Correct Answer & Explanation
Option D
Let's analyze the pattern for 'FLOWER' to 'GMQWFS':
• F → G (+1)
• L → M (+1)
• O → Q (+2)
• W → W (0)
• E → F (+1)
• R → S (+1)
The pattern is +1, +1, +2, 0, +1, +1.
Now, apply this pattern to 'GARDEN'. Since 'GARDEN' also has 6 letters, we apply the same sequence of shifts:
• G → H (+1)
• A → B (+1)
• R → S (+2) (R + 2 = T)
• D → D (0)
• E → F (+1)
• N → O (+1)
So, 'GARDEN' would be coded as 'HBTDFO'. This doesn't match any of the options directly.
Let's re-examine the example code 'FLOWER' to 'GMQWFS'.
F(6) → G(7) = +1
L(12) → M(13) = +1
O(15) → Q(17) = +2
W(23) → W(23) = 0
E(5) → F(6) = +1
R(18) → S(19) = +1
This pattern (+1, +1, +2, 0, +1, +1) is confirmed.
Now, apply this to 'GARDEN':
G(7) → H(8) = H (+1)
A(1) → B(2) = B (+1)
R(18) → T(20) = T (+2)
D(4) → D(4) = D (0)
E(5) → F(6) = F (+1)
N(14) → O(15) = O (+1)
So the code for 'GARDEN' is 'HBTDFO'.
Let's check the options again:
Opt_a: HBSFEO
Opt_b: HBSGFN
Opt_c: HBSGFM
Opt_d: HBSGFO
None of the options match 'HBTDFO'. This indicates a strong possibility of a typo in the question or the options provided, or the designated correct answer.
However, if we are forced to find a pattern that leads to one of the options, and 'D' is the correct answer, let's see what pattern would lead to 'HBSGFO' for 'GARDEN'.
G → H (+1)
A → B (+1)
R → S (+1)
D → G (+3)
E → F (+1)
N → O (+1)
So, the pattern for 'GARDEN' to 'HBSGFO' is (+1, +1, +1, +3, +1, +1).
This pattern is different from the one derived from 'FLOWER' to 'GMQWFS' (+1, +1, +2, 0, +1, +1).
This question is inconsistent. There is no single, consistent pattern that applies to both the example 'FLOWER' and the target word 'GARDEN' to yield one of the options. This is a flawed question.
However, for the sake of providing an explanation, we will assume the pattern that leads to the designated correct answer, 'HBSGFO', for 'GARDEN'. This means the pattern is (+1, +1, +1, +3, +1, +1).
Let's re-evaluate if there's any way the 'FLOWER' example could imply this pattern.
If the pattern for 'FLOWER' was (+1, +1, +1, +3, +1, +1):
F (+1) → G
L (+1) → M
O (+1) → P (not Q)
W (+3) → Z (not W)
E (+1) → F
R (+1) → S
This is clearly not the case. The example 'FLOWER' to 'GMQWFS' has a specific pattern (+1, +1, +2, 0, +1, +1). If this pattern is applied to 'GARDEN', the result is 'HBTDFO'. Since 'HBTDFO' is not an option, and 'D' ('HBSGFO') is marked correct, there's a serious inconsistency.
Given the constraints, if 'D' is the correct answer, the pattern applied to 'GARDEN' is:
• G → H (+1)
• A → B (+1)
• R → S (+1)
• D → G (+3)
• E → F (+1)
• N → O (+1)
This pattern yields 'HBSGFO'. This explanation acknowledges the inconsistency but provides the steps to reach the designated correct answer.