Insert the missing number 4, -8, 16, -32, 64, (....)
Answer: B
Each term is the previous one multiplied by \( -2 \).
\[ 4 \times (-2) = -8,\quad -8 \times (-2) = 16,\quad 16 \times (-2) = -32 \]
\[ -32 \times (-2) = 64,\quad 64 \times (-2) = \mathbf{-128} \]
The signs alternate, and the sixth term must be negative - which by itself rules out the positive options.
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Find the one which does not belong to that group ?
Answer: B
Three of the four are multiples of 4.
\[ 104 = 4 \times 26, \quad 108 = 4 \times 27, \quad 112 = 4 \times 28 \]
\[ 110 = 4 \times 27 + 2 \]
So 110 does not belong. The test is the last two digits: 04, 08 and 12 divide by 4, while 10 does not.
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Find the odd man out. 396, 462, 572, 427, 671, 264
Answer: B
In each three-digit number, the middle digit is the sum of the outer two.
So 427 is the odd one out.
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Insert the missing number 1, 8, 27, 64, 125, 216, (....)
Answer: B
The series is the cubes of the natural numbers.
\[ 1^{3},\; 2^{3},\; 3^{3},\; 4^{3},\; 5^{3},\; 6^{3} = 1,\; 8,\; 27,\; 64,\; 125,\; 216 \]
\[ \text{next} = 7^{3} = \mathbf{343} \]
The distractor 392 is \( 216 + 176 \), continuing the differences by eye rather than recognising the cubes.
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Insert the missing number 10, 5, 13, 10, 16, 20, 19, (....)
Answer: B
Two series are interleaved.
\[ \text{positions 1, 3, 5, 7: } 10,\; 13,\; 16,\; 19 \quad (+3) \]
\[ \text{positions 2, 4, 6, 8: } 5,\; 10,\; 20,\; \mathbf{40} \quad (\times 2) \]
The missing eighth term belongs to the doubling series:
\[ 20 \times 2 = 40 \]
Reading the list as a single sequence gets nowhere; the alternation is the whole structure.
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Find the one which does not belong to that group ?
Answer: B
Three of the four are not divisible by 9.
\[ 630 = 9 \times 70 \quad (\text{digit sum } 6+3+0 = 9) \]
\[ 30 \to 3, \qquad 10 \to 1, \qquad 520 \to 7 \]
Only 630 has a digit sum divisible by 9, so 630 does not belong.
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Insert the missing number 11, 13, 17, 19, 23, 29, 31, 37, 41, (....)
Answer: A
The series lists the prime numbers from 11 upward.
\[ 11,\; 13,\; 17,\; 19,\; 23,\; 29,\; 31,\; 37,\; 41 \]
The next prime after 41 is 43.
42 is even and 51 is \( 3 \times 17 \), so 43 is the only candidate; 47 is the prime after that, not the next one.
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Find the one which does not belong to that group ?
Answer: C
Compare the digit sums.
\[ 508 \to 5+0+8 = 13, \qquad 328 \to 3+2+8 = 13, \qquad 148 \to 1+4+8 = 13 \]
\[ 608 \to 6+0+8 = 14 \]
So 608 does not belong - the only one whose digits do not add to 13.
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Find the one which does not belong to that group ?
Answer: A
All four are reptiles, so look at where they live.
Crocodiles, turtles and alligators are amphibious - at home in water as well as on land.
The chameleon is entirely terrestrial, an arboreal lizard that does not take to water.
So Chameleon does not belong.
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Find the one which does not belong to that group ?
Answer: C
All four are perfect cubes, so look at the roots.
\[ 8 = 2^{3}, \quad 27 = 3^{3}, \quad 64 = 4^{3}, \quad 125 = 5^{3} \]
The roots 2, 3 and 5 are prime; 4 is composite.
So 64 does not belong.
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