Two polygons A and B have number of sides as a and b respectively, wha

Question

Two regular polygons A and B have number of sides as a and b respectively, what is the value of |a − b|?

(1) Sum of interior angles of polygon A is 360 degree greater than that of polygon B.
(2) The number of diagonals of polygon A is 20.

GMATinsight · Answer

Question: |a − b|=?

Statement 1 : Sum of interior angles of polygon A is 360 degree greater than that of polygon B.

CONCEPT : Sum of Interior angles of an  n  sided polygon  = 180*(n-2)

i.e. 180*(a-2) = 180*(b-2) + 380

i.e. (a-2) = (b-2) + 2

i.w. a = b+2

i.e. a-b = 2

i.e. la-bl = 2

SUFFICIENT

Statement 2 : The number of diagonals of polygon A is 18.

CONCEPT : Number of diagonals in an  n  sided polygon  = nC_2 - n = \frac{n*(n-3)}{2}

i.e. a(a-3)/2 = 20
i.e. a(a-3) = 40
i.e. a = 8

But No information about b hence

NOT SUFFICIENT

Answer: Option A

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • Regular polygon A has “a” number of sides.
• Regular polygon B has “b” number of sides.
• We need to find the value of |a – b|
 o i.e. we need to find the positive difference between a and b.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  Sum of interior angles of polygon A is 360 degree greater than that of polygon B.

• We know that  the sum of interior angles of a regular polygon  = (n- 2)*180   degrees, where n is the number of sides. 
• Now, According to this statement:  (a – 2)*180 – (b-2)*180 = 360  degrees
 o  ⟹ a – 2 – b+ 2 = 2 ⟹ a – b = 2   
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.

Statement 2:  The number of diagonals of polygon A is 20.

• This statement gives no information about polygon B.
• So, we cannot find |a – b| from this statement. 
Hence, statement 2 is NOT sufficient.
Thus, the correct answer is  Option A.

sambitspm · Answer

Two regular polygons A and B have number of sides as a and b respectively, what is the value of |a − b|?

(1) Sum of interior angles of polygon A is 360 degree greater than that of polygon B.
(2) The number of diagonals of polygon A is 20.

Solution 
 STATEMENT A: 
Say Polygon A has m sides, and Polygon B has n sides.
So sum of interior angles is (2n-2)90

(2m-2 - 2n+2) * 90 = 360
  SUFFICIENT

STATEMENT B:  
Number of diagonals of Polygon A is given.
Number of diagonals in a polygon is n(n-3)/2
But no information about Polygon B is given, hence   INSUFFICIENT

ANSWER - A

poojakhanduja3017 · Answer

Very easy question. The answer is A 
Statement 1: Sum of interior angles of polygon A is 360 degree greater than that of polygon B.

CONCEPT: Sum of Interior angles of an n-sided polygon =180*(n−2)=180*(n−2)

Step 1: 180*(a-2) = 180*(b-2) + 360
Step 2: (a-2) = (b-2) + 2
Step 3: a = b+2
Step 4: a-b = 2
Answer : la-bl = 2

SUFFICIENT

Statement 2: The number of diagonals of polygon A is 18.
We know nothing about B, hence NOT SUFFICIENT.

Two polygons A and B have number of sides as a and b respectively, wha

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Two polygons A and B have number of sides as a and b respectively, wha

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