Data Sufficiency Question Bank for C-CAT
Topic-wise Data Sufficiency MCQs for CDAC C-CAT preparation with answers and explanations.
Statement I: x² > 0
Statement II: x³ > 0
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Correct Answer: B - Statement II alone is sufficient
Statement I: x² > 0 means x != 0, but x could be positive or negative. Statement II: x³ > 0 means x > 0 (positive). Statement II alone is sufficient.
Statement I: x + y = 10
Statement II: x - y = 4
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Correct Answer: A - Both statements together are sufficient
Using both: x+y=10 and x-y=4. Adding: 2x=14, x=7. Both are needed.
Statement I: n is divisible by 2
Statement II: n is divisible by 3
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Correct Answer: D - Both statements together are sufficient
n divisible by 6 requires divisibility by both 2 and 3. Both statements together confirm this.
Statement I: Circumference is 22 cm
Statement II: Diameter is 7 cm
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Correct Answer: D - Either statement alone is sufficient
From circumference: 2πr = 22, r = 3.5. From diameter: r = 3.5. Either gives the radius.
Statement I: p = q + 5
Statement II: p + q = 15
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Correct Answer: C - Statement I alone is sufficient
Statement I: p = q + 5 means p > q directly. Statement I alone is sufficient.
Statement I: The train crosses a pole in 10 seconds
Statement II: The train is 200m long
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Correct Answer: B - Both statements together are sufficient
Speed = Length/Time. We need both length (200m) and time (10s) to find speed = 20 m/s.
Statement I: Sides are in ratio 3:4:5
Statement II: One angle is 90°
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Correct Answer: C - Either statement alone is sufficient
3:4:5 is a Pythagorean triplet (right triangle). Statement II directly states 90°. Either is sufficient.
Statement I: A is 5 years older than B
Statement II: B is 3 years younger than C who is 25 years old
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Correct Answer: C - Both statements together are sufficient
From II: C = 25, B = 22. From I: A = B + 5 = 27. Both needed.
Statement I: Selling price is ₹120
Statement II: Cost price is ₹100
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Correct Answer: D - Both statements together are sufficient
Profit% = (SP-CP)/CP × 100. Need both SP and CP. Both statements together give the answer: 20%.
Statement I: x + 2 is divisible by 4
Statement II: x is divisible by 2
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Correct Answer: B - Either statement alone is sufficient
Statement II directly says x is divisible by 2 (even). Statement I: if x+2 is divisible by 4, x+2 is even, so x is even. Either is sufficient.
Statement I: Perimeter is 24 cm
Statement II: Length is twice the breadth
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Correct Answer: A - Both statements together are sufficient
From II: L=2B. From I: 2(L+B)=24, so 2(2B+B)=24, 6B=24, B=4, L=8. Area=32 sq cm. Both needed.
Statement I: n is divisible by 4
Statement II: n is divisible by 3
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Correct Answer: C - Both statements together are sufficient
For n to be divisible by 12, it must be divisible by both 3 and 4 (coprime factors). Both statements together are sufficient.
Statement I: Cost of 3 pens is Rs. 60
Statement II: Cost of 2 pens and 3 pencils is Rs. 50
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Correct Answer: C - Statement I alone is sufficient
From Statement I: 1 pen = Rs. 20, so 5 pens = Rs. 100. Statement I alone is sufficient.
Statement I: x - y = 5
Statement II: x/y > 1
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Correct Answer: B - Statement I alone is sufficient
Statement I: x-y=5 means x>y. Statement II: x/y>1 means x>y only if y>0 (not certain). Statement I alone is sufficient.
Statement I: Simple interest for same period is Rs. 200
Statement II: Rate of interest is 10% per annum
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Correct Answer: A - Either statement alone is sufficient
From I: SI=200 for 2 years, Rate=10%. From II: Rate=10% directly. Either gives rate, then CI can be calculated.
