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Thursday, January 25, 2007
"GRE MATH PROBLEM OF THE DAY"
A polygon has 44 diagonals, and then number of sides are ? A) 7 B) 8 C) 9 D) 10 E) 11
Answer is 11. I started with 4, 5, 6 sides of polygon & just saw the pattern. But it took little bit more time than should have for test. Is there any other way to do it?
the pattern of no. of diagnols starting with 4 sided polygon is 2,5,,9,14,20,27,35,44...this is nothing but sum of natural no. i.e.2+3+4+5+6+7+8+9=44 4-5-6-7-8-9-10-11-----sides
simply try this formula n(n+1)/2 9(9+1)/2 = 45(nearly 44) 9+2=11 (always add 2 to n to get the ans. u can try for others also suppose 35 dia
why 11?
ReplyDeleteAnswer is 11. I started with 4, 5, 6 sides of polygon & just saw the pattern. But it took little bit more time than should have for test. Is there any other way to do it?
ReplyDeletedint get it..cud neone explain?
ReplyDeletethe pattern of no. of diagnols starting with 4 sided polygon is 2,5,,9,14,20,27,35,44...this is nothing but sum of natural no. i.e.2+3+4+5+6+7+8+9=44
ReplyDelete4-5-6-7-8-9-10-11-----sides
simply try this formula n(n+1)/2
9(9+1)/2 = 45(nearly 44)
9+2=11 (always add 2 to n to get the ans.
u can try for others also
suppose 35 dia
For a an n sided polygon - the number of diagonals drawm from a vertex is (n-3)
ReplyDeletetherfore if there are x diagonals , then the number of sides will be
n*(n-3)=2x
solve for n
u will gwt 2 values 11 and -8
ans=11