Name: John and Norman

Question: All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derf nor Sivad?


I would do this with a Venn diagram. Draw three circles, one for the Derfs one for the Enajs and one for the Sivads. Label them D, E and S. Since "All Derfs are Enajs" the D circle is inside the E circle

Now look for clues that have specific numbers.

  • "One Sivad is a Derf." tells you that you can put a 1 in the intersection of the S circle and the D circle.

  • "Eight Sivads are Enajs." says that there are 8 in the intersection of the S and E circles. You already have 1 in that intersection so you need 7 more.

  • "Half of all Sivads are Enajs." tells you that there are 8 inside S but outside E.
Thus far you have:


  • "The number of Enajs is 90." and "One-third of all Enajs are Derfs." implies that there are 30 inside D and hence 29 inside D but outside S.

  • Hence to have 90 inside E there must be 58 in the remaining piece of E.

    So, how many Enajs are neither Derf nor Sivad?

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