Dosto, Reasoning ki shuruaat sabse aasan topic se — Number Series. Ismein numbers ki ek line di hoti hai jo kisi chhupe hue niyam (pattern) se bani hoti hai, aur aapko agla number, beech ka gayab number, ya galat number batana hota hai.
CET Group D mein Reasoning ke 15 questions aate hain aur unme se 2–3 series se hote hain. Ye pakke marks hain — pattern dikh gaya to 10 second mein answer.
Sabse achhi baat: yahan ratna kuch nahi hai. Bas ek aadat daalni hai — "pehle antar likho". Aur wahi is chapter ka pura raaz hai. Chalo! 💪
1. ⭐ Series solve karne ka 4-STEP METHOD
⭐ Har series par yahi order lagao
Step 1 — ANTAR: numbers ke neeche difference likho. Fix hai? Badh raha hai? Ghat raha hai?
Step 2 — GUNA/BHAAG: antar mein pattern na mile to check karo agla ÷ pichla (×2? ×3?).
Step 3 — SQUARE/CUBE: phir bhi na mile to squares (1,4,9,16,25,36…) aur cubes (1,8,27,64,125) ke aas-paas dekho.
Step 4 — ALTERNATE: ab bhi na mile to ek chhod ke numbers dekho — do series aapas mein mili hui ho sakti hain.
Step 2 — GUNA/BHAAG: antar mein pattern na mile to check karo agla ÷ pichla (×2? ×3?).
Step 3 — SQUARE/CUBE: phir bhi na mile to squares (1,4,9,16,25,36…) aur cubes (1,8,27,64,125) ke aas-paas dekho.
Step 4 — ALTERNATE: ab bhi na mile to ek chhod ke numbers dekho — do series aapas mein mili hui ho sakti hain.
2. Number Series ke 8 Types
| Type | Example | Niyam |
|---|---|---|
| Fix addition | 3, 7, 11, 15… | +4 har baar |
| Badhta antar | 5, 8, 12, 17… | +3, +4, +5 |
| Ghatta hua | 100, 92, 83, 73… | −8, −9, −10 |
| Multiplication | 2, 6, 18, 54… | ×3 har baar |
| Division | 120, 60, 20, 5… | ÷2, ÷3, ÷4 |
| Square / Cube | 1, 4, 9, 16… / 1, 8, 27… | n² / n³ |
| Mixed (×n ± k) | 3, 7, 15, 31… | ×2 + 1 |
| Alternate (mili hui) | 2, 9, 4, 11, 6, 13… | do alag series ek saath |
3. Solved Examples (har type ka ek)
✏️ Example 1 — 4, 8, 16, 32, ?
Step 1: Antar 4, 8, 16 — khud dugna ho raha hai → matlab guna wala rule hai
Step 2: 8÷4 = 2, 16÷8 = 2 → ×2 → 32 × 2 = 64 ✓
Step 2: 8÷4 = 2, 16÷8 = 2 → ×2 → 32 × 2 = 64 ✓
✏️ Example 2 — 100, 92, 83, 73, ?
Step 1: Antar −8, −9, −10 (har baar 1 zyada ghat raha hai)
Step 2: Agla −11 → 73 − 11 = 62 ✓
Step 2: Agla −11 → 73 − 11 = 62 ✓
✏️ Example 3 — 3, 7, 15, 31, ?
Step 1: Antar 4, 8, 16 — dugna. Sirf +/− se kaam nahi banega
Step 2: Rule check karo: 3×2+1 = 7 ✓, 7×2+1 = 15 ✓, 15×2+1 = 31 ✓
Step 3: 31 × 2 + 1 = 63 ✓
Step 2: Rule check karo: 3×2+1 = 7 ✓, 7×2+1 = 15 ✓, 15×2+1 = 31 ✓
Step 3: 31 × 2 + 1 = 63 ✓
✏️ Example 4 (alternate) — 2, 9, 4, 11, 6, 13, ?
