DATA SUFFICIENCY – Reasoning Notes for CUET, CLAT & IPMAT

 

DATA SUFFICIENCY – Reasoning Notes for

 CUET, CLAT & IPMAT

Data Sufficiency is a high-scoring topic in Logical Reasoning for CUET, CLAT, IPMAT, and other competitive exams. It tests whether the given statements contain enough information to answer a question, NOT your ability to actually solve the question completely.

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⭐ What Is Data Sufficiency?

Data Sufficiency questions provide:

• A Question
• Two Statements (I) and (II)
  Your task is to decide:
  👉 Is the information sufficient to answer the question?

You DO NOT need to compute the final answer.
You only check whether it can be answered.

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⭐ Standard Answer Pattern (Very Important for CUET, CLAT, IPMAT)

Most Data Sufficiency questions use this structure:

A. Statement I alone is sufficient; Statement II alone is not sufficient
B. Statement II alone is sufficient; Statement I alone is not sufficient
C. Both statements together are sufficient but not individually
D. Each statement alone is sufficient
E. Even both statements together are not sufficient

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TYPES OF DATA SUFFICIENCY QUESTIONS

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TYPE 1: Number-Based Data Sufficiency

These involve:

• Odd–even
• Positive–negative
• Divisibility
• Age
• Ratios
• Equations

Example 1 (CUET Style)

Q. What is the value of x?
Statement I: 2x + 6 = 18
Statement II: x² – 11 = 0

Solution:

• From Statement I:
  2x + 6 = 18 → x = 6 (Unique) → Sufficient.
• From Statement II:
  x² – 11 = 0 → x = ±√11 (Two possible values) → Not sufficient.

👉 Answer: A (Statement I alone is sufficient)

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Example 2 (IPMAT Style)

Q. Is x an even number?
Statement I: x = 3k
Statement II: x = 6m

Solution:

• Statement I: x = 3k
  Could be even (k=2 → x=6)
  Could be odd (k=1 → x=3)
  ❌ Not sufficient
• Statement II: x = 6m
  Always even
  ✔ Sufficient

👉 Answer: B

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TYPE 2: Age-Based Data Sufficiency

A favorite in CUET & IPMAT.

Example 3

Q. What is Riya’s present age?

Statement I: Riya is 4 years older than Seema.
Statement II: 5 years ago, the ratio of their ages was 3 : 2.

Solution:

• Statement I: No fixed age → ❌ Not sufficient
• Statement II: Two people, one equation → ❌ Not sufficient
• Combine:
  Let present ages be R and S.
  R = S + 4
  Ratio (5 years ago):
  (R – 5)/(S – 5) = 3/2
  Substituting R = S + 4 gives unique age.

✔ Together sufficient
👉 Answer: C

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TYPE 3: Percentage / Profit–Loss Data

Useful in CUET Business Aptitude + IPMAT Quant.

Example 4

Q. What is the cost price of the article?

Statement I: Selling price is ₹720 at 20% profit.
Statement II: Profit is ₹120.

Solution:

• Statement I:
  CP = SP / 1.20 = 720/1.2 = 600 → ✔ Sufficient
• Statement II:
  Profit = SP – CP = 120
  No additional information → ❌ Not sufficient

👉 Answer: A

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TYPE 4: Geometry & Mensuration Questions

Example 5

Q. What is the area of the rectangle?
Statement I: Length = 12 cm
Statement II: Diagonal = 13 cm, Width = 5 cm

Solution:

• Statement I alone: No width → ❌ Not sufficient
• Statement II alone: Diagonal and width → length = √(13²–5²)=12
  So area = 12×5 → Unique
  ✔ Sufficient

👉 Answer: B

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TYPE 5: Ranking & Ordering

Example 6 (CLAT Style)

Q. What is Rohan’s rank in a class of 40?

St. I: 10 students are ahead of Rohan.
St. II: Rohan is ahead of Sameer who is 15th.

Solution:

• From Statement I: Rank = 11 → ✔ Sufficient
• From Statement II:
  Rohan could be 14th, 13th, 12th… (Anything above Sameer)
  ❌ Not sufficient

👉 Answer: A

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TYPE 6: Direction & Distance

Example 7

Q. In which direction is Neha from the starting point?

St. I: She walked 4 km east and 3 km north.
St. II: She walked 5 km from start.

Solution:

• Statement I: Direction = North-East → ✔ Sufficient
• Statement II: Only distance, no direction → ❌ Not sufficient

👉 Answer: A

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TYPE 7: Time, Work & Speed Problems

Example 8

Q. How long will A take to complete the work alone?

St. I: A and B together finish in 12 days.
St. II: A is twice as fast as B.

Solution:

• Statement I: Not enough → ❌
• Statement II: Relative speed only → ❌
• Combine:
  Let B = x → A = 2x
  Combined: 3x = 1/12 → x = 1/36 → A = 1/18
  Unique → ✔ Sufficient

👉 Answer: C

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TYPE 8: Alphabet, Coding-Decoding, Blood Relations

Example 9 (Blood Relation)

Q. How is A related to C?
St. I: B is the mother of C.
St. II: A is the husband of B.

Solution:

• I alone: No info about A → ❌
• II alone: No info about C → ❌
• Combine: A is father of C → ✔

👉 Answer: C

 

 

📘 DATA SUFFICIENCY – 25 MCQs with Answers & Detailed Solutions

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1. What is the value of x?

