In triangle $ABC$ above, is $AC$ greater than $4?$

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Thu Sep 24, 2020 2:22 am

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In triangle $ABC$ above, is $AC$ greater than $4?$

(1) $BC = 4$
(2) $y = 40$

Answer: A

Source: Princeton Review

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Source: Beat The GMAT — Data Sufficiency | Thu Sep 24, 2020 2:22 am

psarma: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Wed Jun 29, 2011 1:47 am

Re: In triangle $ABC$ above, is $AC$ greater than $4?$

by psarma » Thu Sep 24, 2020 3:45 pm

$\angle bac$ + $\angle abc$ = $\angle bcd$
Thus, $\angle abc$ = 2y i.e 2 $\angle bac$

Option 1 gives the length of side BC, which is 4
As $\angle abc$ = 2 $\angle bac$ , hence the side opposite $\angle abc$ should be greater than side opposite $\angle bac$ .

A is thus sufficient.

Option 2 doesnt give the length of any side or any other useful information, Not sufficient.

Answer is A.

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