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Updated on: 07 Aug 2018, 06:00
Originally posted by EgmatQuantExpert on 28 Nov 2016, 01:03.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:00, edited 10 times in total.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:00, edited 10 times in total.
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D
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Difficulty:
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Mastering Important Concepts Tested by GMAT in Triangles - Exercise Question
Q. Is the perimeter of triangle ABC greater than 12 cm?
1. One side of triangle ABC measures 6 cm
2. The lengths of the three sides of triangle ABC are consecutive positive even integers
Answer Choices
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Mastering Important Concepts Tested by GMAT in Triangles has been explained in detail in the following post:
Mastering Important Concepts Tested By GMAT in Triangle - I
Detailed solution will be posted soon.
Thanks,
Saquib
Quant Expert
e-GMAT
Q. Is the perimeter of triangle ABC greater than 12 cm?
1. One side of triangle ABC measures 6 cm
2. The lengths of the three sides of triangle ABC are consecutive positive even integers
Answer Choices
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Mastering Important Concepts Tested by GMAT in Triangles has been explained in detail in the following post:
Mastering Important Concepts Tested By GMAT in Triangle - I
Detailed solution will be posted soon.
Thanks,
Saquib
Quant Expert
e-GMAT
Updated on: 07 Aug 2018, 06:10
Originally posted by EgmatQuantExpert on 28 Nov 2016, 01:05.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:10, edited 8 times in total.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:10, edited 8 times in total.
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Let's look at the detailed solution of the above problem.
Steps 1 & 2: Understand Question and Draw Inferences
Let’s say the sides of the triangle are a, b, and c.
Let the perimeter of the triangle be X.
Thus, \(X = a + b + c\)
We need to find whether \(X > 12\)
Since we don’t have any other information, let’s move on to the analysis of the statement 1.
Step 3: Analyze Statement 1 independently
Statement 1 says: One side of triangle ABC measures 6 cm.
Let’s assume a = 6 cm
Now, we know that the sum of two sides of a triangle is always greater than the third side.
So, we can write:
\(b + c > a\)
Adding a to both sides of this inequality, we get:
\(a + b + c > 2a\)
That is, \(X > 2a\)
Substituting a = 6 cm in this inequality, we get:
\(X > 12 cm\)
Therefore, statement 1 is sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2 independently
Statement 2 says: The lengths of the three sides of triangle ABC are consecutive positive even integers.
So, the lengths of the sides are \(2n, 2(n+1), 2(n+2)\) cm, where n is a positive integer.
Note: n cannot be equal to 1. For n = 1, the sides of the triangle will be 2, 4, and 6 respectively. Since b + c > a, but in this case 2 + 4 = 6, hence these numbers cannot form the sides of a triangle.
Hence, n > 1
Perimeter \(X = 2n + 2(n+1) + 2(n+2)\)
Now we know \(n>1\), therefore \(n+1>2\)
\(6(n+1) > 6 * 2\)
Which implies \(X > 12\)
Therefore, statement 2 is sufficient to determine if \(X > 12\).
Hence the correct Answer is D
Steps 1 & 2: Understand Question and Draw Inferences
Let’s say the sides of the triangle are a, b, and c.
Let the perimeter of the triangle be X.
Thus, \(X = a + b + c\)
We need to find whether \(X > 12\)
Since we don’t have any other information, let’s move on to the analysis of the statement 1.
Step 3: Analyze Statement 1 independently
Statement 1 says: One side of triangle ABC measures 6 cm.
Let’s assume a = 6 cm
Now, we know that the sum of two sides of a triangle is always greater than the third side.
So, we can write:
\(b + c > a\)
Adding a to both sides of this inequality, we get:
\(a + b + c > 2a\)
That is, \(X > 2a\)
Substituting a = 6 cm in this inequality, we get:
\(X > 12 cm\)
Therefore, statement 1 is sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2 independently
Statement 2 says: The lengths of the three sides of triangle ABC are consecutive positive even integers.
So, the lengths of the sides are \(2n, 2(n+1), 2(n+2)\) cm, where n is a positive integer.
Note: n cannot be equal to 1. For n = 1, the sides of the triangle will be 2, 4, and 6 respectively. Since b + c > a, but in this case 2 + 4 = 6, hence these numbers cannot form the sides of a triangle.
Hence, n > 1
Perimeter \(X = 2n + 2(n+1) + 2(n+2)\)
- \(X = 6n + 6\)
\(X = 6(n+1)\)
Now we know \(n>1\), therefore \(n+1>2\)
\(6(n+1) > 6 * 2\)
Which implies \(X > 12\)
Therefore, statement 2 is sufficient to determine if \(X > 12\).
Hence the correct Answer is D
General Discussion
01 Dec 2016, 22:47
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IMO D
1) consider sides to be 6,a,b
(now to make perimeter less than 12,we need to consider smallest possible values of a and b)
so if a=0.1 then b should be less than 6+0.1 and more than 6-0.1,i.e,
5.9<b<6.1
same can be concluded with smaller values of a such as 0.001,0.0001,e.t.c
SUFFICIENT
2)lengths of sides are consecutive positive even integers:
2,4,6(perimeter=12) but then side with length 6 is not less than sum of other two sides i.e,2+4 ;NOT POSSIBLE
4,6,8 ; 6,8,10 ;etc.(perimeter>12) POSSIBLE values of sides of triangle
SUFFICIENT
Please correct me if I am wrong
Thanks in advance
1) consider sides to be 6,a,b
(now to make perimeter less than 12,we need to consider smallest possible values of a and b)
so if a=0.1 then b should be less than 6+0.1 and more than 6-0.1,i.e,
5.9<b<6.1
same can be concluded with smaller values of a such as 0.001,0.0001,e.t.c
SUFFICIENT
2)lengths of sides are consecutive positive even integers:
2,4,6(perimeter=12) but then side with length 6 is not less than sum of other two sides i.e,2+4 ;NOT POSSIBLE
4,6,8 ; 6,8,10 ;etc.(perimeter>12) POSSIBLE values of sides of triangle
SUFFICIENT
Please correct me if I am wrong
Thanks in advance