Statement I: Total students = 50
Statement II: 80% students passed
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Correct Answer: D - Both statements together are sufficient
Need total and percentage both. 50 × 0.8 = 40 passed. Both statements together needed.
Statement I: Surface area is 150 sq cm
Statement II: Diagonal of one face is 5*sqrt(2) cm
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Correct Answer: A - Either statement alone is sufficient
From I: 6a²=150, a²=25, a=5. Volume=125. From II: face diagonal=a*sqrt(2)=5*sqrt(2), a=5. Volume=125. Either sufficient.
Statement I: A alone takes 12 days
Statement II: B alone takes 18 days
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Correct Answer: B - Both statements together are sufficient
Together: 1/12 + 1/18 = 5/36. Time = 36/5 = 7.2 days. Both statements needed.
Statement I: n is odd
Statement II: n is greater than 10 and less than 15
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Correct Answer: D - Both statements together are sufficient
Statement I alone is not sufficient, and Statement II alone allows 11, 12, 13, or 14. Together, n must be 11 or 13, both of which are prime.
Statement I: Sum of first 3 numbers is 30
Statement II: Sum of last 2 numbers is 20
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Correct Answer: D - Both statements together are sufficient
Total sum = 30 + 20 = 50. Average = 50/5 = 10. Both statements together are sufficient.
Statement I: x² > 25
Statement II: x > 0
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Correct Answer: D - Both statements together are sufficient
Statement I: x² > 25 means x > 5 or x < -5 — not sufficient alone. Statement II: x > 0 — not sufficient alone (x could be 1). Together: x > 0 and x² > 25, so x > 5. Both together are sufficient.
Statement I: a = 2b
Statement II: a - b = 7
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Correct Answer: C - Both statements together are sufficient
Statement I: a = 2b → a + b = 3b, but b is unknown. Statement II: a - b = 7, but a + b is unknown. Together: a = 2b and a - b = 7 → 2b - b = 7 → b = 7, a = 14. a + b = 21. Both together are sufficient.
Statement I: N is divisible by 3
Statement II: N is divisible by 2
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Correct Answer: D - Both statements together are sufficient
A number divisible by 6 must be divisible by both 2 and 3. Statement I alone (div by 3) not sufficient. Statement II alone (div by 2) not sufficient. Together: divisible by 2 and 3 → divisible by 6.
Statement I: Rohan is 5 years older than Sohan.
Statement II: The sum of their ages is 35.
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Correct Answer: D - Both statements together are sufficient
I: R = S + 5 — one equation, two unknowns. II: R + S = 35 — one equation, two unknowns. Together: R = S + 5 and R + S = 35 → 2R = 40 → R = 20. Both together sufficient.
Statement I: One angle of the triangle is 90°.
Statement II: AB² + BC² = AC².
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Correct Answer: A - Either statement alone is sufficient
Statement I directly states there's a 90° angle → right triangle. Statement II: Pythagorean theorem confirms right triangle. Either statement alone is sufficient.
Statement I: The train covers 180 km in 3 hours.
Statement II: The train is traveling at a constant speed.
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Correct Answer: C - Statement I alone is sufficient
Statement I: Speed = 180/3 = 60 km/h. Sufficient alone. Statement II gives no numerical data.
Statement I: p is odd.
Statement II: p is between 10 and 14.
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Correct Answer: C - Both statements together are sufficient
I: p is odd — could be 3 (prime) or 9 (not prime). Not sufficient. II: p ∈ {11, 12, 13} — 11,13 are prime, 12 is not. Not sufficient. Together: odd and between 10-14: p ∈ {11, 13}, both prime. Sufficient.
Statement I: The perimeter is 30 cm.
Statement II: The length is twice the breadth.
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Correct Answer: B - Both statements together are sufficient
I: 2(l+b)=30 → l+b=15. Not sufficient alone. II: l=2b. Not sufficient alone. Together: 2b+b=15 → b=5, l=10. Area=50 cm². Sufficient.
Statement I: N is a multiple of 4.
Statement II: N is a multiple of 6.
