Which of the following statements is/are true? I. 333 > 333 II. 333 > (33)³

Introduction / Context:
This question tests the ability to interpret inequalities and exponential notation correctly. You are given two comparisons, one between a number and itself, and another between a number and an expression involving a power. You must decide whether each statement is true or false, and then choose the option that best summarises your findings. Such items verify basic comfort with greater than symbols and simple exponent computations.

Given Data / Assumptions:

• Statement I: 333 > 333.
• Statement II: 333 > (33)³, meaning 333 is greater than 33 cubed.
• The greater than sign > means strictly larger, not equal to or larger.
• We assume (33)³ means 33 × 33 × 33.

Concept / Approach:
For Statement I, we compare a number with itself. A number can be equal to itself but cannot be strictly greater than itself. Therefore, any statement of the form x > x is false. For Statement II, we must compute or estimate 33³ and then compare it with 333. Since 33³ involves multiplying 33 by itself three times, we expect a result that is much larger than 333. After confirming this, we decide whether the inequality direction in the statement is correct.

Step-by-Step Solution:
Check Statement I: 333 > 333. The left side and right side are exactly the same number. For a strict inequality x > y to be true, x must be larger than y. Here x equals y, so the statement is false. At best we could write 333 ≥ 333, but not 333 > 333. Check Statement II: 333 > (33)³. Compute 33³ by stages. First, 33² = 33 × 33 = 1089. Next, 33³ = 1089 × 33. Multiply 1089 by 33. 1089 × 30 = 32,670 and 1089 × 3 = 3,267. Adding gives 32,670 + 3,267 = 35,937. So (33)³ = 35,937. Compare 333 with 35,937. Clearly 35,937 is much larger than 333. Therefore 333 is not greater than 35,937. The true relation is 333 < 35,937, so Statement II is also false.

Verification / Alternative check:
Even without full multiplication, you can observe that 33² is already 1,089, which is greater than 333. Multiplying by 33 again must produce a number in the tens of thousands. Thus 33³ must exceed 1,089 and is certainly greater than 333. Since the statement claims 333 > 33³, which contradicts this reasoning, we know Statement II is false. Combined with the obvious falsity of Statement I, we conclude that neither statement is true.

Why Other Options Are Wrong:
Option A, claiming only I is true, is wrong because I is false: no number can be strictly greater than itself. Option B, claiming only II is true, is wrong because II is also false, as 33³ is far larger than 333. Option C, claiming both statements are true, is clearly incorrect since both involve reversed inequalities. Only option D correctly states that neither I nor II is true.

Common Pitfalls:
Some candidates misread 333 > 333 as 333 ≥ 333 and mistakenly accept it as true, ignoring the difference between strict and non strict inequalities. Others may see (33)³ and assume it is only slightly bigger than 333, without realising that cube growth is rapid. Confusing 33³ with 3³ or 33² also leads to errors. Always read the inequality symbol carefully and, when powers appear, compute or estimate their magnitude before deciding which side is larger.

Final Answer:
Both statements are false, so the correct choice is “Neither I nor II”, which is option D.