CSE
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Practice Exams

Number Series Reviewer (Professional)

Reviewer's Note: If you can't see the pattern immediately, calculate the "Difference of the Differences." Often, the first layer of subtraction reveals a second layer with a constant pattern.

Number series questions involve finding the next number in a sequence based on a logical pattern. Identifying the pattern is the key to solving these problems.

Sa madaling salita: Hanapin ang logic o pattern sa likod ng mga numero para makuha ang kasunod.

Common Patterns in Number Series

  1. Arithmetic Sequence (Addition/Subtraction): The difference between consecutive numbers is constant.

    • Example: 2, 5, 8, 11, ... (Pattern: +3)
    • Example: 20, 15, 10, 5, ... (Pattern: -5)
    • Hack: Laging pareho ang dinadagdag o binabawas.

  2. Geometric Sequence (Multiplication/Division): The ratio between consecutive numbers is constant.

    • Example: 3, 6, 12, 24, ... (Pattern: ×2)
    • Example: 100, 50, 25, 12.5, ... (Pattern: ÷2)
    • Hack: Laging pareho ang minumultiply o dinidivide.

  3. Squares and Cubes: Numbers follow the sequence of perfect squares or cubes.

    • Squares: 1, 4, 9, 16, 25, ... (12,22,32,42,521^2, 2^2, 3^2, 4^2, 5^2)
    • Cubes: 1, 8, 27, 64, 125, ... (13,23,33,43,531^3, 2^3, 3^3, 4^3, 5^3)
    • Hack: Ito ay mga "perfect squares" o "perfect cubes". Kabisaduhin ang mga ito.

  4. Alternating Series: Two or more sequences are combined in an alternating fashion.

    • Example: 1, 10, 2, 20, 3, 30, ... (Pattern: One series is 1, 2, 3... and the other is 10, 20, 30...)
    • Hack: May dalawang pattern na nagpapalitan. Tingnan ang bawat pangalawang numero.

  5. Changing Differences (Tiered Patterns): The difference between numbers is not constant, but the difference of the differences is.

    • Example: 1, 3, 7, 13, 21, ...
      • Differences: 2, 4, 6, 8 (The difference increases by 2 each time)
    • Hack: Ang "difference" mismo ang may pattern na nadadagdagan.

  6. Fibonacci-like Sequence: The next number is the sum of the previous two numbers.

    • Example: 1, 1, 2, 3, 5, 8, 13, ...
    • Hack: I-add ang huling dalawang numero para makuha ang kasunod.

Strategy for Solving

  1. Find the differences: Subtract numbers to see if there's a pattern. (I-subtract ang magkatabing numero.)
  2. Check for multiplication/division: (Tingnan kung may multiplication logic.)
  3. Look for Alternating patterns: (Tingnan kung tumatalon ang pattern.)
  4. Look for common sets: (Tingnan kung squares o cubes.)

Practice Questions

  1. What is the next number: 4, 9, 14, 19, 24, ?

    • A. 28
    • B. 29
    • C. 30
    • D. 31
    • Answer: B (29).
    • Hack: Ang pattern ay constant addition of 5. (24+5=2924 + 5 = 29).

  2. What is the next number: 2, 6, 18, 54, ?

    • A. 108
    • B. 150
    • C. 162
    • D. 216
    • Answer: C (162).
    • Hack: Ang pattern ay multiplication by 3. (54×3=16254 \times 3 = 162).

  3. Find the next number: 1, 4, 9, 16, 25, ?

    • A. 30
    • B. 35
    • C. 36
    • D. 49
    • Answer: C (36).
    • Hack: Ito ay perfect squares. Ang kasunod ng 525^2 (25) ay 626^2 (36).

  4. Find the next number: 10, 5, 12, 10, 14, 15, ?

    • A. 16
    • B. 18
    • C. 20
    • D. 25
    • Answer: A (16).
    • Hack: Alternating series ito. Isang series ay 10, 12, 14 (+2). Ang isa ay 5, 10, 15 (+5). Ang hinahanap ay kasunod ng 14, kaya 14+2=1614 + 2 = 16.

  5. What is the next number: 1, 3, 6, 10, 15, ?

    • A. 20
    • B. 21
    • C. 25
    • D. 26
    • Answer: B (21).
    • Hack: Ang mga difference ay 2, 3, 4, 5. So ang susunod na idadagdag ay 6. 15+6=2115 + 6 = 21.

  6. Find the next number: 100, 90, 81, 73, ?

    • A. 65
    • B. 66
    • C. 67
    • D. 68
    • Answer: B (66).
    • Hack: Ang binabawas ay 10, tapos 9, tapos 8. Ang susunod na ibabawas ay 7. 73−7=6673 - 7 = 66.

  7. What comes next: 2, 3, 5, 8, 13, ?

    • A. 18
    • B. 20
    • C. 21
    • D. 25
    • Answer: C (21).
    • Hack: Fibonacci sequence. 5+8=135+8 = 13, tapos 8+13=218+13 = 21.

  8. Find the next number: 1, 2, 4, 8, 16, ?

    • A. 24
    • B. 30
    • C. 32
    • D. 64
    • Answer: C (32).
    • Hack: Multiplication by 2. 16×2=3216 \times 2 = 32.

  9. Find the missing number: 5, 11, 23, 47, ?

    • A. 94
    • B. 95
    • C. 96
    • D. 100
    • Answer: B (95).
    • Hack: (Previous×2)+1(Previous \times 2) + 1. So (47×2)+1=94+1=95(47 \times 2) + 1 = 94 + 1 = 95.

  10. What is the next number: 80, 40, 20, 10, ?

    • A. 0
    • B. 2
    • C. 5
    • D. 8
    • Answer: C (5).
    • Hack: Division by 2. 10/2=510 / 2 = 5.

Tip: If you're stuck, write down the differences between the numbers on your scratch paper to see the pattern more clearly.