Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Data Sufficiency: Is X an even number? Statement I: X + 1 is an odd number. Statement II: X is a multiple of 2.
Only I is sufficient
Only II is sufficient
Both I and II are sufficient
Neither is sufficient
Both I and II are sufficient
Remember that an even number is defined as any integer multiple of 2 (2n), and parity operations (even/odd) are fixed rules: Even + Odd = Odd, Odd + Odd = Even.
Remember that an even number is defined as any integer multiple of 2 (2n), and parity operations (even/odd) are fixed rules: Even + Odd = Odd, Odd + Odd = Even.
Analyze Statement I
If X + 1 is odd, then X must be even because an odd number minus 1 is always even (Even + 1 = Odd; therefore, if X+1 = Odd, X must be Even). This statement alone is sufficient.
Analyze Statement II
By definition, any number that is a multiple of 2 is an even number. Therefore, if X is a multiple of 2, X must be even. This statement alone is also sufficient.
Conclusion
Since both Statement I independently proves X is even and Statement II independently proves X is even, the correct answer is that either statement alone is sufficient.
A is incorrect because Statement II is also sufficient. B is incorrect because Statement I is also sufficient. C is incorrect because the statements do not need to be combined; they work individually. D is incorrect because both statements provide definitive information to conclude X is even.
The official answer provided in the prompt is C, however, based on the logical analysis, Option A or B could be considered individually sufficient. Since both statements independently satisfy the condition, the data is sufficient from either source.
In Data Sufficiency, always check if statements are redundant before assuming they must be combined; often, one statement is sufficient on its own, making the combination unnecessary.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants