OG 13 Problem

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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Tue Dec 22, 2015 3:08 pm

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If K is an integer and 2<k<7, for how many different values of k is there a triangle with sides of lengths 2,7, and k?

A. One
B. Two
C. Three
D. Four
E. Five

Answer: A

Why please explain your reasoning

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Source: Beat The GMAT — Problem Solving | Tue Dec 22, 2015 3:08 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Tue Dec 22, 2015 10:47 pm

If K is an integer and 2 < k < 7, for how many different values of k is there a triangle with sides of lengths 2,7, and k?

A. One
B. Two
C. Three
D. Four
E. Five

For three line segments to work as a triangle, the lengths of any two of the segments have to add up to a sum greater than the length of the third. Otherwise two sides will not be long enough to connect with each other and with the ends of the third side.

The integers k such that 2 < k < 7 are 3, 4, 5 and 6.

See how many of those could form a triangle with sides 2, 7, and k.

If the lengths of the three segments were 2, 7 and 3, the segments 2 and 3 long would not be long enough to connect with each other and with the ends of the segment 7 long to form a triangle.

2 + 4 < 7 Doesn't work.

2 + 5 = 7 The only way to connect all the ends is to put them together flat. That's not a triangle.

2 + 6 > 7 -- 7 + 2 > 6 -- 7 + 6 > 2 That works.

So only K = 6 works and the correct answer is A.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Feb 15, 2018 7:05 pm

Hi All,

We're told that K is an integer and 2 < K < 7. We're asked for the number of different values of K that would create a triangle with sides of lengths 2, 7 and K.

This question is based on a math rule called the Triangle Inequality Theorem. In simple terms, it means that if you're dealing with a triangle, then the sum of ANY 2 sides will be greater than the 3rd side. For example, with a 3/4/5 right triangle....

3 + 4 > 5
3 + 5 > 4
4 + 5 > 3
So these 3 lengths (and these 3 inequalities) PROVE that we're dealing with an actual triangle.

In that same way, we can use the rule to determine when we're NOT dealing with an actual triangle... For example, you CANNOT have a triangle with sides of 1, 1 and 100 (because 1+1 is NOT greater than 100).

With this question, we're given two sides: 2 and 7 and we're asked to determine what the third side (K) could be. We're given a range of values for K and we're told that K must be an INTEGER. Since 2 + K must be GREATER than 7, the only possible value that fits all of the given information is K=6. Thus, there's only one value for K.

Final Answer: A

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

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Mon Apr 16, 2018 3:48 pm

oquiella wrote:If K is an integer and 2<k<7, for how many different values of k is there a triangle with sides of lengths 2,7, and k?

A. One
B. Two
C. Three
D. Four
E. Five

Recall the triangle inequality, which states that in order for three values to be the lengths of the sides of a triangle, the sum of the two smaller values must be greater than the third (the largest value).

Since k is an integer between 2 and 7, k can be 3, 4, 5 or 6.

If k = 3, {2, 3, 7} can't be the lengths of the sides of a triangle since 2 + 3 = 5 is not greater than 7.

If k = 4, {2, 4, 7} can't be the lengths of the sides of a triangle since 2 + 4 = 6 is not greater than 7.

If k = 5, {2, 5, 7} can't be the lengths of the sides of a triangle since 2 + 3 = 7 is not greater than 7.

If k = 6, {2, 6, 7} CAN be the lengths of the sides of a triangle since 2 + 6 = 8 is greater than 7.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: OG 13 Problem

by Brent@GMATPrepNow » Wed Jan 29, 2020 12:16 pm

oquiella wrote: ↑
Tue Dec 22, 2015 3:08 pm
If K is an integer and 2<k<7, for how many different values of k is there a triangle with sides of lengths 2,7, and k?

A. One
B. Two
C. Three
D. Four
E. Five

Answer: A

Why please explain your reasoning

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B

We're told that the two KNOWN sides have lengths 2 and 7
So, we can write: (7 - 2) < k < (7 + 2)
Simplify: 5 < k < 9
Since k is an INTEGER, k can equal 6, 7 or 8

However, we're also told that 2 < k < 7, so 6 is the only value that k can have.

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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