Arithmetic Sufficiency

Q: What is the value of integer x? I. x^2 = 25 II. x > 0

Correct Answer: Option C (Both statements together are sufficient, but neither statement alone is sufficient.). Statement I alone gives x = 5 or -5, which is not sufficient. Statement II alone gives x > 0, providing no specific value. Combining both, x must be 5. Both statements together are sufficient.

Q: Is x an even number? I. 3x + 1 is an odd number. II. 5x - 2 is an even number.

Correct Answer: Option D (Each statement alone is sufficient.). From Statement I: 3x + 1 is odd => 3x is even => x is even (since 3 is odd). Sufficient. From Statement II: 5x - 2 is even => 5x is even => x is even. Sufficient. Thus, each statement alone is sufficient.

Q: What is the remainder when positive integer x is divided by 12? I. x leaves a remainder of 4 when divided by 6. II. x leaves a remainder of 10 when divided by 24.

Correct Answer: Option B (Statement II alone is sufficient, but Statement I alone is not.). Statement I: x = 6k + 4. If k=1, x=10 (rem 10 when divided by 12). If k=2, x=16 (rem 4 when divided by 12). Not sufficient. Statement II: x = 24m + 10. Since 24m is a multiple of 12, the remainder when divided by 12 will always be 10. Statement II alone is sufficient.

Q: Is the product a * b * c positive? I. a > 0 and b < 0. II. c < 0.

Correct Answer: Option C (Both statements together are sufficient, but neither statement alone is sufficient.). Statement I gives signs for a (+) and b (-), but c is unknown. Statement II gives the sign for c (-), but a and b are unknown. Together, (+)*(-)*(-) = (+), so the product is strictly positive. Both statements are required.

Q: What is the value of the two-digit number? I. The sum of its digits is 12. II. The difference between the number and the number formed by reversing its digits is 18.

Correct Answer: Option D (Statements I and II together are not sufficient.). Statement II translates to 9|x - y| = 18, so |x - y| = 2. Statement I translates to x + y = 12. Solving these gives two sets of digits: (7, 5) and (5, 7). The number could be 75 or 57. The data is not sufficient to find a unique value.

50 Questions

Practice Arithmetic Sufficiency questions with answers and step-by-step solutions. These problems are curated from recent campus placement test papers (TCS, Infosys, Wipro, Cognizant, Accenture) and competitive government exams (SSC CGL, Bank PO, RRB NTPC, UPSC).

Quick Mode: Practice Questions Timed Mock Test

Arithmetic Sufficiency: Directions & Problem Statements Shared for questions below

DirectionsSet 1: Number Properties

Data Sufficiency: Arithmetic (Medium to Hard Level)

Evaluate the two statements and determine which of the options is correct.

What is the value of integer x?
I. x^2 = 25
II. x > 0

medium

Is x an even number?
I. 3x + 1 is an odd number.
II. 5x - 2 is an even number.

medium

What is the remainder when positive integer x is divided by 12?
I. x leaves a remainder of 4 when divided by 6.
II. x leaves a remainder of 10 when divided by 24.

medium

Is the product a * b * c positive?
I. a > 0 and b < 0.
II. c < 0.

medium

What is the value of the two-digit number?
I. The sum of its digits is 12.
II. The difference between the number and the number formed by reversing its digits is 18.

medium

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Arithmetic Sufficiency

What is the value of integer x?
I. x^2 = 25
II. x > 0

Community Discussion & Shortcut Formulas

Is x an even number?
I. 3x + 1 is an odd number.
II. 5x - 2 is an even number.

Community Discussion & Shortcut Formulas

What is the remainder when positive integer x is divided by 12?
I. x leaves a remainder of 4 when divided by 6.
II. x leaves a remainder of 10 when divided by 24.

Community Discussion & Shortcut Formulas

Is the product a * b * c positive?
I. a > 0 and b < 0.
II. c < 0.

Community Discussion & Shortcut Formulas

What is the value of the two-digit number?
I. The sum of its digits is 12.
II. The difference between the number and the number formed by reversing its digits is 18.

Community Discussion & Shortcut Formulas