In a certain code language, the word "INSTANT" is written as "IOUWESZ". Using the same coding rule, how is the word "FORGET" written in that code language?

Introduction / Context:
This coding decoding question involves position dependent shifts in the alphabet. The word INSTANT is coded as IOUWESZ. Unlike simple Caesar ciphers with a constant shift, here the amount of shift changes with the position of each letter. You must discover this pattern and then apply it to the new word FORGET.

Given Data / Assumptions:

• INSTANT is written as IOUWESZ.
• We must encode FORGET using the same rule.
• Letters follow the standard A to Z order.

Concept / Approach:
We compare each letter of INSTANT with its coded counterpart in IOUWESZ and compute the shift. This reveals how the shift increases step by step. Once we know the shift for each position (first, second, third, etc.), we use the same set of shifts for the letters of FORGET, which also has six letters like the first six positions of INSTANT.

Step-by-Step Solution:
Step 1: Write INSTANT and IOUWESZ aligned: I → I, N → O, S → U, T → W, A → E, N → S, T → Z.Step 2: Compute shifts: I(9) → I(9) is +0, N(14) → O(15) is +1, S(19) → U(21) is +2, T(20) → W(23) is +3, A(1) → E(5) is +4, N(14) → S(19) is +5, T(20) → Z(26) is +6.Step 3: So the pattern is: first letter +0, second +1, third +2, fourth +3, fifth +4, sixth +5, seventh +6.Step 4: Apply the same incremental shifts to FORGET: letters F, O, R, G, E, T.Step 5: F(6) + 0 = F(6); O(15) + 1 = P(16); R(18) + 2 = T(20); G(7) + 3 = J(10); E(5) + 4 = I(9); T(20) + 5 = Y(25).Step 6: Thus, FORGET is coded as FPTJIY.

Verification / Alternative check:
The increasing shift rule matches every letter of INSTANT exactly, so it is highly reliable. Applying the same set of shifts to any six-letter word must give a unique code. When we encode FORGET using +0, +1, +2, +3, +4 and +5, the resulting word FPTJIY matches one of the answer choices exactly, confirming the correctness of the method.

Why Other Options Are Wrong:

• FPOGXI, FOSIGX and FPSKHW show incorrect shifts on multiple letters and do not follow the steadily increasing pattern.
• FQSJHZ would require different, non uniform shifts and cannot be derived from the INSTANT example.

Common Pitfalls:
Students sometimes assume a constant shift for all letters or fail to observe that the amount of shift is increasing position wise. Another mistake is to miscalculate one or two letter positions, which leads to a completely different code word. Always compute the shift carefully for each position using numeric letter values.

Final Answer:
Following the position dependent shifts, FORGET is coded as FPTJIY.