I. 2x + 10 = 30
II. x² – 25 = 0

Answer: A
Solution:
I → x = 10 (unique) → sufficient
II → x = ±5 → two values → insufficient.

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2. What is the age of Rohan?

I. Rohan is 6 years older than Sohan.
II. 5 years ago, their age ratio was 4 : 3.

Answer: C
Solution:
I → no fixed ages
II → two persons, one equation → not enough
Together → two equations → unique values → sufficient.

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3. Is x an even number?

I. x = 5k
II. x = 10m

Answer: B
Solution:
I: x can be odd/even → not enough
II: 10m → always even → sufficient.

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4. What is the area of the rectangle?

I. Length = 12
II. Width = 5; diagonal = 13

Answer: B
Solution:
I → width unknown
II → length can be found using Pythagoras → area known → sufficient.

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5. What is the value of the number?

I. It is divisible by 6.
II. It is divisible by 4.

Answer: E
Solution:
Neither gives unique number; even together many values possible.

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6. Who is the tallest?

I. A is taller than B.
II. C is taller than A.

Answer: E
Solution:
We know C > A > B, but no info about others or final tallest.
Insufficient even combined.

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7. What is the speed of the train?

I. Time taken to cross pole = 6 sec
II. Length of train = 120 m

Answer: C
Solution:
I → cannot find speed without length
II → cannot find speed without time
Together → speed = distance/time.

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8. What is the selling price?

I. Profit = ₹50
II. CP = ₹250, profit % = 20%

Answer: B
Solution:
I → no CP or % → insufficient
II → SP = 250 × 1.2 = 300 → sufficient.

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9. In which direction is A from starting point?

I. A walked 4 km east, then 3 km north.
II. A is 5 km from start.

Answer: A
Solution:
I gives direction NE
II gives only distance.

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10. What is the number?

I. The number is prime.
II. The number is even.

Answer: E
Solution:
Prime + even = only 2, BUT statement II alone allows many values;
Even combined: could be 2 → but I doesn't say number is unique.
Still insufficient because prime itself has many values (I alone).

Wait: Prime + even = always 2
But prime does not necessarily imply even.
I alone: many primes
II alone: many even
Together → 2 only → sufficient.

👉 Correct Answer: C (unique number)

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11. What is Amit’s rank?

I. 18 students are ahead of Amit.
II. Amit is 5th from last in a class of 30.

Answer: D
Solution:
I → rank = 19
II → rank = 30 - 5 + 1 = 26
Each gives rank → both sufficient individually.

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12. Is the triangle right-angled?

I. Sides are 6, 8, 10
II. One angle is 90°

Answer: D
Solution:
I → 6²+8²=10² → right triangle
II → directly right triangle
Each is sufficient.

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13. Who is the mother of Ria?

I. A is the sister of Ria.
II. B is the wife of Ria’s father.

Answer: B
Solution:
I → no info about mother
II → wife of father is mother → sufficient.

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14. What is the perimeter of the square?

I. Side = 7 cm
II. Diagonal = 7√2 cm

Answer: D
Solution:
I → perimeter = 4×7
II → side = 7 → same → both sufficient.

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15. What is the value of y?

I. y – 4 = 10
II. 2y = 28

Answer: D
Each gives unique y → both individually sufficient.

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16. What is the total cost?

I. Unit cost = ₹20
II. Number of units = 15

Answer: C
Both needed to calculate total.

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17. Is number N divisible by 9?

I. Sum of digits of N is 18
II. N is divisible by 3

Answer: A
I → sum = 18 → divisible by 9
II → divisible by 3 does NOT imply divisible by 9.

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18. Who is older, A or B?

I. A was born in 2003
II. B is 3 years younger than A

Answer: D
I → age known
II → B = A – 3 → we know who is older
Each alone sufficient.

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19. Is x > 0?

I. x³ > 0
II. x² = 4

Answer: A
I → x > 0
II → x = ±2 → sign unknown → insufficient.

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20. What is the average of three numbers?

I. Sum of three numbers = 45
II. Each number is odd

Answer: A
I → average = 45/3
II → no values → insufficient.

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21. How many students passed the exam?

I. 60% of 80 students passed.
II. 48 students passed.

Answer: D
I → 48 pass
II → 48 pass
Each sufficient.

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22. What is the rate of simple interest?

I. Interest = ₹300
II. Principal = ₹1000, Time = 3 years

Answer: C
Both needed to calculate R.

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23. Is the number positive?

I. Square of the number is 49
II. The number is odd

Answer: E
I → number = ±7
II → many odd numbers
Even together → still ±7 → sign unknown.

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24. What is length of the train?

I. It crosses a pole in 9 sec at 20 m/s
II. It crosses a 100 m platform in 14 sec

Answer: D
I → L = 20×9 = 180 m
II → (L+100)/14 → L = 96×? No, compute:
(L+100)/14 = speed
But speed unknown. Wait: only time given.
We need speed to find L.
Thus II is NOT sufficient.

Correct Answer → A (only statement I)

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25. What is the value of p?

I. p² – 9 = 0
II. p is positive

Answer: B
I → p = ±3
II → says positive but no value
Combined → p = 3 (unique)
But B means II alone sufficient—incorrect.

Correct Answer → C