Correct Answer & Explanation
Option D
Let's analyze the pattern for 'TRAIN' to 'RPIYL':
• T → R (-2)
• R → P (-2)
• A → Y (A - 2 = Z, then Y) (-2)
• I → I (0)
• N → L (-2)
This pattern is not consistent. Let's re-examine.
Let's look at the positions of the letters:
T (20) → R (18) = -2
R (18) → P (16) = -2
A (1) → Y (25) = -2 (1 - 2 = -1, which is 25 in a 26-letter cycle)
I (9) → I (9) = 0
N (14) → L (12) = -2
The pattern is -2, -2, -2, 0, -2.
Now, apply this pattern to 'BUS'. Since 'BUS' has 3 letters, we need to apply the first three operations of the pattern (-2, -2, -2).
• B → Z (B - 2 = A, then Z) (-2)
• U → S (U - 2) (-2)
• S → Q (S - 2) (-2)
Therefore, 'BUS' is coded as 'ZSQ'. This is not among the options. This indicates that the initial pattern analysis or the question/options might be flawed.
Let's try another common type of coding: alternating shifts or a different sequence.
What if the pattern is -2 for all letters?
T(-2) → R
R(-2) → P
A(-2) → Y
I(-2) → G
N(-2) → L
This would make 'TRAIN' → 'RPYGL'. But the given code is 'RPIYL'. The 'I' (0 shift) and 'Y' (instead of G) are different.
Let's re-evaluate 'TRAIN' to 'RPIYL' with a more complex or alternating pattern.
T (20) → R (18) = -2
R (18) → P (16) = -2
A (1) → I (9) = +8 (This doesn't seem right. 'I' is the 3rd letter in 'RPIYL', not 'Y')
Let's write them vertically:
T R A I N
R P I Y L
T → R (-2)
R → P (-2)
A → I (+8) (This is a very large jump, unlikely for a simple code)
I → Y (+16) (Even larger, definitely not a simple shift)
N → L (-2)
This implies that the coding is not a simple letter-by-letter shift. It could be position-based or a specific mapping.
Let's assume there's a typo in the example 'RPIYL'. If it was 'RPYGL' (all -2), then 'BUS' would be 'ZSQ'.
Let's look at the options for 'BUS':
'ATQ', 'AQZ', 'ATY', 'ATZ'.
If we assume a common pattern for entrance exams, it's usually a consistent shift or an alternating shift. The example 'TRAIN' to 'RPIYL' is problematic.
However, if we are forced to find a pattern that leads to one of the options, let's look at the options and try to work backward or find a simpler pattern.
Let's assume the question is valid and there's a pattern. The 'I' in 'RPIYL' corresponding to 'A' in 'TRAIN' is the main anomaly. And 'Y' corresponding to 'I'.
Let's re-examine the example. Is it possible that the letters are shifted by a varying amount?
T → R (-2)
R → P (-2)
A → I (+8)
I → Y (+16)
N → L (-2)
This is not a simple pattern.
Let's consider if the question meant 'TRAIN' is coded as 'RPIYL' where each letter is coded based on some rule.
What if the pattern is related to the position of the letter? Or a fixed sequence of shifts?
Let's assume the shift values are -2, -2, -2, -2, -2 for 'TRAIN' resulting in 'RPYGL'. If the question has a typo and meant 'RPYGL', then for 'BUS':
B → Z (-2)
U → S (-2)
S → Q (-2)
Result: ZSQ. (Not in options)
Let's assume the correct answer is D: 'ATZ'.
If 'BUS' is coded as 'ATZ':
B → A (-1)
U → T (-1)
S → Z (+7) (or S → T (+1) if the option was ATU)
This is also not consistent.
Let's re-examine the question and options. This question is proving to be difficult due to apparent inconsistencies. Let's try to find a pattern that might lead to one of the options by looking at the options themselves.
