Question 1

In a certain code, the word "SOBER" is written by shifting every letter one position backward in the alphabet (S->R, O->N, B->A, E->D, R->Q). Using the same rule, how will "LOTUS" be written?

Accepted Answer

Introduction / Context:This problem belongs to the basic coding–decoding family where each letter of a word is transformed using a consistent substitution rule. Recognizing a uniform shift across all letters is a common exam pattern in verbal reasoning. Given Data / Assumptions: "SOBER" is written as a coded word by shifting letters backward by 1 place in the alphabet. We must apply the same letter shift to "LOTUS". Alphabet order assumed: A B C ... X Y Z; after A backward wraps to Z if needed. Concept / Approach:The rule is: for each letter, replace it with the previous alphabet letter. Example: B becomes A, C becomes B, and so on. This is a Caesar shift of -1 applied uniformly to all positions. Step-by-Step Solution:L -> KO -> NT -> SU -> TS -> RTherefore "LOTUS" becomes "KNSTR". Verification / Alternative check:Apply the same -1 shift to "SOBER": S->R, O->N, B->A, E->D, R->Q. The stated example demonstrates the very rule; our application to "LOTUS" is consistent. Why Other Options Are Wrong: MPUWT: mixes +1 changes; does not follow uniform -1. KMSTR: the second letter M implies -1 from N, not from O; inconsistent rule. LMRST: leaves first letter unchanged; not a -1 shift for all positions. None of these: invalid because KNSTR is valid and present. Common Pitfalls:Candidates sometimes shift only vowels or only consonants, or shift forward instead of backward. Another error is applying different shifts to different positions. Final Answer:KNSTR

Question 2

If the word "MEAT" is written as "TEAM" by swapping the first and last letters while keeping the middle order the same, then how will "BALE" be written in the same rule?

Accepted Answer

Introduction / Context:This question tests recognition of a simple positional transformation: interchanging the first and last letters while keeping the middle letters in their original order. Given Data / Assumptions: "MEAT" becomes "TEAM". The operation is to swap the first and last letters only. The internal sequence (middle letters) remains unchanged. Concept / Approach:For a 4-letter word ABCD, the transformed form is DBCA, i.e., swap A and D while leaving B and C intact. Step-by-Step Solution:BALE: first letter B, last letter E, middle letters A and L.Swap first and last: E _ _ B.Keep middle letters A and L in the same order to obtain EALB. Verification / Alternative check:Apply rule back to "TEAM": swapping first and last gives "MEAT", confirming consistency. Why Other Options Are Wrong: ELAB / EABL / EBLA: These disturb the order of the middle letters A and L. None of these: Not applicable since EALB fits perfectly. Common Pitfalls:Altering the order of the middle letters or attempting a full reversal instead of a boundary swap. Final Answer:EALB

Question 3

If "WATER" is encoded as "YCVGT" by shifting every letter forward by 2 positions in the alphabet (W->Y, A->C, T->V, E->G, R->T), then which word is encoded as "HKTG"?

Accepted Answer

Introduction / Context:This is a classic Caesar cipher problem with a constant forward shift. The example "WATER" -> "YCVGT" reveals a +2 shift applied uniformly to each letter. Given Data / Assumptions: Encoding rule: shift each letter +2 positions (A->C, B->D, ..., Y->A, Z->B). We are given the code "HKTG" and must find the original word. Concept / Approach:To decode a +2 cipher, shift letters backward by 2 positions. We apply -2 to each letter in "HKTG". Step-by-Step Solution:H -> FK -> IT -> RG -> ETherefore the decoded word is FIRE. Verification / Alternative check:Re-encode FIRE with +2: F->H, I->K, R->T, E->G which returns HKTG. Perfect consistency. Why Other Options Are Wrong: IRFE / REFI / ERIF: These are jumbled permutations, not the result of a uniform -2 decode. None of these: Not applicable because FIRE works exactly. Common Pitfalls:Shifting in the wrong direction, or mixing different shifts across positions. Final Answer:FIRE

Question 4

If "TABLECLOTH" is coded as "XEMRANRIXT" by a fixed letter-to-letter substitution based on positions in that specific word, then using the same mapping, how is "HOTEL" coded?

Accepted Answer

Introduction / Context:Some coding problems use a word-specific positional mapping rather than a universal shift. Here, "TABLECLOTH" is mapped to "XEMRANRIXT" position by position. We must reuse that mapping for any letter that appears in "TABLECLOTH". Given Data / Assumptions: TABLECLOTH -> XEMRANRIXT We need code for "HOTEL". Every letter H, O, T, E, L appears in the source word. Concept / Approach:Create a direct mapping from each source letter to its coded counterpart by aligning positions. Step-by-Step Solution:Positions: T A B L E C L O T HCodes: X E M R A N R I X THence the map: T->X, A->E, B->M, L->R, E->A, C->N, O->I, H->T.For "HOTEL": H->T, O->I, T->X, E->A, L->R giving "TIXAR". Verification / Alternative check:Rechecking the pairwise mapping confirms consistency for repeated letters L and T in the source. Why Other Options Are Wrong: RIXAT / TAXIR / RAXIT: These are permutations of the correct letters, but the order dictated by H,O,T,E,L is unique and yields TIXAR. None of these: Not applicable. Common Pitfalls:Assuming a Caesar shift, or confusing a many-to-one mapping. This cipher is strictly positional for the letters present in the key word. Final Answer:TIXAR

Question 5

If the word CARING is coded as EDVGKC, how will the word CASKET be coded using the same letter shifting pattern?

Accepted Answer

Introduction / Context:This is a word-coding question where each letter of the input word is transformed into another letter using a consistent rule. You are told that the word CARING becomes EDVGKC, and you must apply the exact same transformation pattern to a new word, CASKET, to find its coded form. The key is to detect the letter-by-letter shifting rule (how many steps forward or backward in the alphabet) and then repeat it precisely for the second word. Given Data / Assumptions:We use the English alphabet A to Z and shift letters forward or backward by a fixed number of positions. Wrap-around (after Z comes A, before A comes Z) is assumed if needed, though it will not be required here. CARING is coded as EDVGKC We must code CASKET using the same rule Alphabet positions: A=1, B=2, ..., Z=26 Concept / Approach:Compare each letter in CARING with the corresponding letter in EDVGKC and compute the shift. Often, such problems use a symmetric pattern: the first few letters move forward by increasing steps, and the last few letters move backward by the same increasing steps. Once the shift pattern is identified (like +2, +3, +4, then -2, -3, -4), apply it to the new word position-by-position. Step-by-Step Solution:First, find shifts from CARING to EDVGKC, then apply the same shifts to CASKET. Step 1: C -> E. C(3) to E(5) is +2.Step 2: A -> D. A(1) to D(4) is +3.Step 3: R -> V. R(18) to V(22) is +4.Step 4: I -> G. I(9) to G(7) is -2.Step 5: N -> K. N(14) to K(11) is -3.Step 6: G -> C. G(7) to C(3) is -4.So the shift pattern is: +2, +3, +4, -2, -3, -4.Now apply this to CASKET:Step 7: C +2 = E.Step 8: A +3 = D.Step 9: S +4 = W.Step 10: K -2 = I.Step 11: E -3 = B.Step 12: T -4 = P.Therefore, CASKET is coded as EDWIBP. Verification / Quick Check:The pattern is symmetric: the first half moves forward by 2, 3, 4 and the second half moves backward by 2, 3, 4. CASKET has 6 letters like CARING, so the same six-position rule fits perfectly. The computed letters (E, D, W, I, B, P) match a listed option, confirming consistency. Why Other Options Are Wrong:EDXIBP: The third letter should be W (S +4), but X implies a +5 shift at position 3.EDWIAP: The fifth letter must be B (E -3), but A indicates an incorrect backward shift.EDWPAI: The fourth letter should be I (K -2), but P is far off and breaks the -2 step rule.EDWI BQ: The last letter must be P (T -4), but Q implies -3, not -4. Common Pitfalls:A frequent mistake is to apply only forward shifts to every letter, or to reuse the same shift value for all positions. Another common error is to miss the mirror nature of the rule, where the last letters reverse direction (negative shifts). Also, do not guess from similar-looking options; always compute each letter carefully using the exact step for that position. Final Answer:The correct coded form of CASKET is EDWIBP.

Question 6

If "DEMOCRATIC" is written as "EDMORCATCI" by swapping positions (1↔2, 5↔6, 9↔10) and leaving other positions unchanged, then how will "CONTINUOUS" be written using the same positional swaps?