Step 1: Seedha antar bekaar (+7, −5, +7, −5…) — ye ishara hai ki do series mili hui hain
Step 2: Ek chhod ke dekho: 2, 4, 6 (+2) aur 9, 11, 13 (+2)
Step 3: Ab pehli wali ki baari → 6 + 2 = 8 ✓
Step 2: Ek chhod ke dekho: 2, 4, 6 (+2) aur 9, 11, 13 (+2)
Step 3: Ab pehli wali ki baari → 6 + 2 = 8 ✓
4. Missing Number (beech ka gayab)
✏️ Example — 5, 10, ?, 20, 25
Step 1: Dono taraf se pattern check karo — pichhle se aage (+5) aur agle se peeche (−5)
Step 2: Dono taraf se 15 aata hai → answer 15 ✓
Rule: beech wala answer hamesha dono taraf se verify karo — tabhi pakka maano.
Step 2: Dono taraf se 15 aata hai → answer 15 ✓
Rule: beech wala answer hamesha dono taraf se verify karo — tabhi pakka maano.
5. Wrong Number (galat number dhundo)
✏️ Example — 4, 9, 16, 24, 36 mein galat kaunsa?
Step 1: Ye squares lag rahe hain: 2² = 4, 3² = 9, 4² = 16, ?, 6² = 36
Step 2: 5² = 25 hona chahiye tha, par likha hai 24 → galat number = 24 ✓
Rule: pehle poore pattern ka niyam pakdo, phir dekho kaunsa number us niyam ko tod raha hai.
Step 2: 5² = 25 hona chahiye tha, par likha hai 24 → galat number = 24 ✓
Rule: pehle poore pattern ka niyam pakdo, phir dekho kaunsa number us niyam ko tod raha hai.
6. Kaam ke Numbers (ratt lo — series pehchanne mein help karte hain)
| Squares | 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 |
|---|---|
| Cubes | 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000 |
| Primes | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 |
| ×2 wale | 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 |
✏️ Type 1 — "Agla number batao"
Sabse common. 4-step method lagao. Options bhi dekho — agar antar bada hai to answer bhi bada hoga; bahut chhota option turant cut kar do.
✏️ Type 2 — "Beech ka gayab number"
Dono taraf se check karna zaroori hai. 5, 10, ?, 20, 25 → 15 (aage se +5, peeche se −5 — dono match ✓).
✏️ Type 3 — "Galat number pehchano"
Pehle niyam pakdo (jaise squares), phir jo number niyam tod raha ho wahi answer. 4, 9, 16, 24, 36 → 24 galat (25 hona chahiye tha).
✏️ Type 4 — "Do series mili hui"
Antar mein +, − ki ulti-pulti chal dikhe (jaise +7, −5, +7) → turant ek chhod ke numbers alag karo. 2, 9, 4, 11, 6, 13 → (2,4,6) aur (9,11,13).
✏️ Type 5 — "Series ka niyam poocha jaye"
Kabhi-kabhi "is series ka niyam kya hai?" pucha jata hai. Jawab options mein hi hota hai — har option ko pehle do numbers par test karo, jo fit baithe wahi sahi.
Trick 1: Antar likhna aadat bana lo
Numbers ke neeche difference
Sawal dekhte hi pencil se antar likh do. 70% series wahin khatam. Ye ek aadat poore topic ka shortcut hai.
Numbers ke neeche difference
Sawal dekhte hi pencil se antar likh do. 70% series wahin khatam. Ye ek aadat poore topic ka shortcut hai.
Trick 2: Antar khud dugna = guna wala rule
Diffs 4, 8, 16 → ×2 ka rule
Jab antar bhi tezi se badhe (dugna/teen guna), to +/− chhod ke ×2, ×2+1, ×3−1 type rules check karo.
Diffs 4, 8, 16 → ×2 ka rule
Jab antar bhi tezi se badhe (dugna/teen guna), to +/− chhod ke ×2, ×2+1, ×3−1 type rules check karo.
Trick 3: Bada jump = square/cube dekho
24 ≈ 25−1 · 63 ≈ 64−1 · 26 ≈ 27−1
Number kisi square/cube ke ekdum paas ho to series shayad n²±1 ya n³±1 wali hai.
24 ≈ 25−1 · 63 ≈ 64−1 · 26 ≈ 27−1
Number kisi square/cube ke ekdum paas ho to series shayad n²±1 ya n³±1 wali hai.
Trick 4: Ulti-pulti chaal = alternate series
+7, −5, +7, −5 → do series
Antar mein plus-minus badalta rahe to seedha ek chhod ke numbers alag kar lo. Dono aasan nikal aayengi.
+7, −5, +7, −5 → do series
Antar mein plus-minus badalta rahe to seedha ek chhod ke numbers alag kar lo. Dono aasan nikal aayengi.
Trick 5: Options se ulta chalo
Answer options ko series mein rakh ke dekho
Pattern na pakad aaye to har option ko aakhir mein rakh ke antar check karo — jo antar ka pattern poora kare wahi sahi. 20 second mein kaam.
Answer options ko series mein rakh ke dekho
Pattern na pakad aaye to har option ko aakhir mein rakh ke antar check karo — jo antar ka pattern poora kare wahi sahi. 20 second mein kaam.
❌ Galti 1: Pehle do numbers dekh ke rule maan lena
3, 6 dekh ke "×2" maan liya — par series 3, 6, 9, 12 (+3) bhi ho sakti hai! Rule ko teen-chaar numbers par test karo, tabhi aage badho.
❌ Galti 2: Ghatti series mein sign ulta karna
100, 92, 83, 73 mein antar −8, −9, −10 hai (badh raha hai). Agla −11 hai, −7 nahi. Ghatti series mein dhyan dugna rakho.
❌ Galti 3: Alternate series ko ek hi series maan lena
2, 9, 4, 11 mein seedha antar bemtlab hai. Ulta-seedha antar dikhe to do series hain — ye pehchanne mein hi answer chhupa hai.
❌ Galti 4: Beech wale number ko ek taraf se check karna
Sirf pichhle se aage dekh ke answer mat do — agle se peeche bhi verify karo. Dono match karein tabhi sahi.
❌ Galti 5: Wrong-number wale sawal mein pehla number badalna
Zyadatar wrong-number sawalon mein pehla number sahi hota hai — usse hi niyam banta hai. Galti aksar beech mein hoti hai.
Series ka pehla step?tap 👆
Antar (difference) likho
4-step method ka order?tap 👆
Antar → ×/÷ → square/cube → alternate
Antar khud dugna ho raha hai → ?tap 👆
Guna wala rule (×2, ×2+1)
4, 8, 16, 32 → agla?tap 👆
64 (×2)
5, 8, 12, 17 → agla?tap 👆
23 (+3, +4, +5, +6)
3, 7, 15, 31 → agla?tap 👆
63 (×2 + 1)
100, 92, 83, 73 → agla?tap 👆
62 (−8, −9, −10, −11)
2, 9, 4, 11, 6, 13 → agla?tap 👆
8 (do series: 2,4,6 aur 9,11,13)
Squares 1 se 15 tak?tap 👆
1,4,9,16,25,36,49,64,81,100,121,144,169,196,225
Cubes 1 se 10 tak?tap 👆
1,8,27,64,125,216,343,512,729,1000
2 ki power series?tap 👆
2,4,8,16,32,64,128,256,512,1024
50 tak kitne prime?tap 👆
15 (2 se 47 tak)
Beech ka number kaise verify?tap 👆
Dono taraf se — aage aur peeche
Wrong number kaise dhundein?tap 👆
Pehle niyam pakdo, phir niyam todne wala pakdo
4, 9, 16, 24, 36 → galat kaun?tap 👆
24 (25 hona chahiye tha)
120, 60, 20, 5 → agla?tap 👆
1 (÷2, ÷3, ÷4, ÷5)
Antar mein +, − badalta rahe → ?tap 👆
Alternate (do mili hui series)
Pattern na mile to aakhri hathiyar?tap 👆
Options ko series mein rakh ke test karo
| Ishara (clue) | Matlab |
|---|---|
| Antar fix hai | Simple +/− series |
| Antar barabar badh raha | +3, +4, +5 type |
| Antar khud dugna | ×2 ya ×2±k ka rule |
| Numbers tezi se bade | ×3, ×4 ya square/cube |
| Number square ke paas | n² ± 1 |
| Antar mein +/− badalta | Alternate — 2 series |
| Beech ka gayab | Dono taraf se verify |
| Galat number | Niyam pakdo → todne wala dhundo |
| Kuch samajh na aaye | Options ko test karo |
| Squares yaad | 1…225 (15 tak) |
| Cubes yaad | 1…1000 (10 tak) |
| Primes yaad | 2…47 (15 primes) |
Practice (exam-style)
Q1. Find the next number: 4, 8, 16, 32, ?
