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Basic Quantitative Data Sufficiency

Introduction

Basic Quantitative Data Sufficiency problems test whether the given statements provide enough information to answer a numerical question - not to actually calculate the answer.

This pattern is crucial because it builds logical clarity and helps you decide if available data is sufficient or insufficient for solving a problem.

Pattern: Basic Quantitative Data Sufficiency

Pattern

Key idea - You are not asked to find the value, but to check if the value can be found from the statements.

Typical question format: A numerical question followed by two statements (I) and (II). You must determine which statement(s) give enough data to answer the question.

Step-by-Step Example

Question

What is the value of X?
(I) X + 5 = 10
(II) 2X = 10

Solution

  1. Step 1: Analyze Statement (I)

    From (I): X + 5 = 10 ⇒ X = 5. Hence, (I) alone gives a unique value of X.

  2. Step 2: Analyze Statement (II)

    From (II): 2X = 10 ⇒ X = 5. Hence, (II) alone also gives a unique value of X.

  3. Step 3: Compare Sufficiency

    Each statement independently provides enough data to find X. Therefore, either statement alone is sufficient.

  4. Final Answer:

    Each statement alone is sufficient.

  5. Quick Check:

    Both statements lead to X = 5 → consistent value ✅

Quick Variations

1. Sometimes both statements are needed when one gives a relation but not a value.

2. Sometimes neither statement provides enough data.

3. Always check for uniqueness of result - not just presence of an equation.

Trick to Always Use

  • Step 1: Check each statement separately for sufficiency.
  • Step 2: If neither is sufficient alone, combine them logically.
  • Step 3: Don’t actually compute the value - only judge if you can.

Summary

Summary

  • Focus on whether the data is sufficient, not on finding the actual answer.
  • Check each statement independently before combining.
  • Mark sufficiency only if a unique result is guaranteed.
  • Be cautious of ambiguous or incomplete numerical information.

Example to remember:
If (I) says X + 5 = 10 and (II) says 2X = 10 → both individually give X = 5, so each is sufficient.

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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