If 'BUS' is 'ATZ' (Option D):
B (2) → A (1) = -1
U (21) → T (20) = -1
S (19) → Z (26) = +7
This is not a simple pattern.
Let's revisit the 'TRAIN' to 'RPIYL' pattern assuming a typo in the question and the intended pattern is simple.
If 'TRAIN' was coded as 'RPIYL' with a consistent pattern, it's not obvious.
What if the pattern for 'TRAIN' is:
T → R (-2)
R → P (-2)
A → I (+8)
I → Y (+16)
N → L (-2)
This is highly unlikely for an ANM GNM exam.
Let's look for a pattern where the shifts are small integers.
Let's consider the possibility of a mistake in the question or options. However, if we must choose, let's try to find a pattern that makes sense for at least some letters.
Consider the pattern of decreasing shifts:
T (-2) → R
R (-2) → P
A (-2) → Y (this is correct if we wrap around)
I (0) → I (This is the problematic one if we assume a decreasing shift)
N (-2) → L
If the pattern is -2, -2, -2, -2, -2, then TRAIN → RPYGL. Not RPIYL.
Let's assume the question meant 'TRAIN' is coded as 'RPIYL' where the letters are rearranged or some other complex coding is used. But for 'BUS', we need a consistent rule.
Let's assume the pattern is -1 for the first two letters and then something else.
If 'BUS' is 'ATZ' (Option D):
B → A (-1)
U → T (-1)
S → Z (+7)
Let's try to find a pattern that makes sense for 'TRAIN' to 'RPIYL' if the 'I' and 'Y' are not simple shifts.
What if the pattern is based on vowels/consonants?
TRAIN: T(C), R(C), A(V), I(V), N(C)
RPIYL: R(C), P(C), I(V), Y(C), L(C)
This doesn't directly help with the shifts.
Let's assume the pattern for the first two letters is -2, then it changes.
T → R (-2)
R → P (-2)
For 'BUS':
B → Z (-2)
U → S (-2)
So 'BS' would be 'ZS'. The third letter 'S' in 'BUS' needs to be coded. If the pattern is -2, -2, -2, then 'S' → 'Q'. So 'ZSQ'.
Let's re-evaluate the source of the problem. If 'TRAIN' is 'RPIYL', and 'BUS' is 'ATZ'.
TRAIN:
T → R (-2)
R → P (-2)
A → I (+8)
I → Y (+16)
N → L (-2)
BUS:
B → A (-1)
U → T (-1)
S → Z (+7)
These two examples follow entirely different patterns. This indicates a problem with the question or options provided. However, in an exam, one must pick the best possible answer.
Let's assume the pattern is simpler, and there's a typo in the given 'TRAIN' code. If the code for 'TRAIN' was meant to be 'RPYGL' (all letters shifted by -2), then 'BUS' would be 'ZSQ'. This is not an option.
Let's assume the pattern is -1 for the first two letters and then for the third letter it's different.
If 'BUS' is 'ATZ':
B → A (-1)
U → T (-1)
S → Z (+7)
Let's try to find a pattern where 'TRAIN' to 'RPIYL' and 'BUS' to 'ATZ' (option D) are consistent.
This is very difficult to find a consistent pattern. This question seems problematic.
However, if we are forced to choose and D is the correct answer, then the pattern for 'BUS' is B-1=A, U-1=T, S+7=Z. This is not a consistent simple pattern.
Let's re-examine the question and options. Perhaps the numbers are involved.
TRAIN = 20,18,1,9,14
RPIYL = 18,16,9,25,12
Differences: -2, -2, +8, +16, -2
This is not a simple pattern for an ANM GNM exam.
Let's assume the question has a typo and the pattern is simpler, for example, a consistent -1 shift for all letters.
TRAIN (-1) → SQZHM (Not RPIYL)
BUS (-1) → ATR (Not ATZ)
Let's assume the pattern is -1, -1, -1...
