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06 May 2020, 22:39
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:26) correct
29%
(01:23)
wrong
based on 95
sessions
History
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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.
(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.
Updated on: 02 Mar 2025, 10:59
Originally posted by GMATinsight on 06 May 2020, 23:07.
Last edited by Bunuel on 02 Mar 2025, 10:59, edited 2 times in total.
Last edited by Bunuel on 02 Mar 2025, 10:59, edited 2 times in total.
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Bunuel
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
07 May 2020, 04:24
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Bunuel
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 \(⟹ a – 2 – b+ 2 = 2 ⟹ a – b = 2\)
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.
Thus, the correct answer is Option A.
