12 Days of Christmas GMAT Competition - Day 1: A 10m stick is broken i

Question

12 Days of Christmas GMAT Competition with Lots of Fun

A 10m stick is broken into four pieces of lengths a, b, c, and d by making three cuts on the stick. Can the four pieces form a quadrilateral?

(1) d > c > b > a
(2) d > a + b + c

Archit3110 · Answer

So as to form a quadrilateral the sum of the lengths of the shortest three sides of a quadrilateral must be longer than the longest side

given length is 10 m
#1
d > c > b > a
case 1 :
5>2.5>2>0.5
not possible to form quadrilateral as sum of three sides is equal to longest side
case 2:
4>3>2.5>0.5
yes , quadrilateral can be formed 
insufficient
#2
d > a + b + c
this is opposite to property of length of quadrilateral
sufficient to say that lengths a, b, c, and d cannot form a quadrilateral
 OPTION B is correct

Kinshook · Answer

Given: A 10m stick is broken into four pieces of lengths a, b, c, and d by making three cuts on the stick.

Asked: Can the four pieces form a quadrilateral?

(1) d > c > b > a
Case 1: A quadrilateral is possible with sides d=4>c=3>b=2>a=1
Case 2: A quadrilateral can not be formed when d=7>c=1.2>b=1>a=.8
NOT SUFFICIENT

(2) d > a + b + c
A quadrilateral can not be formed since length of one side is greater than sum of other 3 sides.
If we lay other 3 sides in a straight line for maximum length, d can not join the 2 extremes.
SUFFICIENT

IMO B

rxb266 · Answer

A 10m stick is broken into four pieces of lengths a, b, c, and d by making three cuts on the stick. Can the four pieces form a quadrilateral?

This is very straight to the point question and can be solved by assuming values.

(1) d > c > b > a

Here there are 2 cases:

Case 1:
d = 9.4
c = 0.3
b = 0.2
a = 0.1
Clearly here d > a + b + c and thus a quadrilateral can not be formed.

Case 2:
d = 4
c = 3
b = 2
a = 1
With these values a quadrilateral can be formed.

Statement 1 is clearly INSUFFICIENT

(2) d > a + b + c

This statement is similar to the case 1 that we considered for statement A and is Clearly sufficient. With d > a + b + c, we can conclude with certainity that a quadrilateral can never be formed.

Hence, Statement 2 is clearly SUFFICIENT

Answer: Option B

kungfury42 · Answer

Concept:   In any n-sided polygon, the sum of any (n-1) sides must always be greater than the remaining side. This can be visualized as the remaining side being the straight line (hence shortest) distance between the two vertices.

Application:   Statement 1 tells us that d>c>b>a.

Now let's take case 1: d=4, c=3, b=2, and a=1. In this case, each side is less than the sum of the remaining 3 sides. Possible Quadrilateral.

Let's take case 2: d=10, c=3, b=2, and a=1. In this case, "side d" is greater than the sum of the remaining 3 sides. Quadrilateral not possible.

Hence Statement 1 is insufficient in itself. But Statement 2 explicitly tells us that d>a+b+c which is a clear violation of a Quadrilateral's basic property as discussed above. Hence, it is sufficient to comment that such a Quadrilateral would not be possible.

Hence, option B.

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Bekobod · Answer

A 10m stick is broken into four pieces of lengths a, b, c, and d by making three cuts on the stick. Can the four pieces form a quadrilateral?

My approach is as follows:
The sum of 3 sides of quadrilateral should be greater than the fourth. This means a+b+c>d

(1) d > c > b > a 
given a=1 b=2 c=3 d=4 it is possible to form quadrilateral since the sum of any 3 sides is greater then the fourth one;
given a=1.2 b=1.5 c=1.7 and d=5.6 it is impossible to form quadrilateral, as 1.2+1.5+1.7<5.6; Hence, st (1) is  Not Sufficient

(2) d > a + b + c
This statement is the oppositte of a+b+c>d. For that reason, it is impossible to form quadrilateral.  Sufficient

Answer:  B

Pallav0777 · Answer

Question is can the sides form a quadrilateral?

The first statement can result in two possible answers:
CASE 1 Eg: 4,3,2,1 Here Quadrilateral possible
 
CASE 2 Eg: 6,2,0.55,0.45 Here, length of one side is greater than the sum of other three sides, so Quadrilateral not possible.

The second statement is self sufficient to answer the question of whether a Quadrilateral can be formed because there is only one possible case of "no Quadrilateral can be formed" when one side is greater than the sum of other three sides.

Hence, Correct Ans B (only II Sufficient)

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Bunuel · Answer

GMATWhiz Official Explanation: Step 1: Analysis of the Question Stem. • We have a 10m stick is broken into four pieces a, b, c, and d. o We need to find out if we can form a quadrilateral using these 4 pieces. o This is a Yes-No type DS question. • The concept is a logical extension of the triangle inequality theorem (The theorem suggests that the sum of any two sides must be greater than the third side) o Let’s extend it for quadrilateral. o Consider the following diagram: https://gmatclub.com/forum/download/file.php?id=69640 o We can see (eye estimation) AB is the longest.  Now AB is the shortest distance (straight tine) between A and B.  Whereas AD + DC + CB is a path connecting A and B taking a couple of detours. • Thus, AD + DC + CB > AB (where AB is the longest side) for any quadrilateral. o Here, the information of 10 cm is not of much significance. We can now move to statement analysis. Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: d > c > b > a • We see that ‘d’ is the longest side here. • However, we do not know d > c + b + a or not. o For instance, we can have d = 4, c = 3, b = 2, and a = 1.  Here d < a + b + c,  Thus, we get a quadrilateral. o We can also have d = 6, c = 2, b = 1.5, and a = 0.5.  Here we have d > a + b + c.  Thus, we do not get a quadrilateral. Thus, we do not get a conclusive Yes or No. Hence, this statement is insufficient to answer the question. We can eliminate options A and D. Statement 2: d > a + b + c • We have already established that the length of the longest side must be less than the sum of the length of the other three sides. • As per this statement we have d > a + b + c, thus a, b, c, and d will NOT form a quadrilateral. This statement is sufficient and thus we can eliminate option C and E. The answer is option B. 2022-12-15_17-22-42.png

12 Days of Christmas GMAT Competition - Day 1: A 10m stick is broken i

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