2
A given code transforms GULMOHAR into TFONLSZI. Using the same code, what would PIPAL transform into?
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Solution: Step 1: Analyze the given code for GULMOHAR to TFONLSZI.
Step 2: Observe the pattern: G(7) to T(20), U(21) to F(6), L(12) to O(15), M(13) to N(14), O(15) to L(12), H(8) to S(19), A(1) to Z(26), R(18) to I(9).
Step 3: Identify that each letter is shifted by a certain rule: G + 13 = T (7 + 13 = 20), U - 15 = F (21 - 15 = 6), and so on.
Step 4: Determine the exact rule: The shifts are based on positions in the alphabet and appear to be related to achieving a sum of 27.
Step 5: Apply the rule to PIPAL: P(16) -> 27 - 16 = 11 = K, I(9) -> 27 - 9 = 18 = R, P(16) -> 27 - 16 = 11 = K, A(1) -> 27 - 1 = 26 = Z, L(12) -> 27 - 12 = 15 = O.
Step 6: Conclude that PIPAL coded is KRKZO.
4
Determine the code word for 'mangoes' in the given code language using the provided sets of coded phrases.
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Solution: Step 1: Analyze Statement I.
(1) 'Te Le Pa Na' = 'You eat many mangoes'
(2) 'Le Na Da' = 'You sell mangoes'
Comparing (1) and (2), common codes are 'Le', 'Na'. Common words are 'You', 'mangoes'. So {'Le', 'Na'} corresponds to {'You', 'mangoes'}. Statement I alone is insufficient.
Step 2: Analyze Statement II.
(3) 'Ge Na Se La Le' = 'They eat bananas and mangoes'
(4) 'Ne De Le La' = 'Who others eat bananas'
Comparing (1) from Statement I and (4) from Statement II:
'You eat many mangoes' (Te Le Pa Na)
'Who others eat bananas' (Ne De Le La)
Common word is 'eat'. Common code word is 'Le'. Thus, 'Le' means 'eat'. Statement II alone is insufficient.
Step 3: Combine Statement I and Statement II.
We found 'Le' means 'eat'.
Now, from {'Le', 'Na'} <=> {'You', 'mangoes'} (from Step 1).
Since 'Le' means 'eat', and 'eat' is not 'You' or 'mangoes', there was an error in my initial common word deduction for Statement I. Let's restart the combination.
Revised Combination:
1. 'Te Le Pa Na' -> 'You eat many mangoes'
2. 'Le Na Da' -> 'You sell mangoes'
3. 'Ge Na Se La Le' -> 'They eat bananas and mangoes'
4. 'Ne De Le La' -> 'Who others eat bananas'
Compare (1) and (4): The only common word is 'eat'. The only common code is 'Le'. So, 'Le' = 'eat'.
Now substitute 'Le' = 'eat' into (1) and (3):
(1) 'Te eat Pa Na' -> 'You eat many mangoes'. Remaining: {'Te', 'Pa', 'Na'} -> {'You', 'many', 'mangoes'}.
(3) 'Ge Na Se La eat' -> 'They eat bananas and mangoes'. Remaining: {'Ge', 'Na', 'Se', 'La'} -> {'They', 'bananas', 'mangoes'}.
Now compare (1) (modified) and (3) (modified):
Common code is 'Na'. Common word is 'mangoes'.
Therefore, 'Na' means 'mangoes'.
Step 4: Conclude. Both Statement I and Statement II together are sufficient to determine the code for 'mangoes'.
6
A specific coding system replaces alphabets with numbers. If STREAM is coded as 23-24-22-9-5-17, what would be the code for BROOK?
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Solution: Step 1: Analyze the given coding pattern for STREAM: S=23, T=24, R=22, E=9, A=5, M=17.
Step 2: Identify the pattern: S(19)+4=23, T(20)+4=24, R(18)+4=22, E(5)+4=9, A(1)+4=5, M(13)+4=17.
Step 3: Apply the pattern to BROOK: B(2)+4=6, R(18)+4=22, O(15)+4=19, O(15)+4=19, K(11)+4=15.
Step 4: Determine the code for BROOK: 6-22-19-19-15.
Step 5: Match the code to the given options.
9
Given specific symbols denote certain relationships, determine which conclusions are definitely true based on the provided statements.
