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Dr. Gary Gruber's Brain Teasers, Vol. 4

June 26, 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. A music store offers successive discounts of 30% and 10% on an pair of cymbals. The equivalent single discount would be:

A. 34 percent

B. 36 percent

C. 37 percent

D. 38 percent

E. 40 percent 

3. If there are 24 singers at a party and each singer shakes another singer’s hand, how many handshakes are there?

4. What can we infer from the following:

“Every child Sam knows likes modern music and every adult Sam knows likes Renaissance music. Mike likes modern music and Sandra likes Renaissance music”

A. Mike cannot be an adult.

B. Sandra cannot be a child.

C. If Sam knows Sandra and Mike, Sandra must be an adult and Mike must be a child.

D. If Sam knows Mike, but not Sandra, Mike must be a child.

E. None of the above.

5. How many musical groups can be formed from a pool of three people, where a musical group can consist of 1 to 3 people.

A. 3

B. 4

C. 5

D. 6

E. 7

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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. Note: A symphony is not played with a piano, it is played with an orchestra.

2. C. The equivalent single discount is less than the sum of the discounts. Start with $100. 30% discount gives you $70 price. 10% discount on $70 gives you a price of $63. $100 - $63 = $37 discount which is equivalent to a 37% discount on $100.

3.  276. 24 combinations taken 2 at a time, e.g., from a,b,c,d,e .... ab, ac, bc, etc. we get (24 x 23)/2. This is how we get this: Each singer can shake hands with 23 other singers, so we have 24x23 possible combinations. But because it takes two singers to make a handshake, we must divide this product by 2, so we get (24x23)/2 or 276.

4. E. Mike may be an adult that likes modern music and Sandra can be a child that likes Renaissance music.

5. E. 7 If people are denoted by a,b,c you have three solos, three duets, and one trio:  a,b,c, ab, ac, bc, abc.

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: