2
Identify the number that does not follow the established pattern in the sequence: 10, 14, 16, 18, 21, 24, 26.
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Solution: Step 1: Examine the given sequence of numbers: 10, 14, 16, 18, 21, 24, 26.
Step 2: Observe the properties of each number (e.g., even or odd).
- 10 is an even number.
- 14 is an even number.
- 16 is an even number.
- 18 is an even number.
- 21 is an odd number.
- 24 is an even number.
- 26 is an even number.
Step 3: Identify the number that deviates from the common pattern.
All numbers in the sequence are even, except for 21. Therefore, 21 is the odd one out.
17
Count the total number of triangles present in the provided geometric figure.
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Solution: Step 1: Identify and count the simplest triangles (one component): AFJ, FJK, FKB, BKG, JKG, JGC, HJC, HIJ, DIH, DEI, EIJ, AEJ. (12 triangles)
Step 2: Identify and count triangles composed of two components: JFB, FBG, BJG, JFG, DEJ, EJH, DJH, DEH. (8 triangles)
Step 3: Identify and count triangles composed of three components: AJB, JBC, DJC, ADJ. (4 triangles)
Step 4: Identify and count triangles composed of six components: DAB, ABC, BCD, ADC. (4 triangles)
Step 5: Sum all identified triangles: 12 + 8 + 4 + 4 = 28.
Step 6: Therefore, there are 28 triangles in the given figure.
18
Identify the missing term in the sequence: 15, ?, 39, 71, 135, 263
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Solution: Step 1: Analyze the given series: 15, ?, 39, 71, 135, 263
Step 2: Calculate differences between consecutive terms:
- ? - 15
- 39 - ?
- 71 - 39 = 32
- 135 - 71 = 64
- 263 - 135 = 128
Step 3: Observe the pattern in differences: 8, 16, 32, 64, 128 (doubling each time)
Step 4: Apply the pattern to find the missing difference:
- First difference should be 8: ? - 15 = 8
Step 5: Solve for the missing number: ? = 15 + 8 = 23
Step 6: Verify the sequence with the found number:
15, 23, 39, 71, 135, 263
Step 7: Confirm the differences: 8, 16, 32, 64, 128
19
Count the total number of parallelograms in the provided figure.
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Solution: Step 1: Label the figure for systematic counting.
Step 2: Count parallelograms composed of two components: ADME, DFNM, EMOG, FHJN, MNKO, GOLI, HBJN, NJKO, OKLI, FHNM, MNOG, DFME, HJKN, NKLO, OLCI, FNOM, MOIG, DMGE (Total: 18).
Step 3: Count parallelograms composed of four components: HOKB, NILJ, FGOH, HOLJ, NICK, FGIN, FMJB, DENH, MGKJ, MGCL, DEIO, FMLK, AENF, AGOD, DMJH, DOKF, EILM, EGKN (Total: 18).
Step 4: Count parallelograms composed of six components: AEJH, DAIL, DECL, DEJB, HILB, HICJ (Total: 6).
Step 5: Count parallelograms composed of eight components: FGKB, FGCK, AGKF (Total: 3).
Step 6: Sum all counted parallelograms: 18 + 18 + 6 + 3 = 45.