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Solution: Step 1: Interpret the symbols - % (greater than), > (equal to), = (not less than), @ (not equal to), # (less than), * (not greater than).
Step 2: Analyze statements - P > S, S @ T, P # R.
Step 3: Convert to standard inequality terms - P > S, S ≠T, P < R.
Step 4: Evaluate Conclusion I - S > R is not supported because P < R and P > S does not guarantee S > R.
Step 5: Evaluate Conclusion II - P @ T or P ≠T is supported because P = S and S ≠T, hence P ≠T.
Step 6: Conclusion II is true.
10
In a code, EQUITY is written as FSXMYE. What is the code for MARKET?
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Solution: Step 1: Identify the pattern in EQUITY to FSXMYE
- E+1=F, Q+2=S, U+3=X, I+4=M, T+5=Y, Y+6=E
Step 2: Apply the pattern to MARKET
- M+1=N, A+2=C, R+3=U, K+4=O, E+5=J, T+6=Z
Step 3: Determine the code for MARKET
- The code for MARKET is NCUOJZ.
12
How is 'No' coded in the code language? Determine if the provided statements are sufficient.
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Solution: Step 1: Analyze Statement I, which provides two coded sentences:
- 'Ne Pa Sic Lo' means 'But No None And'
- 'Pa Lo Le Ne' means 'If None And But'
Step 2: Compare the two sentences in Statement I. Identify common words: 'But', 'None', 'And'. Identify common code words: 'Ne', 'Pa', 'Lo'.
Step 3: This implies that the set {'Ne', 'Pa', 'Lo'} corresponds to the set {'But', 'None', 'And'}.
Step 4: In the first sentence ('Ne Pa Sic Lo' means 'But No None And'), if 'Ne', 'Pa', 'Lo' are codes for 'But', 'None', 'And', then the remaining code word 'Sic' must be the code for the remaining word 'No'.
Step 5: Therefore, Statement I alone is sufficient to determine the code for 'No'.
Step 6: Analyze Statement II, which provides two coded sentences:
- 'Le Se Ne Sic' means 'If No None Will'
- 'Le Pi Se Be' means 'Not None If All'
Step 7: From the first sentence of Statement II, we see 'No' is present. Comparing the two sentences in Statement II, common words are 'If', 'None'. Common codes are 'Le', 'Se'.
Step 8: This implies {'Le', 'Se'} corresponds to {'If', 'None'}. In the first sentence, 'Ne Sic' remain for 'No Will'. We cannot uniquely determine 'No' from 'Ne' or 'Sic'. So, Statement II alone is not sufficient.
Step 9: Therefore, Statement I alone is sufficient while Statement II alone is not sufficient.
13
In a coding system, 'OFFICE' is encoded as 422168 and 'CEREAL' as 683857. What is the code for 'CLAIR'?
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Solution: Step 1: Analyze given codes: 'OFFICE' = 422168 and 'CEREAL' = 683857
Step 2: Determine alphabet-number substitutions: O=4, F=2, I=1, C=6, E=8, R=3, A=7, L=5
Step 3: Apply substitutions to 'CLAIR': C=6, L=5, A=7, I=1, R=3
Step 4: Combine numbers: 65813
19
Given the coding rule where 'Corden' is coded as 'zrogbq', identify the original word that is coded as 'pxivro'.
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Solution: Step 1: Analyze the coding pattern from 'Corden' to 'zrogbq' by comparing corresponding letter positions (A=1, Z=26):
C (3) -> z (26): C - 3 = Z (3-3=0, which wraps to 26)
O (15) -> r (18): O + 3 = R
R (18) -> o (15): R - 3 = O
D (4) -> g (7): D + 3 = G
E (5) -> b (2): E - 3 = B
N (14) -> q (17): N + 3 = Q
Step 2: The coding pattern is an alternating shift of -3, +3, -3, +3, -3, +3 for consecutive letters.
Step 3: To find the original word for 'pxivro', we need to apply the reverse operations: +3, -3, +3, -3, +3, -3.
p (16) -> p + 3 = s (19)
x (24) -> x - 3 = u (21)
i (9) -> i + 3 = l (12)
v (22) -> v - 3 = s (19)
r (18) -> r + 3 = u (21)
o (15) -> o - 3 = l (12)
Step 4: Therefore, the original word is 'sulsul'.