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a,b, and c represent the side lengths of a certain triangle

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Carcass
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a,b, and c represent the side lengths of a certain triangle [#permalink] New post   04 Mar 2021, 02:35
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a,b, and c represent the side lengths of a certain triangle

Quantity A
Quantity B
2a + 3b
2b+c


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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A
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a,b, and c represent the side lengths of a certain triangle [#permalink] New post   04 Mar 2021, 07:24
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Carcass wrote:
a,b, and c represent the side lengths of a certain triangle

Quantity A
Quantity B
2a + 3b
2b + c



Let's first simplify the question using matching operations (my favorite Quantitative Comparison strategy)

Given:
Quantity A: 2a + 3b
Quantity B: 2b + c

Subtract 2b from both quantities to get:
Quantity A: 2a + b
Quantity B: c

Key property: 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

Since c is the length of the third side, we can apply the property to write: a - b < c < a + b
If c < a + b, it must also be true that c < a + b + a (since a > 0)
In other words, it must be true that c < 2a + b

Answer: A

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Re: a,b, and c represent the side lengths of a certain triangle [#permalink] New post   04 Mar 2021, 07:41
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Carcass wrote:
a,b, and c represent the side lengths of a certain triangle

Quantity A
Quantity B
2a + 3b
2b+c


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation


We know, any side in a triangle is less than the sum of other 2 sides and greater than the positive difference between other 2.

Here, \(|a - b| < c < a + b\)

Col. A: \(2a + 3b\)
Col. B: \(2b + c\)

Subtract \(2b\) from both sides;

Col. A: \(2a + b\)
Col. B: \(c\)

Since \(c < a + b\), it must also be less than \(2a + b\)

Hence, option A
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Re: a,b, and c represent the side lengths of a certain triangle [#permalink] New post   18 Jul 2023, 17:04
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Re: a,b, and c represent the side lengths of a certain triangle [#permalink]
18 Jul 2023, 17:04
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