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Correct Answer: B - Either statement alone is sufficient
Statement I: multiple of 4 → always even. Sufficient. Statement II: multiple of 6 → always even. Sufficient. Either alone is sufficient.
Statement I: A is taller than B and C.
Statement II: D is shorter than A.
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Correct Answer: B - Both statements together are sufficient
I: A > B and A > C, but D's height unknown. II: A > D, but B and C unknown. Together: A > B, A > C, A > D. A is tallest. Sufficient.
Statement I: 2x + 3 = 15
Statement II: x is a positive integer.
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Correct Answer: C - Statement I alone is sufficient
Statement I: 2x + 3 = 15 → 2x = 12 → x = 6. Sufficient alone. Statement II only narrows the type, not the value.
Statement I: Cost price is ₹200.
Statement II: Selling price is ₹250.
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Correct Answer: A - Both statements together are sufficient
Need both CP and SP for profit%. I gives CP=200, II gives SP=250. Profit = 50, Profit% = 25%. Both together sufficient.
Statement I: m - n > 0
Statement II: m + n > 0
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Correct Answer: C - Statement I alone is sufficient
Statement I: m - n > 0 directly means m > n. Sufficient alone.
Statement I: The day after tomorrow is Wednesday.
Statement II: Yesterday was Sunday.
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Correct Answer: A - Either statement alone is sufficient
Statement I: Day after tomorrow = Wednesday → Today = Monday. Sufficient. Statement II: Yesterday = Sunday → Today = Monday. Sufficient. Either alone is sufficient.
Statement I: All sides of ABCD are equal.
Statement II: All angles of ABCD are 90°.
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Correct Answer: C - Both statements together are sufficient
I: All sides equal → could be a rhombus. Not sufficient. II: All angles 90° → could be a rectangle. Not sufficient. Together: equal sides + all 90° = square. Sufficient.
Statement I: The sum of the numbers is 75.
Statement II: The largest number is 25.
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Correct Answer: B - Statement I alone is sufficient
Statement I: Average = 75/5 = 15. Sufficient alone. Statement II is irrelevant for computing the average.
Statement I: Angle ABC < 90°.
Statement II: Angle ABC = 60°.
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Correct Answer: D - Either statement alone is sufficient
I: Directly says < 90° → acute. Sufficient. II: 60° < 90° → acute. Sufficient. Either alone sufficient.
Statement I: 60% of students passed.
Statement II: Total students = 200.
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Correct Answer: A - Both statements together are sufficient
I: 60% passed, but don't know total. II: Total = 200, but don't know pass rate. Together: 60% of 200 = 120 passed. Sufficient.
Statement I: N = 23.
Statement II: N leaves remainder 3 when divided by 10.
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Correct Answer: B - Either statement alone is sufficient
I: 23 ÷ 5 = remainder 3. Sufficient. II: If N mod 10 = 3, then N ends in 3, so N mod 5 = 3. Sufficient. Either alone is sufficient.
Statement I: A sum of ₹1000 becomes ₹1200 in 2 years at simple interest.
Statement II: The interest earned is ₹200.
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Correct Answer: B - Statement I alone is sufficient
Statement I: SI = 200, P = 1000, T = 2. R = (200 × 100)/(1000 × 2) = 10%. Sufficient alone. Statement II alone doesn't give P and T.
Statement I: X is a factor of 12.
Statement II: X < 10.
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Correct Answer: B - Statement I alone is sufficient
Statement I: Factors of 12 are 1,2,3,4,6,12. All of these are also factors of 24. So if X is a factor of 12, it's definitely a factor of 24. Sufficient alone.
Statement I: A car takes 4 hours to travel from A to B.
Statement II: The car's speed is 60 km/h.
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Correct Answer: D - Both statements together are sufficient
I: Time = 4 hours, but speed unknown. II: Speed = 60 km/h, but time unknown. Together: Distance = 60 × 4 = 240 km. Sufficient.
