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Age-Based Data Sufficiency

Introduction

Age-based Data Sufficiency problems यह test करते हैं कि दिए गए information से किसी व्यक्ति या group की age(s) uniquely पता लगाई जा सकती है या नहीं। ऐसे questions आमतौर पर present, past या future ages के relations पर आधारित होते हैं। लक्ष्य exact age निकालना नहीं, बल्कि यह तय करना है कि statements उसको uniquely determine करने के लिए sufficient हैं या नहीं।

यह pattern इसलिए महत्वपूर्ण है क्योंकि इसमें arithmetic reasoning और logical analysis - दोनों skills की जरूरत होती है, जो aptitude और reasoning exams के लिए key हैं।

Pattern: Age-Based Data Sufficiency

Pattern

मुख्य विचार - Verbal relations (“older than”, “after 5 years”, “twice as old”, आदि) को equations में translate करें और check करें कि कौन-से statement(s) required age को uniquely determine कर पाते हैं।

सामान्यत: stems पूछते हैं जैसे “X की present age क्या है?” या “A और B की ages का ratio क्या है?” हर statement age relations का कुछ हिस्सा देता है - आपको judge करना होता है कि अकेला या दोनों मिलकर sufficient हैं या नहीं।

Step-by-Step Example

Question

Riya की present age क्या है?
(I) Riya अपने brother से 5 साल छोटी है।
(II) उसके brother की age 5 साल बाद 25 होगी।

Solution

  1. Step 1: From (I)

    Riya = Brother - 5. Brother की present age नहीं पता, इसलिए (I) अकेला insufficient है।

  2. Step 2: From (II)

    Brother की age 5 साल बाद 25 ⇒ present age = 25 - 5 = 20. लेकिन Riya से उसका relation नहीं दिया → (II) अकेला insufficient।

  3. Step 3: Combine (I) & (II)

    (II) से Brother = 20. (I) से Riya = 20 - 5 = 15. दोनों statements मिलकर Riya की age uniquely मिल जाती है।

  4. Final Answer:

    Both statements together are necessary

  5. Quick Check:

    Combine → Brother = 20 → Riya = 15 ✅

Quick Variations

1. दो-person relations (जैसे father-son, husband-wife, friends)।

2. “years ago” या “years hence” वाले multi-step differences।

3. Ratio-based age questions जहाँ present ages multiples या fractions में दिए हों।

4. Total या combined ages वाले questions।

Trick to Always Use

  • Step 1 → हर statement को variables में equation की तरह लिखें (जैसे A = B + 5)।
  • Step 2 → Check करें कि क्या एक equation alone target variable uniquely दे सकती है।
  • Step 3 → अगर नहीं, देखें कि क्या दोनों equations मिलकर solvable pair बनाती हैं।

Summary

Summary

  • हर age relation को algebraic equation में convert करें।
  • Statement sufficiency ≠ actual solution - सिर्फ यह check करना है कि solution uniquely मिल सकता है या नहीं।
  • Single relation आमतौर पर insufficient; दो independent relations अधिकतर sufficient होते हैं।
  • “years ago” और “years hence” को हमेशा ध्यान से adjust करें।

याद रखने वाला Example:
(I) Riya = Brother - 5; (II) Brother after 5 years = 25 ⇒ दोनों मिलकर Riya = 15 देते हैं।

Practice

(1/5)
1. What is Amit’s present age?<br>(I) Amit is 5 years younger than his mother.<br>(II) Amit’s mother was 38 years old 8 years ago.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Amit = Mother - 5. Mother’s current age not given → (I) insufficient.

  2. Step 2: Analyze (II)

    Mother’s age 8 years ago = 38 ⇒ Mother’s present age = 38 + 8 = 46. (II) alone does not give Amit’s age because relation is required → (II) insufficient.

  3. Step 3: Combine

    From (II): Mother = 46. From (I): Amit = 46 - 5 = 41. Both statements together determine Amit’s age uniquely.

  4. Final Answer:

    Both statements together are necessary → Option D

  5. Quick Check:

    Mother = 46 → Amit = 41 ✅
Hint: Use 'years ago' to find present age, then apply difference relation.
Common Mistakes: Assuming one relational statement without a numeric value can yield exact age.
2. What is Sita’s present age?<br>(I) Sita is twice as old as her brother.<br>(II) Sita is 28 years old.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Sita = 2 × Brother. Brother’s age unknown → (I) insufficient to find Sita’s numeric age.

  2. Step 2: Analyze (II)

    Sita = 28 gives her present age directly → (II) alone is sufficient.

  3. Final Answer:

    Only (II) is sufficient → Option B

  4. Quick Check:

    (II) provides Sita’s age = 28 ✅
Hint: A direct numeric statement about the asked age is sufficient by itself.
Common Mistakes: Overcomplicating when a direct value is provided.
3. Find Ravi’s present age.<br>(I) Ravi was 10 years old 5 years ago.<br>(II) Ravi is twice his sister’s age.
easy
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Both statements together are necessary
D. Each statement alone is sufficient

Solution

  1. Step 1: Analyze (I)

    Five years ago Ravi = 10 ⇒ Present age = 10 + 5 = 15. (I) alone sufficient.

  2. Step 2: Analyze (II)

    Ravi = 2 × Sister → Sister’s age unknown → (II) insufficient alone.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    (I) → Ravi = 15 ✅
Hint: Convert 'years ago' to present by adding the years back.
Common Mistakes: Misreading time reference (e.g., using 'years hence' instead of 'years ago').
4. What is Anu’s present age?<br>(I) Anu is 30 years old.<br>(II) Anu is 15 years older than her brother, and her brother is 15 years old.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Anu = 30 is given directly → (I) sufficient.

  2. Step 2: Analyze (II)

    Brother = 15 and Anu = Brother + 15 ⇒ Anu = 15 + 15 = 30 → (II) also sufficient.

  3. Final Answer:

    Each statement alone is sufficient → Option C

  4. Quick Check:

    (I) → 30; (II) → 15 + 15 = 30 ✅
Hint: If either statement independently yields the same numeric age, choose 'each alone sufficient'.
Common Mistakes: Assuming both are needed when each already gives the age.
5. What is Vikram’s present age?<br>(I) Vikram is 40 years old.<br>(II) Vikram is 10 years older than his wife.
medium
A. Only (I) is sufficient
B. Only (II) is sufficient
C. Each statement alone is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: Analyze (I)

    Vikram = 40 given directly → (I) sufficient.

  2. Step 2: Analyze (II)

    Vikram = Wife + 10 → Wife’s age unknown → (II) insufficient alone.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    (I) → Vikram = 40 ✅
Hint: A direct numeric statement about the target age is sufficient.
Common Mistakes: Trying to use a comparative relation alone when no base value is provided.

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