💡 Har baar ×2 → 32 × 2 = 64.
Practice (exam-style)
Q2. Find the next number: 5, 8, 12, 17, ?
💡 Antar +3, +4, +5 → agla +6 → 17 + 6 = 23.
Practice (exam-style)
Q3. Find the next number: 1, 4, 9, 16, 25, ?
💡 Squares: 1², 2², 3², 4², 5² → agla 6² = 36.
Practice (exam-style)
Q4. Find the next number: 2, 6, 18, 54, ?
💡 Har baar ×3 → 54 × 3 = 162.
Practice (exam-style)
Q5. Find the next number: 100, 92, 83, 73, ?
💡 Antar −8, −9, −10 → agla −11 → 73 − 11 = 62.
Practice (exam-style)
Q6. Find the next number: 3, 7, 15, 31, ?
💡 Rule ×2 + 1 → 31 × 2 + 1 = 63.
Practice (exam-style)
Q7. Find the next number: 2, 3, 5, 7, 11, 13, ?
💡 Prime numbers ki series → 13 ke baad agla prime 17.
Practice (exam-style)
Q8. Find the next number: 1, 8, 27, 64, ?
💡 Cubes: 1³, 2³, 3³, 4³ → agla 5³ = 125.
Practice (exam-style)
Q9. Find the next number: 7, 11, 19, 35, ?
💡 Antar +4, +8, +16 (dugna) → agla +32 → 35 + 32 = 67.
Practice (exam-style)
Q10. Find the missing number: 5, 10, ?, 20, 25
💡 +5 ki series — aage se 10+5 = 15, peeche se 20−5 = 15 (dono match ✓).
Practice (exam-style)
Q11. Find the WRONG number in the series: 4, 9, 16, 24, 36
💡 Squares ki series (2²,3²,4²,5²,6²) → 24 ki jagah 25 hona chahiye tha.
Practice (exam-style)
Q12. Find the next number: 120, 60, 20, 5, ?
💡 ÷2, ÷3, ÷4 → agla ÷5 → 5 ÷ 5 = 1.
Practice (exam-style)
Q13. Find the next number: 6, 12, 21, 33, ?
💡 Antar +6, +9, +12 → agla +15 → 33 + 15 = 48.
Practice (exam-style)
Q14. Find the next number: 2, 9, 4, 11, 6, 13, ?
💡 Do mili hui series: (2, 4, 6…) aur (9, 11, 13…) → ab pehli ki baari → 6 + 2 = 8.
Number series ka poora khel 4-STEP METHOD par hai: pehle antar likho → na mile to ×/÷ check karo → phir square/cube ke aas-paas dekho → aakhir mein alternate (ek chhod ke) numbers. Antar khud dugna ho raha ho to samajh jao rule ×2 ± k hai. Beech ka gayab number hamesha dono taraf se verify karo, aur wrong-number wale sawal mein pehle niyam pakdo phir niyam todne wala. Squares (1–225), cubes (1–1000) aur primes (2–47) ratt lo — inhe pehchanne se aadha kaam ho jata hai. Aur agar kuch na sujhe to options ko hi series mein rakh ke test kar lo! 🚀