Accepted Answer

Introduction / Context:This question checks careful tracking of positional swaps. The example "DEMOCRATIC" -> "EDMORCATCI" shows specific pairs are exchanged while others stay fixed. Given Data / Assumptions: Swap positions 1↔2, 5↔6, 9↔10. All other positions remain the same. Target word: CONTINUOUS (10 letters). Concept / Approach:Index letters 1 through 10, perform the indicated swaps, then read the result left to right. Step-by-Step Solution:Original (index): 1 C, 2 O, 3 N, 4 T, 5 I, 6 N, 7 U, 8 O, 9 U, 10 S.Swap 1↔2: O C ...Swap 5↔6: positions 5 I and 6 N become N I.Swap 9↔10: positions 9 U and 10 S become S U.Keep others (3 N, 4 T, 7 U, 8 O) unchanged.Final string: O C N T N I U O S U -> "OCNTNIUOSU". Verification / Alternative check:Applying the same swap schedule back will return the original, as swaps are involutive. Why Other Options Are Wrong: OCTNNIOUSU / OTCNINUOUS / OTNCINUOSU: Each misplaces one or more letters around the 3–6 or 9–10 zones. None of these: Not needed since a valid option exists. Common Pitfalls:Mistiming swaps or performing additional swaps; writing after each swap step helps avoid mistakes. Final Answer:OCNTNIUOSU

Question 7

In a certain code, P is written as "#", A as "%", C as "$", and E as "@". Using the same code, how is "PEACE" written?

Accepted Answer

Introduction / Context:This is a direct symbol substitution problem. Each letter has a unique symbol mapping and the coded word is formed by replacing letters in order. Given Data / Assumptions: P -> # A -> % C -> $ E -> @ Target word: PEACE Concept / Approach:Replace letters one by one according to the mapping without rearranging positions. Step-by-Step Solution:P -> #E -> @A -> %C -> $E -> @Therefore "PEACE" is "#@%$@". Verification / Alternative check:Check each symbol against the mapping; all positions agree. Why Other Options Are Wrong: #@%@#: wrong at the 4th position (should be $ for C). #@#$@: wrong at the 3rd position (should be % for A). %#@$%: wrong order of letters; also ends with % instead of @. None of these: Not applicable as #@%$@ is valid. Common Pitfalls:Accidentally reordering letters or mixing the symbols for A and C since both are non-alphabetic and easy to confuse. Final Answer:#@%$@

Question 8

If "DELHI" is coded as "73541" and "CALCUTTA" as "82589662" using a consistent letter-to-digit mapping, then what is the code for "CALICUT"?

Accepted Answer

Introduction / Context:Letter–digit substitution with consistency across multiple examples is a staple pattern. We infer the mapping from two given words and reuse it. Given Data / Assumptions: DELHI -> 73541 CALCUTTA -> 82589662 Find code for CALICUT. Concept / Approach:Map each letter to its digit based on the examples. From DELHI we get D->7, E->3, L->5, H->4, I->1. From CALCUTTA we get C->8, A->2, L->5, C->8, U->9, T->6, T->6, A->2. Step-by-Step Solution:C->8A->2L->5I->1C->8U->9T->6Therefore "CALICUT" becomes 8251896. Verification / Alternative check:All letters appear in the mapping derived from the two examples; consistency holds. Why Other Options Are Wrong: 5279431 / 5978213 / 8543691: contain digits inconsistent with the deduced mapping at multiple positions. None of these: Not applicable since a consistent code exists. Common Pitfalls:Assuming position-based digits or averaging across examples; here the mapping is letter-specific and fixed. Final Answer:8251896

Question 9

If in a certain code the word "DAUGHTER" is written as "TERDAUGH" by moving the last three letters to the front, then how will "APTITUDE" be written using the same operation?

Accepted Answer

Introduction / Context:This tests recognition of a rotation operation: relocating a fixed block of letters from the end of a word to its beginning. Given Data / Assumptions: DAUGHTER -> TERDAUGH Operation: take the last three letters and place them at the front. Apply to APTITUDE. Concept / Approach:For a word W = X Y Z where Z are the last three letters, the coded form is Z X Y. Step-by-Step Solution:APTITUDE -> last three letters = U D E.Move UDE to front, leave the rest A P T I T unchanged.Result: UDEAPTIT. Verification / Alternative check:Applying the inverse (moving first three to end) returns the original, confirming correctness. Why Other Options Are Wrong: DEUAPTIT / DUEAPTIT: these permute the last-three block incorrectly. DAUEPTIT: intermixes the block with the original middle letters. None of these: Not needed since UDEAPTIT is valid. Common Pitfalls:Reversing the last-three block or moving four letters by mistake. Final Answer:UDEAPTIT

Question 10

The code "165135" represents the word "peace" using alphabet positions (p=16, e=5, a=1, c=3, e=5). Using the same rule, which word is represented by "1215225"?

