Brain Teasers
Gary R. Gruber, the author of more than 30 test-prep books (drgarygruber.com), designed this challenge to test your problem-solving skills. Remember: Creative people look outside the realm of normal thinking to solve problems.
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- If I have 3 dimes, 3 nickels, and 3 quarters, how many ways can I make change for $1?
- How many state names in the U.S. begin with the same letter as the state’s capital city?
- Three friends eat breakfast at a restaurant. They estimate that the bill will be $30, so each pays $10. When the bill comes, it is $25. They each take $1 back, leaving the remaining $2 as a tip. Each has paid $9, and 3 x $9 = $27. But $27 plus $2 is only $29. Where did the extra dollar go?.
- What English word contains all the vowels in alphabetical order?
- You have 12 balls which are identical in all ways, except one ball is heavier than the rest. With a balance scale, how could you determine in three weighings which is the heavy ball?
- Complete the analogy: hamlet : village ::
(A) street : sidewalk
(B) highway : car
(C) building : skyscraper
(D) photograph : portrait
(E) cottage : house
- A four-sided figure has sides of lengths a, b, c, and d. Sides of lengths c and d meet at a right angle. Sides of lengths a and d meet at a 140-degree angle. Sides of lengths b and c meet at a 40-degree angle. Is (a x a) - (c x c) greater than, equal to, or less than (d x d) - (b x b)?
- What is the next letter in the sequence: s t n o j k g h
(A) g
(B) c
(C) d
(D) e
(E) f
- a does not equal b, and a + b is greater than 0. Is 2ab divided by (a + b) greater than, equal to, or less than (a + b) divided by 2?
| Answers: Click here to reveal extended quiz answers and explanations. |
- Write an equation where n is the number of nickels, d is the number of dimes, and q is the number of quarters:
5n + 10d + 25q = 100.
Start with the smallest numbers for n, d, and q that satisfy the equation. Starting with n = 0 and d = 0, then q =4, which cannot be true since the most q can be is 3. If we try n = 0 and d = 1, then we get 25q = 90, which doesn’t give us a whole number for q. You will find that you can satisfy the equation if n = 1, d = 2, and q = 3 and also if n = 3, d = 1, and q = 3. So there are two ways to make change.
- There are four states: Honolulu–Hawai‘i, Oklahoma City–Oklahoma, Indianapolis–Indiana, and Dover–Delaware.
- The $2 tip came from the $27 the customers paid, not from the $3 they got back.
- facetious
- Weigh six balls against the other six. Whichever group tips the scale has the heavier ball. From that group, weigh three against three. Whichever group tips the scale has the heavier ball. From that group, weigh one against one. If they balance, the heavy ball is the remaining one; if they don’t, the one that tips the scale is the heavy one.
- (E) cottage : house Put the analogy in a very specific sentence. Hamlet is a small village as cottage is a small house.
- equal to Draw the figure and notice that there are two right angles. With the use of the Pythagorean Theorem, we get (a x a) + (b x b) = (c x c) + (d x d).
Thus we find that (a x a) – (c x c) = (d x d) – (b x b).
- (D) e. The sequence is arranged in pairs: st no jk gh
Note that we have a pattern gh (i) jk (lm) no (pqr) st, where the letters in parens increase by one letter in the sequence. Thus the next two letters in the original sequence must be ef since the pattern will be preserved:
gh (no letters) gh (i) jk (lm) no (pqr) st
- less than Compare 2ab divided by (a + b) with (a + b) divided by 2 by manipulating the inequality or equality: Multiply both sides by 2 and then by (a + b). Then multiply out (a + b) x (a + b) and subtract the 4ab on the left side from both sides. You will get 0 as compared with (a – b) x (a – b). Since a is not equal to b (given), 0 is always less than (a – b) x (a – b).
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