Algebra

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 04, 2010 5:48 am

If a, b, c are real numbers such that a < b <c and a + b + c = 6, ab + bc + ca = 9, then which among the following is definitely true?

(1)0 < a < 1
(2)1 < b < 3
(3)3 < c< 4
(4)All of them
(5)None of them

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Source: Beat The GMAT — Problem Solving | Thu Feb 04, 2010 5:48 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Thu Feb 04, 2010 6:22 am

harsh.champ wrote:If a, b, c are real numbers such that a < b <c and a + b + c = 6, ab + bc + ca = 9, then which among the following is definitely true?

(1)0 < a < 1
(2)1 < b < 3
(3)3 < c< 4
(4)All of them
(5)None of them

I will go for b

Since if b>3 a<3 which is not possible
and if b<1 cannot satisfy the given equations

Purely hunch based

Always borrow money from a pessimist, he doesn't expect to be paid back.

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Thu Feb 04, 2010 6:26 am

ajith wrote:
harsh.champ wrote:If a, b, c are real numbers such that a < b <c and a + b + c = 6, ab + bc + ca = 9, then which among the following is definitely true?

(1)0 < a < 1
(2)1 < b < 3
(3)3 < c< 4
(4)All of them
(5)None of them
I will go for b

Since if b>3 a<3 which is not possible
and if b<1 cannot satisfy the given equations

Purely hunch based

________________
Actually,I solved the question using the equations:-
(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)
and (a-b)^2 + (b-c)^2 + (c-a)^2 >0 [square is always a positive number or zero]

Can you get to the answer applying the formal technique??

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