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In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st q

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In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st q [#permalink] New post   09 Aug 2020, 21:32
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In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st quadrant and OA < AB. Is area of ∆OAB > 60?

1) Coordinates of Point A are (5, 12)
2) Coordinates of Point B are (12, 0)



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Drb89
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Re: In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st q [#permalink] New post   09 Aug 2020, 22:06
IMO A

From statement 1, h=12. Now if OA =AC, then OB=10. But since OA > AB, OB>10, Hence Area > 60

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Re: In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st q [#permalink] New post   09 Aug 2020, 22:12
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for given ∆ OAB ; O is 0,0 and given condition that OA<AB ; target is area of ∆ OAB >60
#1Coordinates of Point A are (5, 12) ;
so point B would be √(5-x)^2+(12)^2 >13 or say x(x-10)>0 ; x>10 ; such that base OB least is 10.1 and the area of ∆ is least 1/2*10.1*12 ; 60.1 hence sufficient
#2 Coordinates of Point B are (12, 0)
here with given condition OA<AB ; we can have both yes & no cases of area eg A (5,2) and B (12,0) and A 5,12 and B (12,0) insufficient ;
OPTION A correct



GMATinsight wrote:
In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st quadrant and OA < AB. Is area of ∆OAB > 60?

1) Coordinates of Point A are (5, 12)
2) Coordinates of Point B are (12, 0)



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In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st q [#permalink] New post   10 Aug 2020, 04:26
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the tricky point here is to observe what oa<ab does. to do this just draw a perpendicular from point a to ob. and name it c. you will realize that 2oc<ob .
now using statement 1: we have height as ac=12 and oc is 5 then ob >10 ('2oc'). now using triangle formula half*base (10+) *height(12) >60 hence sufficient.
statement 2 is clearly insufficient alone.


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Re: In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st q [#permalink] New post   10 Aug 2020, 04:35
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GMATinsight wrote:
In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st quadrant and OA < AB. Is area of ∆OAB > 60?

1) Coordinates of Point A are (5, 12)
2) Coordinates of Point B are (12, 0)

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Re: In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st q [#permalink] New post   10 Aug 2020, 11:26
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Hey all, nice to meet everyone here - but what if point B is on the left side of the origin? I don't think anything prevents that in the question statement
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Re: In ∆OAB the point O is the origin, B is on X-axis, point A is in 1st q [#permalink]
10 Aug 2020, 11:26
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