Raised Fist0

Basic Quantitative Data Sufficiency

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

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: Basic Quantitative Data Sufficiency

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

  • 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?
(I) X + 6 = 14
(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?
(I) Y + Z = 10
(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.
(I) 5Z - 10 = 0
(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.
(I) M + 2 = 7
(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?
(I) 2P + 3Q = 14
(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.