Question

If \( wxyz \neq 0 \), in which quadrant of the rectangular cartesian coordinate system does \( (x, y) \) lie? Statement (I): \( (x, z) \) lies in the first quadrant.
Statement (II): \( (w, y) \) lies in the third quadrant.

• A. Statement (I) alone is sufficient.
• B. Statement (II) alone is sufficient.
• C. Both statements (I) and (II) are sufficient.
• D. Neither statement is sufficient.

Hint:

To determine the quadrant of a point, you must know the sign of both the x-coordinate and the y-coordinate. If statements give you partial information, consider if combining them completes the pair.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This logical reasoning problem involves letter coding. The goal is to decipher the transformation rule turning 'WATER' into 'YCVGT' and use it on 'FIRE'.


Step 2: Key Formula or Approach:
Determine the alphabetical shift applied to each letter in the sample word, then replicate this exact shift for the target word.


Step 3: Detailed Explanation:
Examining the letter shifts in 'WATER':
W (+2 positions) \(\rightarrow\) Y
A (+2 positions) \(\rightarrow\) C
T (+2 positions) \(\rightarrow\) V
E (+2 positions) \(\rightarrow\) G
R (+2 positions) \(\rightarrow\) T
The established rule is advancing each letter by 2 spots in the alphabet.
Implementing this rule on 'FIRE':
F (+2 positions) \(\rightarrow\) H
I (+2 positions) \(\rightarrow\) K
R (+2 positions) \(\rightarrow\) T
E (+2 positions) \(\rightarrow\) G
This yields the coded word 'HKTG'.


Step 4: Final Answer:
The correct choice is (B).