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Odd One Out
Spot the outsider using the stated rule. The obvious answer is not always the right one.
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Tough question
Three integers have exactly three positive divisors. Which is the odd one out?
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- 1. Three integers have exactly three positive divisors. Which is the odd one out?
- A. 49
- B. 121
- C. 143 (answer)
- D. 169
49, 121 and 169 are prime squares with three divisors. 143 = 11 × 13 has four: 1, 11, 13 and 143. - 2. Three fractions have terminating decimal expansions. Which is the odd one out?
- A. 7/40
- B. 11/24 (answer)
- C. 13/80
- D. 17/125
A reduced fraction terminates in base ten only if its denominator has no prime factors except 2 and 5. 24 contains 3. - 3. Three words contain a, e, i, o and u exactly once each. Which is the odd one out?
- A. Educational (answer)
- B. Sequoia
- C. Facetious
- D. Abstemious
Educational contains a twice. The other three words contain each of the five standard vowel letters exactly once. - 4. Three words become a different common English word when reversed. Which is the odd one out?
- A. Drawer
- B. Stressed
- C. Window (answer)
- D. Reward
Drawer reverses to reward, stressed to desserts and reward to drawer. Window reverses to wodniw. - 5. Three are triangular numbers, formed by adding 1 + 2 + ... + n. Which is the odd one out?
- A. 36
- B. 45
- C. 55
- D. 65 (answer)
36, 45 and 55 are sums through 8, 9 and 10. The next triangular number is 66, not 65. - 6. Three lengths can be a right triangle's hypotenuse with positive whole-number legs. Which is the odd one out?
- A. 13
- B. 19 (answer)
- C. 25
- D. 17
5-12-13, 7-24-25 and 8-15-17 are Pythagorean triples. No two positive integer squares sum to 19 squared. - 7. Three words have letters in alphabetical order, allowing repeats. Which is the odd one out?
- A. Almost
- B. Chintz
- C. Effort
- D. Being (answer)
Almost, chintz and effort have non-decreasing alphabetical order. Being ends in g after n, breaking the order. - 8. Three integers leave remainder 1 when divided by 8. Which is the odd one out?
- A. 121
- B. 145
- C. 171 (answer)
- D. 193
121, 145 and 193 are one more than a multiple of 8. 171 = 8 × 21 + 3. - 9. Three words alternate consonant and vowel letters throughout. Only a, e, i, o and u count as vowels. Which is the odd one out?
- A. Banana
- B. Potato
- C. Tomato
- D. Carrot (answer)
Banana, potato and tomato alternate consonants and vowels. Carrot contains adjacent consonants. - 10. Three integers equal the sum of the cubes of their decimal digits. Which is the odd one out?
- A. 153
- B. 370
- C. 371
- D. 372 (answer)
153 = 1 + 125 + 27, 370 = 27 + 343, and 371 = 27 + 343 + 1. The digit cubes of 372 sum to 378. - 11. Three words contain exactly three e letters. Which is the odd one out?
- A. Bookkeeper
- B. Committee (answer)
- C. Employee
- D. Beehive
Bookkeeper, employee and beehive each contain three e letters. Committee contains two. - 12. Three numbers are perfect squares. Which is the odd one out?
- A. 10201
- B. 10404
- C. 10609
- D. 10818 (answer)
101 squared is 10201, 102 squared is 10404 and 103 squared is 10609. 104 squared is 10816, not 10818.
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