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SEDULOUS :

The sum of 5 consecutive integers is 35. How many of the five consecutive integers are prime numbers

FETTER :

In a game, exactly six inverted cups stand side by side in a straight line, and each has exactly one ball hidden under it. The cups are numbered consecutively 1 through 6. Each of the balls is painted a single solid color. The colors of the balls are green, magenta, orange, purple, red, and yellow. The balls have been hidden under the cups in a manner that conforms to the following conditions: The purple ball must be hidden under a lower-numbered cup than the orange ball. The red ball must be hidden under a cup immediately adjacent to the cup under which the magenta ball is hidden. The green ball must be hidden under cup 5. Which of the following could be the colors of the balls under the cups, in order from 1 through 6

A cistern has two taps (which fill it in 12 min. and 15 min. respectively) and an exhaust tap. When all the three taps are opened together it takes 20 min. to fill the cistern. How long will the exhaust tap take to empty it