TRAIN (-1) → SQZHM
BUS (-1) → ATR (Not ATZ)
Let's assume the pattern is -2, -2, -2...
TRAIN (-2) → RPYGL (Not RPIYL)
BUS (-2) → ZSQ (Not ATZ)
Given the complexity and lack of a simple, consistent pattern that fits both the example and an option, there's a high probability of an error in the question or options. However, if forced to select, and assuming D is correct, the pattern applied to 'BUS' would be B-1=A, U-1=T, S+7=Z. This is not derivable from 'TRAIN' to 'RPIYL' in a straightforward manner.
Let's try to find a pattern that might lead to 'ATZ' from 'BUS'.
B → A (-1)
U → T (-1)
S → Z (+7)
This is a specific pattern. Let's see if 'TRAIN' could follow a similar pattern, perhaps alternating or based on position.
Let's assume the pattern is -1 for consonants and +7 for vowels, or something complex.
Given the level, it's usually a simple shift or alternating shift. The example 'TRAIN' to 'RPIYL' is highly irregular if interpreted as letter-by-letter shifts.
Let's assume the question has a typo and 'TRAIN' was coded as 'RPYGL' (all -2 shift). Then 'BUS' would be 'ZSQ'. This is not an option.
Let's assume the question has a typo and 'TRAIN' was coded as 'SQZHM' (all -1 shift). Then 'BUS' would be 'ATR'. This is not an option.
Let's assume the question has a typo and the pattern is -2, -2, -2, -2, -2 for 'TRAIN' (R P Y G L). Let's assume for 'BUS' the pattern is also -2, -2, -2 (Z S Q).
Let's consider the possibility that the pattern is specific to the word 'BUS'.
If 'BUS' is coded as 'ATZ'.
B → A (-1)
U → T (-1)
S → Z (+7)
This is not a simple consistent pattern. Let's assume the question intended a simple pattern, but the example is flawed. If the pattern is simply -1 for each letter, then 'BUS' would be 'ATR'. Not an option.
If the pattern is -2 for each letter, then 'BUS' would be 'ZSQ'. Not an option.
Let's look at the options again. 'ATQ', 'AQZ', 'ATY', 'ATZ'.
All start with A. So B-1=A. All have T as the second letter. So U-1=T. The third letter varies: Q, Q, Y, Z.
So the pattern for the first two letters is -1, -1.
Now, for the third letter 'S'.
S → Q (-2)
S → Z (+7)
S → Y (+6)
So if the pattern is -1, -1, then for the third letter 'S' in 'BUS', it could be -2 (giving ATQ), +7 (giving ATZ), or +6 (giving ATY).
Let's re-examine 'TRAIN' to see if it can give us a clue for the third letter of 'BUS'.
T R A I N
R P I Y L
If the pattern is -1, -1, and then something else:
T → S (-1)
R → Q (-1)
A → Z (-1)
I → H (-1)
N → M (-1)
This would give 'SQZHM'. This is not 'RPIYL'.
This question is highly problematic. However, if we assume the first two letters of 'BUS' follow a -1 shift, and we need to choose an option, then the third letter 'S' must be coded differently.
If the pattern is -1, -1, and then for the third letter 'S' it is +7 to get 'Z', then 'ATZ' is the answer.
Let's assume the question has a typo and 'TRAIN' was coded as 'SQZHM' (all -1). Then 'BUS' would be 'ATR'.
Given the options, and the commonality of the first two letters 'AT', the pattern for 'BUS' starts with -1, -1.
B (-1) → A
U (-1) → T
Now for 'S'. If 'ATZ' is the answer, then S → Z. This is S (+7) → Z.
So the pattern for 'BUS' is (-1, -1, +7).
Can we find this pattern in 'TRAIN' to 'RPIYL'?
T (-1) → S (not R)
R (-1) → Q (not P)
This confirms the pattern from 'TRAIN' to 'RPIYL' is not (-1, -1, +7).
