triangle

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sumasajja: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Wed Jul 20, 2011 12:36 pm; Thanked: 2 times

by sumasajja » Wed Jul 27, 2011 10:07 pm

if x,y and z are the three angles of a triangle and are integers such that x<y<z,then the least and the greatest possible values of x+z are
a]59 and 91
b]59 and 135
c]91 and 178
d]120 and 135
e]120 and 179
the answer is c

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Source: Beat The GMAT — Problem Solving | Wed Jul 27, 2011 10:07 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jul 27, 2011 10:56 pm

sumasajja wrote:if x,y and z are the three angles of a triangle and are integers such that x<y<z,then the least and the greatest possible values of x+z are
a]59 and 91
b]59 and 135
c]91 and 178
d]120 and 135
e]120 and 179
the answer is c

x + z will be least when y is maximum. The greatest value among the 3 angles, so that their sum is 180Âº, is 90Âº. Now since y < z, so z = 90Âº. Next, we move on to the possible values of x and z. Minimum value of x = 1, and maximum possible value of y (considering x < y < z) = 89Âº (we have taken it as 89Âº, as z = 90Âº).

So, least value of x + z = 1 + 90 = 91

Now, x + z will b greatest when y is minimum. In this case x = 1, y = 2, z = 177 (so that x + y + z = 180Âº). So, the greatest value of x + z = 1 + 177 = 178.

The correct answer is C.

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ArpanaAmishi: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Sun Jun 06, 2010 10:52 pmFollowed by: 1 member; Thanked: 2 times

by ArpanaAmishi » Thu Jul 28, 2011 1:09 am

Hi Anurag,
I am not clear on 'x + z will be least when y is maximum. The greatest value among the 3 angles, so that their sum is 180Âº, is 90Âº. Now since y < z, so z = 90Âº'

Request to elaborate on this.

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Jul 28, 2011 3:24 am

ArpanaAmishi wrote:Hi Anurag,
I am not clear on 'x + z will be least when y is maximum. The greatest value among the 3 angles, so that their sum is 180Âº, is 90Âº. Now since y < z, so z = 90Âº'

Request to elaborate on this.

You are right. Since z > y, that's why in this case I have taken z = 90, and y = 89, which is the 2nd largest value so that the condition y < z is true.

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