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Bethany invited several couples to her house in the country. The man in each couple invited 4 male friends, each of whom in turn invited x male friends. The woman in each couple invited 5 female friends, each of whom invited y female friends. In all, how many men were invited?
(1) 253 people were invited in all.
(2) More women than men were invited.
(1) 253 people were invited in all.
(2) More women than men were invited.
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14 Apr 2007, 07:11
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Men * 4x + Women * 5y = total , but men = women (couples)
so, n4x + n5y = n(4x+5y)
1. n(4x+5y) = 253 => 4x + 5y = 253/n , since n has to be an integer, there are only two possible values, 11 and 23 (by prime factorization)
if we try n = 11 => 4x + 5y = 23 = 4(2) + 5(3), unique sol'n.
if we try n = 23 => 4x + 5y = 11 => won't work , so n must be 11
and x =2, y=3, Therefore, A is sufficient
so, n4x + n5y = n(4x+5y)
1. n(4x+5y) = 253 => 4x + 5y = 253/n , since n has to be an integer, there are only two possible values, 11 and 23 (by prime factorization)
if we try n = 11 => 4x + 5y = 23 = 4(2) + 5(3), unique sol'n.
if we try n = 23 => 4x + 5y = 11 => won't work , so n must be 11
and x =2, y=3, Therefore, A is sufficient
