In the rectangular coordinate system above, if OB

Question

download.png In the rectangular coordinate system above, if OB < BC then is the area of the triangle ABC lesser than 12 square units? (1) Point A lies above the line y = 5 (2) The mid-point of B and C is (6, 0)

EMPOWERgmatRichC · Answer

Hi TARGET730,

In DS questions, you have to be careful about any pictures that you're given - as a general rule, you CANNOT trust any pictures in DS questions. From the drawing, it "looks like" the base of the triangle is bigger than the height of the triangle, but we DO NOT KNOW that for sure. It might be that the base and the height are equal; it might also be that the height is bigger than the base. As such, we can only use the math "facts" that we're given to try to answer this question.

We're told that the length of OB is less than the length of BC. We're asked if the area of the triangle is less than 12. This is a YES/NO question.

Fact 1: Point A lies above the line Y = 5.

This tells us that the height of the triangle is > 5, but it dos not tell us anything about the base.

IF....
Height = 6
Base = 6
Area = (1/2)(6)(6) = 18 and the answer to the question is NO.

IF.....
Height = 6
Base = 1
Area = (1/2)(1)(6) = 3 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: The mid-point of B and C is (6,0)

This Fact limits the possible base of the triangle, since OB < BC, the range for the base is....4 < base < 12, but tells us nothing about the height.
The examples that we used in Fact 1 (above) would fit here.
Fact 2 is INSUFFICIENT

Combined, we could have...
Base = 6
Height = 6
Area = (1/2)(6)(6) = 18 and the answer to the question is NO.

Base = 4.1
Height = 5.1
Area = (1/2)(4.1)(5.1) = just above 10 and the answer to the question is YES.
Combined, INSUFFICIENT

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

hi target 730,

ans E.. FOR THIS QUESTION..
but just a point that each statement does convey a pertinant point..
1) statement 1 tells us that height is 5 or >5.. insufficient since the Q asks <12, we will take the lowest value of 
2) statement 2 tells us the width, here it gives the lowest value for width to be 4... insufficient..
combined if we take the lowest value for area..1/2*5*4=10 ao area >10 so not sufficient

however if the coord were (8,0).. the lowest value of base would be 16/3..
so lowest area = 1/2*5*16/3 >12 so ans would be combined sufficient..

my point we have to read the values very minutely..

vinyasgupta · Answer

hi  chetan2u ,
I have a question in the second statement

As (6,0)      is the midpoint of BC ,so BX=XC=BC/2 and you have taken the lowest value for width to be 4

so   BX=XC=4/2=2  
according to this   B( ,0)   and   C( ,0)  
which means   B(4,0)   and   C(8,0)  
this gives  OB=BC=4 
but in the stem it is given that OB<BC.

CrackverbalGMAT · Answer

Hi all,
To calculate the area of the triangle we need base and the height here
That is we got to check
 ½ (BC)(height)<12?
1). Statement 1 is insufficient.
 This talks only about height. This says height is greater than or equal to 5. 
2). Statement 2 is insufficient.
This talks only about base which is BC. This says base length can be 6 or 8.
B(3.0) and C(9,0)
B(2,0) and C(10,0)
Together sufficient, 
Height minimum we can take is 5 and base minimum can be 6. Then the area is 15.
Always the area going to be greater than 12.
Together sufficient.
So the answer is C.

TARGET730 · Answer

CrackVerbalGMAT,

I think the answer is E. What if B is (3.9, 0) and C is (8.1,0) ? In this case BC = 4.2, which is greater than OB.

Area will be 10.5 which is less than 12

EMPOWERgmatRichC · Answer

Hi CrackVerbalGMAT,

The prompt never states that the co-ordinates are integers and there are more possible values for the base of the triangle in Fact 2 than the 6 and 8 that you noted. If you try minimizing the base and the height of the triangle, you'll get the correct answer.

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

hi vinay...

you are right that OB<BC....
however i have taken it as OB = BC because that is the value slightly above max value it can take and if it still does not satisfy the equation at slightly higher value than its max value, it will not satisfy at any other value..
also it is easier and faster to work with integer than x.9999 and other value as y.0001....

In the rectangular coordinate system above, if OB < BC then is the are

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