Statement I: x > 0
Statement II: y > 0
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Correct Answer: B - Both statements together are sufficient
I: x > 0, but y could be negative. Not sufficient. II: y > 0, but x could be negative. Not sufficient. Together: both positive → product positive. Sufficient.
Statement I: The sum of its digits is 9.
Statement II: The difference of its digits is 3.
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Correct Answer: D - Neither statement is sufficient
I: Digit sum = 9 → many possibilities (18, 27, 36, 45, 54, 63, 72, 81, 90). II: Digit difference = 3 → many possibilities. Together: sum=9, diff=3 → digits are 6,3 or 3,6. Number could be 63 or 36. Still not unique. Neither sufficient.
Statement I: The year is divisible by 4.
Statement II: The year is not divisible by 100.
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Correct Answer: A - Both statements together are sufficient
Leap year rules: divisible by 4, but not by 100 unless also by 400. I: 2024 ÷ 4 = 506, yes. But if divisible by 100, need to check 400. Not sufficient alone. II: Not divisible by 100, but don't know if divisible by 4. Not sufficient alone. Together: divisible by 4 and not by 100 → leap year. Sufficient.
Statement I: Each side is 8 cm.
Statement II: The area of the triangle is 16√3 cm².
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Correct Answer: A - Either statement alone is sufficient
I: Perimeter = 3 × 8 = 24 cm. Sufficient. II: Area of equilateral triangle = (√3/4)a². So (√3/4)a² = 16√3 → a² = 64 → a = 8. Perimeter = 24. Sufficient. Either alone sufficient.
Statement I: P earns more than Q and R.
Statement II: S earns less than Q.
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Correct Answer: A - Both statements together are sufficient
I: P > Q and P > R. Don't know about S. II: S < Q. Don't know about P or R. Together: P > Q > S and P > R. So P earns the most. Sufficient.
Statement I: The total surface area is 150 cm².
Statement II: Each edge is 5 cm.
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Correct Answer: A - Either statement alone is sufficient
I: 6a² = 150 → a² = 25 → a = 5 → V = 125 cm³. Sufficient. II: V = 5³ = 125 cm³. Sufficient. Either alone sufficient.
Statement I: n is odd.
Statement II: n is not divisible by 2.
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Correct Answer: C - Either statement alone is sufficient
I: n odd → n² odd. Sufficient. II: Not divisible by 2 → n is odd → n² odd. Sufficient. Both statements say the same thing. Either alone sufficient.
Statement I: a + b = 10
Statement II: a + c = 15
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Correct Answer: A - Neither statement is sufficient
I: a + b = 10 → a = 10 - b, b unknown. II: a + c = 15 → a = 15 - c, c unknown. Together: two equations, three unknowns. Cannot determine a uniquely. Neither sufficient.
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Correct Answer: A - I alone sufficient
I directly says x-y>0, so x>y. II is not sufficient if signs are unknown.
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Correct Answer: C - Either alone sufficient
If n2 is even, n is even. If n+1 is odd, n is even. Either statement is sufficient.
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Correct Answer: A - I alone sufficient
I gives x=4 uniquely. II gives x=4 or -4, so it is not sufficient alone.
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Correct Answer: C - Either alone sufficient
I satisfies Pythagoras, so right triangle. II directly says one angle is 90 degrees.
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Correct Answer: A - I alone sufficient
A number is divisible by 9 if digit sum is divisible by 9. I is sufficient; II is not.
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Correct Answer: A - I alone sufficient
Average of a and b is (a+b)/2. I gives it directly as 25.
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Correct Answer: B - II alone sufficient
Having exactly two positive factors is the definition of a prime number. Odd alone is not enough.
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Correct Answer: A - I alone sufficient
Profit occurs exactly when SP > CP. I is sufficient.
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Correct Answer: C - Both needed
A number divisible by both 2 and 3 is divisible by 6. Both statements are needed.
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Correct Answer: A - I alone sufficient
A is 140% of B, so A:B=7:5. II gives a difference but not the ratio.