- A pattern starts: 2, 6, 3, 9, 4, 12, 5, 15, ... The pattern continues in the same way. Which number appears in the 16th position?
Answer: 24
The pattern alternates: odd positions follow +1 sequence (2,3,4,5,...), even positions are 3 times the previous term (6,9,12,15,...). Position 16 is even, so it's 3 times position 15. Position 15 = 8 (continuing the +1 pattern), so position 16 = 8×3 = 24. Choice A multiplies by 6 instead of 3. Choice B gives position 15 value. Choice D assumes position 16 continues the +1 pattern.
- Study the figure. What number should replace the question mark?
Answer: 33
Each increment doubles (1,2,4,8,16). Adding 16 to 17 gives 33. Other choices add 14,15, or 17.
- Look at this number pattern: 96, 48, 44, 22, 18, 9, ?, ?. What are the next two numbers?
Answer: 5, 4.5
The pattern alternates: divide by 2, then subtract 4. 96÷2=48, 48-4=44, 44÷2=22, 22-4=18, 18÷2=9, 9-4=5, 5÷2=4.5. So the next two are 5, 4.5. Choice A subtracts 4 twice. Choice B skips the subtract 4 step. Choice C applies subtract 4 then divide by 2 in wrong order.
- Refer to the diagram. What number should replace the question mark?
Answer: 4
Each number is half of the one before it: 64→32→16→8→4. So the missing term is 4. 2 and 6 are nearby halves or thirds; 8 repeats an earlier term.
- Look at the figure. Which number should fill the last square?
Answer: 25
The numbers are perfect squares: 12,22,32,42, so the next is 52=25. The other options are not perfect squares in order. - Study the diagram. Which number should replace the question mark?
Answer: 30
The pattern alternates: +2 then ×2. 4→6 (+2), 6→12 (×2), 12→14 (+2), 14→28 (×2), so next is 28→30 (+2). Other choices ignore this alternating rule.
- Based on the diagram, which number should fill the empty box?
Answer: 3
Each term is half the previous: 48→24→12→6→3. Only 3 fits. Other answers divide by 12, 16, or 10 instead of 2.
- Refer to the figure. Which number completes the sequence?
Answer: 37
Each term is n2+1: 12+1=2, 22+1=5, 32+1=10, 42+1=17, 52+1=26, so 62+1=37. Other choices come from adding 8,9, or 10 instead of 11. - A sequence alternates between two operations: ×2 and +5. Starting with 3, the sequence is 3, 6, 11, 22, 27, 54, ... If this pattern continues, what operation is applied to get the 10th term?
Answer: Add 5
The pattern alternates ×2, +5, ×2, +5, ... Position 1→2 uses ×2, position 2→3 uses +5, position 3→4 uses ×2, etc. To get the 10th term from the 9th term: positions with even numbers use +5 (2→3, 4→5, 6→7, 8→9, 9→10). So 9→10 uses +5. Choice B would be correct for odd-numbered transitions. Choices C and D aren't part of the alternating pattern.
- Based on the bar graph below, what height should the bar for Step 5 have?
Answer: 81
Each bar is triple the height of the previous one: 1, 3, 9, 27. Tripling 27 gives 81. Other choices come from adding or doubling instead of tripling.
- Study the graph below. What value should replace the question mark?
Answer: 63
Differences double: +2,+4,+8,+16,+32. The last recorded value 31 plus 32 equals 63. Other answers add incorrect differences.
- In a sequence, the first term is 5. Each term after the first follows this rule: if the position number is odd, add 8; if the position number is even, subtract 3. What is the 7th term?
Answer: 21
Starting with 5: Position 1 (odd): 5. Position 2 (even): 5-3=2. Position 3 (odd): 2+8=10. Position 4 (even): 10-3=7. Position 5 (odd): 7+8=15. Position 6 (even): 15-3=12. Position 7 (odd): 12+8=21. Choice A adds 8 incorrectly at position 6. Choice C subtracts 3 incorrectly at position 7. Choice D applies +8 twice at the end.
- In a growing pattern, the differences between consecutive terms are: 4, 12, 36, 108, ... If the first term is 10, what is the 5th term?
Answer: 170
The differences multiply by 3 each time: 4, 12, 36, 108. So the terms are: 10, 10+4=14, 14+12=26, 26+36=62, 62+108=170. The 5th term is 170. Choice B adds an extra difference. Choice C miscalculates 62+108. Choice D assumes differences add rather than following the ×3 pattern.