This question is seriously flawed. The example 'TRAIN' to 'RPIYL' does not follow a simple, consistent, or easily derivable pattern for ANM GNM level, and the pattern that would lead to 'ATZ' for 'BUS' is also not consistently derivable from the example.
However, if we must choose, and assuming the question is solvable, let's look for a very simple, albeit potentially hidden, pattern.
Let's assume the question has a typo and 'TRAIN' is coded as 'RPIYL' where the first two letters are -2, and the last letter is -2. The middle two are problematic.
Let's assume the pattern is -1 for all letters. Then 'BUS' would be 'ATR'. Not an option.
Let's assume the pattern is -2 for all letters. Then 'BUS' would be 'ZSQ'. Not an option.
Let's assume the question is designed such that the pattern is derived from 'TRAIN' and applied to 'BUS'.
If we assume the pattern for 'TRAIN' is (-2, -2, +8, +16, -2), it's too complex.
Let's try to find a pattern that is common in coding-decoding questions and might lead to one of the options.
If the pattern is -1, -1, -1 for 'BUS', then 'ATR'.
If the pattern is -1, -1, -2 for 'BUS', then 'ATQ'. (Option A)
If the pattern is -1, -1, +7 for 'BUS', then 'ATZ'. (Option D)
If the pattern is -1, -1, +6 for 'BUS', then 'ATY'. (Option C)
Let's reconsider 'TRAIN' to 'RPIYL'.
T R A I N
R P I Y L
What if it's a skipping pattern? Or a reverse order?
N I A R T
L Y I P R
This doesn't work.
Let's assume the question meant a simple -1 for all letters, but the options are for a different pattern, or the example is flawed.
If the pattern is -1 for all letters, then 'BUS' is 'ATR'. Not an option.
Let's assume the pattern is -2 for all letters. Then 'BUS' is 'ZSQ'. Not an option.
Given the options, and the common 'AT' prefix, the first two letters of 'BUS' are B-1=A and U-1=T. So the pattern starts with -1, -1.
Now for 'S'.
If S-2 = Q (Option A)
If S+7 = Z (Option D)
If S+6 = Y (Option C)
Now, let's try to find a pattern in 'TRAIN' that might include -1, -1, and then something else.
T R A I N
R P I Y L
T → R (-2)
R → P (-2)
A → I (+8)
I → Y (+16)
N → L (-2)
This is highly inconsistent. Given that this is a medium-level question, there should be a straightforward pattern.
Let's assume there's a typo in the question and 'TRAIN' was coded as 'RPYGL' (all -2). Then 'BUS' would be 'ZSQ'.
Let's assume the question has a typo and 'TRAIN' was coded as 'SQZHM' (all -1). Then 'BUS' would be 'ATR'.
Since the provided correct answer is D ('ATZ'), let's work backward from there. This means for 'BUS', the pattern is B-1=A, U-1=T, S+7=Z.
This pattern is (-1, -1, +7).
Now, how does 'TRAIN' to 'RPIYL' fit this?
T (-1) → S (not R)
R (-1) → Q (not P)
A (+7) → H (not I)
I (-1) → H (not Y)
N (-1) → M (not L)
This confirms the question is flawed. The example and the correct answer for 'BUS' do not follow a consistent simple pattern. However, for the purpose of providing an explanation, we must assume the pattern that leads to the designated correct answer 'ATZ' for 'BUS'.
Therefore, the pattern applied to 'BUS' is:
• B → A (-1)
• U → T (-1)
• S → Z (+7)
This specific pattern leads to 'ATZ'. There is no consistent pattern derivable from the 'TRAIN' example that would apply to 'BUS' to yield 'ATZ'. This type of question (where the example doesn't consistently follow the rule for the target word) is generally considered poorly constructed. However, if forced to select, we assume the pattern for 'BUS' that yields the correct option.