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Math Expert V
Joined: 02 Sep 2009
Posts: 58401
In triangle ABC, AB = 5 and AC = 3. Which one of the following is the  [#permalink]

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Question Stats: 46% (01:12) correct 54% (00:59) wrong based on 68 sessions

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In triangle ABC, AB = 5 and AC = 3. Which one of the following is the measure of the length of side BC ?

(A) BC < 7
(B) BC = 7
(C) BC > 7
(D) BC ≤ 7
(E) It cannot be determined from the information given

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GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5008
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In triangle ABC, AB = 5 and AC = 3. Which one of the following is the  [#permalink]

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Bunuel wrote:
In triangle ABC, AB = 5 and AC = 3. Which one of the following is the measure of the length of side BC ?

(A) BC < 7
(B) BC = 7
(C) BC > 7
(D) BC ≤ 7
(E) It cannot be determined from the information given

third side rule BC should be <=7 but no lower than 2
; IMO E
Target Test Prep Representative D
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Re: In triangle ABC, AB = 5 and AC = 3. Which one of the following is the  [#permalink]

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Bunuel wrote:
In triangle ABC, AB = 5 and AC = 3. Which one of the following is the measure of the length of side BC ?

(A) BC < 7
(B) BC = 7
(C) BC > 7
(D) BC ≤ 7
(E) It cannot be determined from the information given

Since a side of a triangle must be more than the difference of the other two sides and less than the sum of the other sides, we see that:

5 - 3 < BC < 5 + 3

2 < BC < 8

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Intern  B
Joined: 20 Apr 2019
Posts: 26
Re: In triangle ABC, AB = 5 and AC = 3. Which one of the following is the  [#permalink]

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ScottTargetTestPrep

option B - BC=7 satisfies the condition 2<BC<8 right?
Why is it wrong? Can you please clarify my doubt.
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Re: In triangle ABC, AB = 5 and AC = 3. Which one of the following is the  [#permalink]

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moropa2018 wrote:
ScottTargetTestPrep

option B - BC=7 satisfies the condition 2<BC<8 right?
Why is it wrong? Can you please clarify my doubt.

Given only that the lengths of two sides of a triangle are 3 and 5, all we can say about the third side is that it has to be between 2 and 8, exclusive. BC = 7 happens to fall in that range, however, the question is not asking “Which of the following could be the length of BC?”, it is asking for the exact length and we don’t have enough information to determine that. If we were given the angle between the sides of length 3 and 5, we would be able to use some identities involving trigonometric functions to determine the length of BC or if we were given the perimeter, likewise. But just knowing the length of two sides and nothing else, we can’t.
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Senior Manager  S
Joined: 12 Sep 2017
Posts: 302
In triangle ABC, AB = 5 and AC = 3. Which one of the following is the  [#permalink]

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Hello ScottTargetTestPrep!

I am a bit confused, I know that the range of the third side is between 3 and 7, inclusive.

But why in some other questions in GMAT we just have to consider the max or min value? (attached exercise)

In the attached one, the answer is C, but in order to answer that, we must avoid the superior limit.

-7 = or < x < or = 4

Kind regards!
Attachments gmat.jpg [ 392.48 KiB | Viewed 451 times ]

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Re: In triangle ABC, AB = 5 and AC = 3. Which one of the following is the  [#permalink]

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In the exercise you provided, the strict inequality vs. non-strict inequality issue and the fact that x is an integer are the reasons you are avoiding the lower bound (though I can understand what you mean by "superior limit", it is actually a totally unrelated topic, usually abbreviated "limsup"; that's why I am avoiding that terminology).

When you solve the inequality |2x + 3| =< 12, you will obtain that x is between -7.5 and 4.5, inclusive. Since we are also given that x is an integer, we conclude that x is between -7 and 4, inclusive. So, x is greater than or equal to -7, which is the same thing (since x is an integer) as saying x is strictly greater than -8. Notice that if we were not given that x is an integer, the sentences "x is greater than or equal to -7" and "x is strictly greater than -8" would be very different; for instance, x = -7.5 would have been excluded in the former but included in the latter.

Long story short, there is no rule to tell us to avoid the upper or lower bounds in a non-strict inequality; we just have to keep in mind the pieces of information the question has provided us (such as the information that x is an integer) and do our analysis in the light of that information to find the correct answer.
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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: In triangle ABC, AB = 5 and AC = 3. Which one of the following is the   [#permalink] 25 Apr 2019, 18:22
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