Insert the missing number 8, 24, 12, 36, 18, 54, (....)
Answer: A
The operations alternate between multiplying by 3 and halving.
\[ 8 \times 3 = 24,\quad 24 \div 2 = 12,\quad 12 \times 3 = 36,\quad 36 \div 2 = 18,\quad 18 \times 3 = 54 \]
\[ 54 \div 2 = \mathbf{27} \]
Continuing with a multiplication instead would give 162; the alternation is what makes the next step a division.
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Find the one which does not belong to that group ?
Answer: D
All four are animals, so the grouping must be finer than that.
Cats, dogs and tigers are carnivores - flesh-eaters with the teeth and gut to match.
The elephant is a herbivore, living on grasses, leaves and bark.
So ELEPHANT does not belong. Word length is a red herring: CAT and DOG have three letters, TIGER five, so size of word is not the shared property.
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Find the one which does not belong to that group ?
Answer: A
Three of the four are multiples of 3.
\[ 48 = 3 \times 16, \quad 75 = 3 \times 25, \quad 84 = 3 \times 28 \]
\[ 35 = 5 \times 7 \]
So 35 does not belong. Its digit sum is 8, which is not divisible by 3, while the others give 12, 12 and 12.
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Find the one which does not belong to that group ?
Answer: D
Each number is a digit written next to its own cube:
The fourth would have to be 464. The 16 attached to it is \( 4^{2} \), the square rather than the cube, which is precisely the trap.
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Find the odd man out. 6, 9, 15, 21, 24, 28, 30
Answer: A
Every number here is a multiple of 3 except one.
\[ 6,\; 9,\; 15,\; 21,\; 24,\; 30 \;\text{are all divisible by 3} \]
\[ 28 = 3 \times 9 + 1 \]
So 28 is the odd man out. Its digit sum is 10, which is not divisible by 3 - the quickest test.
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Find the one which does not belong to that group ?
Answer: B
Compare the steps between letters, allowing the alphabet to wrap round:
UAWY runs the same three steps in the opposite order, so it is the odd one out. To match the others it would have to be UWSY.
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Find out the wrong number in the series 6, 12, 48, 100, 384, 768, 3072
Answer: C
Each even term of the series is obtained by multiplying the previous term by 2.
2nd term = (1st term) x 2 = 6 x 2 = 12
4th term = (3rd term) x 2 = 48 x 2 = 96.
6th term = (5th term) x 2 = 384 x 2 =768.
4th term should be 96 instead of 100.
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Find the one which does not belong to that group ?
Answer: D
Three of the four numbers are prime.
\[ 41,\; 43,\; 53 \;\text{are prime} \]
\[ 57 = 3 \times 19 \]
So 57 does not belong. Its digit sum is 12, a multiple of 3 - 57 is a classic "looks prime but isn't" number.
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Find out the wrong number in the series 40960, 10240, 2560, 640, 200, 40, 10
Answer: C
Each term is the previous one divided by 4.
\[ 40960 \to 10240 \to 2560 \to 640 \to 160 \to 40 \to 10 \]
The fifth term should be \( 640 \div 4 = 160 \), not 200.
So 200 is the wrong number - and \( 200 \div 4 = 50 \), which would not give the 40 that follows.
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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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