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Comparison Type (Greater / Smaller)

Introduction

इस pattern में दो quantities को compare किया जाता है ताकि यह तय किया जा सके कि कौन-सा greater, smaller या equal है। यहाँ exact values निकालने को नहीं कहा जाता - सिर्फ यह तय करना होता है कि दिए गए data से यह comparison sufficiently establish होता है या नहीं।

Pattern: Comparison Type (Greater / Smaller)

Pattern

मुख्य concept - यह तय करना कि दिए गए statements conclusively दिखा सकते हैं कि A > B, A < B या A = B।

हर statement equations, ratios या relations दे सकता है। आपको check करना है कि क्या ये A और B के बीच clear comparison establish करने के लिए पर्याप्त हैं।

Step-by-Step Example

Question

कौन greater है - A या B?
(I) A = B + 3
(II) A² = B² + 9

Solution

  1. Step 1: Statement (I) analyze करें

    (I): A = B + 3 ⇒ A - B = 3 → एक positive constant।
    इसलिए A हमेशा B से बड़ा होगा, चाहे B का sign कुछ भी हो।
    ✅ (I) अकेला sufficient है।

  2. Step 2: Statement (II) analyze करें

    (II): A² = B² + 9 ⇒ A² - B² = 9 ⇒ (A - B)(A + B) = 9.
    यहाँ result A और B के specific values पर depend करता है (A - B = 9 भी हो सकता है, 3 भी, यहाँ तक कि -9 भी)।
    इसलिए (II) अकेला ambiguous है। ❌ Insufficient.

  3. Step 3: Combine

    (I) पहले से definite answer देता है; (II) combined होने पर भी नया या helpful data नहीं देता।

  4. Final Answer:

    Only (I) is sufficient

  5. Quick Check:

    (I) → A - B = 3 → A हमेशा बड़ा है ✅
    (II) → multiple possibilities ❌

Quick Variations

1. Differences से comparison (A - B = constant)।

2. Ratios से comparison (A/B = k) - जो अक्सर B के sign पर depend करता है।

3. Squares या absolute values ambiguity पैदा कर सकते हैं जब तक sign का clear idea न हो।

Trick to Always Use

  • Step 1: A - B को express करने की कोशिश करें - देखें कि वह हमेशा positive है, negative है या zero।
  • Step 2: जब equations में A², |A| या ratios हों, sign ambiguity पर खास ध्यान दें।
  • Step 3: अगर किसी variable का sign result बदल सकता है, तो वह statement sufficient नहीं है।

Summary

Summary

  • Statement तभी sufficient है जब वह हमेशा A > B, A < B या A = B establish कर दे।
  • Value या sign पर depend करने वाले results ⇒ insufficient।
  • Statements को पहले independently और फिर जरूरत हो तो combined check करें।
  • Squares या absolute values अक्सर direction खो देते हैं - इन्हें carefully handle करें।

याद रखने वाला उदाहरण:
(I) A = B + 3 → A हमेशा बड़ा (sufficient)।
(II) A² = B² + 9 → ambiguous (insufficient)।

Practice

(1/5)
1. Which is greater - A or B?<br>(I) A = B + 4<br>(II) A² = B² + 16
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)

    A = B + 4 ⇒ A - B = 4 → A is always 4 greater than B. Hence, A > B always.

  2. Step 2: Analyze (II)

    A² = B² + 16 ⇒ A² - B² = 16 ⇒ (A - B)(A + B) = 16. The result depends on values of A and B, so it’s ambiguous.

  3. Final Answer:

    Only (I) is sufficient → Option A

  4. Quick Check:

    (I) → A - B = 4 → A > B always ✅
Hint: If A - B is a positive constant, it’s always sufficient.
Common Mistakes: Treating squared difference as clear directional information.
2. Which is greater - A or B?<br>(I) A/B = 2<br>(II) A + B = 0
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: From (I)

    A/B = 2 ⇒ A = 2B. If B > 0, A > B; if B < 0, A < B → depends on sign of B → insufficient.

  2. Step 2: From (II)

    A + B = 0 ⇒ A = -B. Alone, cannot compare without specific sign values.

  3. Step 3: Combine

    From (I) and (II): 2B = -B ⇒ 3B = 0 ⇒ B = 0 ⇒ A = 0 → A = B. Combined gives equality conclusively.

  4. Final Answer:

    Both statements together are necessary → Option C

  5. Quick Check:

    Only when combined we get A = B ✅
Hint: If ratio and sum are given, combine to resolve sign ambiguity.
Common Mistakes: Assuming ratio alone is sufficient without considering sign cases.
3. Compare values of X and Y.<br>(I) X - Y = 5<br>(II) X + Y = 20
medium
A. Each statement alone is sufficient
B. Only (I) is sufficient
C. Only (II) is sufficient
D. Both statements together are necessary

Solution

  1. Step 1: From (I)

    X - Y = 5 → X is always greater than Y by 5 units → sufficient.

  2. Step 2: From (II)

    X + Y = 20 → can’t decide which is greater without relative info → insufficient.

  3. Final Answer:

    Only (I) is sufficient → Option B

  4. Quick Check:

    (I) → clear X > Y ✅
Hint: Difference (X-Y) directly determines direction of comparison.
Common Mistakes: Misreading sum (X+Y) as comparison indicator.
4. Which is greater - P or Q?<br>(I) P + Q = 20<br>(II) P - Q = 0
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)

    P + Q = 20 → gives total, not comparison → insufficient.

  2. Step 2: Analyze (II)

    P - Q = 0 ⇒ P = Q → comparison clear (equal).

  3. Final Answer:

    Only (II) is sufficient → Option B

  4. Quick Check:

    (II) alone → P = Q ✅
Hint: When difference equals zero, both are equal → sufficient.
Common Mistakes: Assuming totals (sums) reveal comparisons.
5. Compare M and N.<br>(I) M² = N²<br>(II) M = N
medium
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)

    M² = N² ⇒ M = ±N → could be equal or opposite → insufficient.

  2. Step 2: Analyze (II)

    M = N → clearly M and N are equal → sufficient.

  3. Final Answer:

    Only (II) is sufficient → Option B

  4. Quick Check:

    (I) ambiguous sign; (II) clear equality ✅
Hint: Square equations lose sign direction - insufficient alone.
Common Mistakes: Assuming M² = N² implies M = N always.

Mock Test

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