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Math Revolution GMAT Instructor V
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The lengths of two sides of a certain triangle are 3 and 9. What is th  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 69% (00:56) correct 31% (00:50) wrong based on 134 sessions

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[GMAT math practice question]

The lengths of two sides of a certain triangle are 3 and 9. What is the length of the 3rd side of the triangle?

1) The perimeter of the triangle is 20
2) The length of the 3rd side of the triangle is a multiple of 4

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Re: The lengths of two sides of a certain triangle are 3 and 9. What is th  [#permalink]

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Let the third side of triangle= x

Statement 1: 3+9+x=20; x=8 [Suff]

Statement 2: x is a multiple of 4

Note: a) The length of any side of a triangle must be larger than the positive difference of the other two sides.

So x must be greater than (9-3)= 6

b) The length of any side of a triangle must be smaller than the sum of the other two sides.

So x must be smaller than (9+3)= 12

8 is the only multiple of 4 which is greater than 6 but smaller than 12. [Suff]

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The lengths of two sides of a certain triangle are 3 and 9. What is th  [#permalink]

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Top Contributor
MathRevolution wrote:
[GMAT math practice question]

The lengths of two sides of a certain triangle are 3 and 9. What is the length of the 3rd side of the triangle?

1) The perimeter of the triangle is 20
2) The length of the 3rd side of the triangle is a multiple of 4

Target question: What is the length of the 3rd side of the triangle?

Given: The other two sides have lengths 3 and 9

Statement 1: The perimeter of the triangle is 20
Let x = the length of the third side
If the perimeter is 20, we can write: 3 + 9 + x = 20
Solve to get: x = 8
So, the answer to the target question is 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The length of the 3rd side of the triangle is a multiple of 4

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

Let x = the length of the third side
So, we can write: 9 - 3 < x < 9 + 3
Simplify: 6 < x < 12
Since 8 is the only multiple of 4 between 6 and 12, we can conclude that x = 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Originally posted by BrentGMATPrepNow on 19 Feb 2018, 12:32.
Last edited by BrentGMATPrepNow on 28 Apr 2018, 09:01, edited 1 time in total.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9014
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The lengths of two sides of a certain triangle are 3 and 9. What is th  [#permalink]

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=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Assume $$x$$ is the length of the 3rd side of the triangle.
Since we have 1 variable ($$x$$) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Note:
Since (using the triangle inequality) $$x > 9 + 3 = 12$$ and $$x < 9 – 3 = 6$$, we have $$6 < x < 12.$$

Condition 1)
$$x + 3 + 9 = 20$$
Thus $$x = 8$$.
Condition 1) is sufficient.

Condition 2)
The only integer between $$6$$ and $$12$$ that is a multiple of $$4$$ is $$8.$$
Thus, $$x = 8$$.
Condition 2) is sufficient, too.

In addition, since conditions 1) and 2) are similar, D is most likely to be the answer.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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_________________ Re: The lengths of two sides of a certain triangle are 3 and 9. What is th   [#permalink] 26 Dec 2019, 10:31

# The lengths of two sides of a certain triangle are 3 and 9. What is th  