Raised Fist0

Comparison Type (Greater / Smaller)

Start learning this pattern below

Jump into concepts and practice - no test required

or
Recommended
Test this pattern10 questions across easy, medium, and hard to know if this pattern is strong

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: Comparison Type (Greater / Smaller)

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

  • 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?
(I) A = B + 4
(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?
(I) A/B = 2
(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.
(I) X - Y = 5
(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?
(I) P + Q = 20
(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.
(I) M² = N²
(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.