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The lengths of two sides of a certain triangle are 3 and 9.

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The lengths of two sides of a certain triangle are 3 and 9.

by Max@Math Revolution » Mon Feb 19, 2018 12:22 am
[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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by Brent@GMATPrepNow » Mon Feb 19, 2018 12:30 pm
Max@Math Revolution wrote: 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

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Tue Feb 20, 2018 11:51 pm
=>

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.

Therefore, D is the answer.

Answer: D

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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