also you can drop as stmnt (1) tells you AB is not equal to AC )

Now case (a) , lets assume BC = AC = m and AB = 2m.
Is this triangle possible , no not all . The Reason is it violates the triangle property . The third side always got be less than sum of other 2 sides and is always greater than difference of other 2 sides
Here AB = sum of other 2 sides .is equal to sum of BC and AC..So this case doesnt hold true. Ruled out


Thus with 2 stmnts we know for sure its not a isosceles triangle

[papgust]

Wonderful explanation! Thanks.

[Sue2010]

Can you please explain why OA is not B.

Since AB = 2 BC, AC cannot be equal to BC as it will then violate the triangle property. So, in my opinion, Option B itself is sufficient to answer this question. Can someone please clarify. Thanks!

[liferocks]

Can you please explain why OA is not B.

Since AB = 2 BC, AC cannot be equal to BC as it will then violate the triangle property. So, in my opinion, Option B itself is sufficient to answer this question. Can someone please clarify. Thanks!

But AC can be equal to AB.

[Sue2010]

Yes!!! Thank u..

[STEVEN SPIELBERG]

IMOC. Thanks Rohan_Vus & others .

[kstv]

2) AB = 2BC
for ABC to be a isos. triangle
AB should be = AC (if AC = BC, then AC+BC = AB which is not possible as any two sides have to be > the third side)
but no info whether they are
1) If x° = y° then it is a isos triangle
the obverse is not suff to negate that it is not a isos triangle
Combining
x<> y so AB is <> AC so sufficient to say that it is not an isos. triangle
IMO C