If A ,B , and C are points on the plane, is AB

Question

If A ,B , and C are points on the plane, is AB <10 ?

(1) AC + BC = 10
(2) AB + AC > 10

jakolik · Answer

Hello,

Are you sure the answer is E and not A?

Statement 1
Consider Triangle ABC,
Sum of any two sides is greater than third side so AC+BC = 10 > AB
Statement 1 is sufficient

Statement 2
AB+AC>10 Not sufficient
AB = 1 AC=11
AB=11 AC= 11
Both satisfy statement 2.

regards,
Jack

kanhaiya · Answer

@Jack, nowhere in the question its mentioned that ABC would form a triangle...

@mods-- why a DS question is posted in PS section?

jakolik · Answer

kanhaiya you are right and I fell into the trap

Thanks.

dungtd · Answer

I am sorry for the wrong post!

metallicafan · Answer

Although it is not mentioned that the points form a triangle, really there is a traingle!
IMO is A.

What do you think Bunuel?

Bunuel · Answer

E is correct.

The point here is that A, B and C can be collinear.

For example:

A----(8)----B-(1)-C  --> AC+BC=9+1=10 (statement 1) and AB + AC=8+9=17>10 (statement 2) --> AB=8<10, so answer is YES;

A----(8)----C-(2)-B  --> AC+BC=8+2=10 (statement 1) and AB + AC=10+8=18>10 (statement 2) --> AB=10, so answer is NO.

chaoswithin · Answer

Statement 1 is insufficient because ACB could be a line.

so if AC + BC = 10. then AB could be 10 which is not less than 10.

bumpbot · Answer

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If A ,B , and C are points on the plane, is AB < 10 ?

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