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Dr. Gary Gruber's Brain Teasers, Vol. 2

April 9, 2014

1. Complete the analogy:
MUSIC is to VIOLIN as:

(A) notes is to composer
(B) sound is to musical instrument
(C) crayon is to drawing
(D) furniture is to carpentry tools
(E) symphony is to piano

2. Some students gather for a rehearsal in the chorus room. Fourteen play instruments, eight are singers, and two are neither instrumentalists nor singers. If five of the people are both singers and instrumentalists, how many people are in the room?

(A) 3
(B) 17
(C) 19
(D) 24
(E) 29

3. Fill in the blanks:
The famous composer Richard Wagner was frequently intolerant; moreover, his strange behavior caused some of his acquaintances to _____ the composer whenever possible.

(A) contradict
(B) interrogate
(C) shun
(D) revere
(E) tolerate

4. You’re on a game show and behind one of three doors is a Stradivarius violin. Behind the other two doors is a Johann Sebastian Bach doll. After you choose one of the doors, the host opens one of the other doors, which contains a stuffed Johann Sebastian Bach doll. Then he turns back to you and says, “Do you want to change doors, or stick with the one you picked?” Going strictly by the odds (probability), should you make the change?

5. Which name is missing from the sequence:

Pierre Monteux, Enrique Jorda, Joseph Krips, Seiji Ozawa, Edo de Waart, Michael Tilson Thomas?

A. Herbert Blomstedt
Leonard Bernstein
Kurt Mazur
Fritz Reiner
Georg Solti







1. D. Put MUSIC and VIOLIN in a sentence relating the two words. Music is played on a violin by someone that knows how to play a violin, just as furniture is created by carpentry tools by a person that knows how to use carpentry tools. (“Crayon” is not done with a “drawing.” Drawing is done with a crayon. And: Symphony is not played with a piano — it is played with an orchestra.)

2. C. Use a “Venn” Diagram or write down all the possibilities.

    Total number of people are:
    (a) instrumentalists and not singers (14 minus 5 equals 9).
    (b) Singers who are not instrumentalists (8 minus 5 equals 3).
    (c) Singer-instrumentalists (5).
    (d) People who are neither singers nor instrumentalists. (2)
    Adding a,b,c, and d, we get 9 + 3 + 5 + 2 = 19.

3. C. The key word is “moreover.” Taken together with “intolerant,” “moreover, his strange behavior,” would probably lead people to avoid (or shun) the composer.

4. YES. Your odds of picking the door with the Stradivarius behind it have increased by 33 percent. By sticking with the door you chose you would have a 1/3 chance of getting the Stradivarius. But if you changed doors, you would have a 2/3 chance of getting the Stradivarius.

5. A. The names in the question represent, from the past to the present, the music directors of the San Francisco Symphony. Between Edo De Waart and Michael Tilson Thomas, the music director of the Symphony was Herbert Blomstedt.

Dr. Gary R. Gruber is recognized as the leading authority on standardized tests and the originator of the critical thinking skills used to prepare for them. The author of more than 40 books with over 7 million copies sold, his lifelong mission is to get the nation to be passionate about problem solving and to develop and hone critical thinking abilities. Check out his website: