The weights of 4 boxes are 90, 30, 20 and 50 kilograms. Which of the following cannot be the total weight, in kilograms; of any combination of these boxes and in a combination a box can be used only once?
150
Possible sums from {90, 30, 20, 50} (each used at most once): 20, 30, 50, 70, 80, 90, 100, 110, 120, 140, 160, 170, 190.
Check options: 190 = 90+30+20+50, 170 = 90+30+50, 100 = 30+20+50. But 150 cannot be formed by any subset.
Hence the answer is 150.
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- There are deers and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?
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- A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has". A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have?
- A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold?
There are fourteen teams playing in a tournament. If every team plays one match with every other team, how many matches will be played in the tournament?
