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Basic Quantitative Data Sufficiency

Introduction

Basic Quantitative Data Sufficiency problems यह test करते हैं कि दिए गए statements किसी numerical question का उत्तर देने के लिए पर्याप्त जानकारी देते हैं या नहीं - न कि वास्तव में answer निकालना है।

यह pattern महत्वपूर्ण है क्योंकि यह logical clarity विकसित करता है और यह तय करने में मदद करता है कि दिया हुआ data किसी problem को solve करने के लिए sufficient है या insufficient।

Pattern: Basic Quantitative Data Sufficiency

Pattern

मुख्य विचार - आपसे value निकालने को नहीं कहा जाता, बल्कि यह check करने को कहा जाता है कि क्या statements से value निकाली जा सकती है।

Typical question format: एक numerical question के बाद दो statements (I) और (II) दिए होते हैं। आपको तय करना होता है कि कौन-सा statement (या दोनों) question का उत्तर देने के लिए पर्याप्त data देता है।

Step-by-Step Example

Question

X का value क्या है?
(I) X + 5 = 10
(II) 2X = 10

Solution

  1. Step 1: Statement (I) analyze करें

    (I) से: X + 5 = 10 ⇒ X = 5. इसलिए, (I) अकेले X का unique value देता है।

  2. Step 2: Statement (II) analyze करें

    (II) से: 2X = 10 ⇒ X = 5. इसलिए, (II) अकेले भी X का unique value देता है।

  3. Step 3: Sufficiency compare करें

    दोनों statements independently पर्याप्त data देते हैं। इसलिए, कोई भी statement अकेला sufficient है।

  4. Final Answer:

    Each statement alone is sufficient.

  5. Quick Check:

    दोनों statements से X = 5 आता है → consistent value ✅

Quick Variations

1. कभी-कभी दोनों statements चाहिए होते हैं जब एक सिर्फ relation देता है पर value नहीं।

2. कभी-कभी कोई भी statement पर्याप्त data नहीं देता।

3. हमेशा uniqueness check करें - सिर्फ equation होना पर्याप्त नहीं।

Trick to Always Use

  • Step 1: हर statement को अलग-अलग sufficiency के लिए check करें।
  • Step 2: अगर कोई भी statement अकेला sufficient न हो, तो दोनों को combine करें।
  • Step 3: Value निकालने की कोशिश न करें - सिर्फ यह judge करें कि निकाल सकते हैं या नहीं।

Summary

Summary

  • Focus इस पर करें कि data sufficient है या नहीं, value पर नहीं।
  • हर statement को पहले independently check करें।
  • Unique result guaranteed हो तभी sufficient मानें।
  • Ambiguous या अपूर्ण numerical information से सावधान रहें।

याद रखने वाला Example:
If (I) says X + 5 = 10 और (II) says 2X = 10 → दोनों individually X = 5 देते हैं, इसलिए दोनों sufficient हैं।

Practice

(1/5)
1. What is the value of X?<br>(I) X + 6 = 14<br>(II) X^2 = 64
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)

    From (I): X + 6 = 14 ⇒ X = 8 (unique value).

  2. Step 2: Analyze (II)

    From (II): X^2 = 64 ⇒ X = ±8 (two possible values) → ambiguous.

  3. Step 3: Compare

    Only (I) yields a unique value, (II) alone is ambiguous. Therefore only (I) is sufficient.

  4. Final Answer:

    Only (I) is sufficient → Option A

  5. Quick Check:

    (I) → X=8; (II) allows ±8 so insufficient alone ✅
Hint: If a squared relation gives ± values, check linear equations for uniqueness.
Common Mistakes: Calling X^2 = value sufficient without sign info.
2. What is the value of Y?<br>(I) Y + Z = 10<br>(II) Z = 2
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)

    (I) gives Y + Z = 10 → relation with two variables; alone not sufficient.

  2. Step 2: Analyze (II)

    (II) gives Z = 2 → alone does not determine Y.

  3. Step 3: Combine

    Substitute Z = 2 into (I): Y + 2 = 10 ⇒ Y = 8. Both together are necessary.

  4. Final Answer:

    Both statements together are necessary → Option D

  5. Quick Check:

    Relation + numeric value ⇒ unique Y = 8 ✅
Hint: A relation with two unknowns needs a numeric value for one to solve the other.
Common Mistakes: Treating a single relation with two unknowns as sufficient.
3. Find the value of Z.<br>(I) 5Z - 10 = 0<br>(II) Z^2 = 4
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)

    5Z - 10 = 0 ⇒ 5Z = 10 ⇒ Z = 2 (unique value).

  2. Step 2: Analyze (II)

    Z^2 = 4 ⇒ Z = ±2, ambiguous (two possible values).

  3. Step 3: Compare

    Only (I) yields a unique value; (II) is ambiguous alone. Therefore only (I) is sufficient.

  4. Final Answer:

    Only (I) is sufficient → Option A

  5. Quick Check:

    (I) → Z = 2 uniquely; (II) allows ±2 so insufficient by itself ✅
Hint: Linear eqns with one variable remove ± ambiguity from squared forms.
Common Mistakes: Calling Z^2 = value sufficient without sign resolution.
4. Find the value of M.<br>(I) M + 2 = 7<br>(II) 2M = 10
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)

    From (I): M + 2 = 7 ⇒ M = 5 (unique).

  2. Step 2: Analyze (II)

    From (II): 2M = 10 ⇒ M = 5 (unique).

  3. Step 3: Compare

    Each statement independently gives the same unique value M = 5; therefore each alone is sufficient.

  4. Final Answer:

    Each statement alone is sufficient → Option C

  5. Quick Check:

    (I) → M=5; (II) → M=5 so each suffices ✅
Hint: If two different forms both give the same single value, mark 'Each statement alone is sufficient'.
Common Mistakes: Assuming both must be combined even when each gives the same unique result.
5. What is the value of P?<br>(I) 2P + 3Q = 14<br>(II) P = -0.5
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)

    2P + 3Q = 14 is a relation with two variables → cannot determine P alone.

  2. Step 2: Analyze (II)

    P = -0.5 ⇒ directly provides P (unique value) without need for (I).

  3. Step 3: Compare

    Only (II) yields the unique P; (I) alone is insufficient. Therefore only (II) is sufficient.

  4. Final Answer:

    Only (II) is sufficient → Option B

  5. Quick Check:

    (II) → P = -0.5 uniquely; (I) needs Q so insufficient ✅
Hint: An explicit assignment for the target variable makes the other relation unnecessary.
Common Mistakes: Treating relations as sufficient when the target variable is not isolated.

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