Accepted Answer

Introduction / Context:Many coding questions represent words by concatenating alphabet positions of letters. Here, "peace" -> 16 5 1 3 5 equals 165135 when concatenated. We must reverse the process. Given Data / Assumptions: Alphabet index: a=1, b=2, ..., z=26. 165135 corresponds to p e a c e (16 5 1 3 5). We must match 1215225 to a candidate word. Concept / Approach:Try to parse 1215225 into valid 1–2 digit alphabet positions matching a common word from the options. Step-by-Step Solution:Check "love": letters l o v e.l=12, o=15, v=22, e=5 -> concatenation 12 15 22 5 equals 1215225.Hence 1215225 corresponds to "love". Verification / Alternative check:None of the other options map cleanly to 1215225 under simple concatenation of positions. Why Other Options Are Wrong: lead: 12 5 1 4 -> 12514, not 1215225. loop: 12 15 15 16 -> 12151516. aura: 1 21 18 1 -> 12181. None of these: Not applicable; "love" fits perfectly. Common Pitfalls:Forgetting that letters beyond 9 use two digits, which affects segmentation. Final Answer:love

Question 11

If PARK is coded as 5394, SHIRT as 17698, and PANDIT as 532068 using a consistent letter-to-digit mapping, then what is the code for NISHAR?

Accepted Answer

Introduction / Context:Here we infer a unique digit for each letter from multiple examples, then encode a new word using that deduced mapping. Given Data / Assumptions: PARK -> 5 3 9 4 SHIRT -> 1 7 6 9 8 PANDIT -> 5 3 2 0 6 8 Concept / Approach:From these, deduce: P->5, A->3, R->9, K->4, S->1, H->7, I->6, T->8, N->2, D->0. The mapping is consistent across the samples. Step-by-Step Solution:N->2I->6S->1H->7A->3R->9Hence NISHAR -> 261739. Verification / Alternative check:Cross-checking letters that appear in multiple given words (e.g., P, A, I, T) confirms the mapping is stable. Why Other Options Are Wrong: 266734 / 231954 / 201739: each mismaps at least one letter compared to the established mapping. None of these: Not needed since 261739 is consistent. Common Pitfalls:Misreading digit order from the examples or assuming position-based digits; here digits are letter-specific, not position-specific. Final Answer:261739

Question 12

In a certain code, words are encoded using the Atbash substitution (A↔Z, B↔Y, C↔X, ...). If "CERTAIN" is coded as "XVIGZRM" and "SEQUENCE" as "HVJFVMXV", how is "REQUIRED" coded?

Accepted Answer

Introduction / Context:Atbash cipher maps each letter to its mirror in the alphabet: A↔Z, B↔Y, C↔X, etc. The examples confirm this exact mapping. Given Data / Assumptions: CERTAIN -> XVIGZRM SEQUENCE -> HVJFVMXV We need the code for REQUIRED. Concept / Approach:Apply Atbash per letter: r->i, e->v, q->j, u->f, i->r, r->i, e->v, d->w. Step-by-Step Solution:R -> IE -> VQ -> JU -> FI -> RR -> IE -> VD -> WThus "REQUIRED" -> "IVJFRIVW". Verification / Alternative check:Testing random letters from the examples reproduces their given codes, validating the mapping. Why Other Options Are Wrong: FJIVWVIR / VJIFWTRY / WVJRIFVI: sequences conflict with Atbash at multiple positions. None of these: Not required since a correct option exists. Common Pitfalls:Reversing the word instead of mirroring letters, or applying a Caesar shift. Atbash is a fixed one-to-one mapping. Final Answer:IVJFRIVW

Question 13

In a coded language, a word is written in reverse order. If "BRINJAL" becomes "LAJNIRB", how will "LADYFINGER" be written?

Accepted Answer

Introduction / Context:Some coding problems simply reverse the order of letters in a word. The given example confirms full reversal without any substitution. Given Data / Assumptions: Rule: write letters from last to first. BRINJAL -> LAJNIRB. Target: LADYFINGER. Concept / Approach:Reverse the sequence of characters exactly. Step-by-Step Solution:LADYFINGER reversed is REGNIFYDAL.Breakdown: LADY | FINGER → reverse each position to get REGNIF + YDAL. Verification / Alternative check:Reverse "LAJNIRB" to retrieve "BRINJAL", confirming the rule. Why Other Options Are Wrong: RNEGIFYDAL / RINEGIFYDAL / RGENIFYDAL: these have local transpositions that do not match strict reversal. None of these: Not applicable since a precise reversal is listed. Common Pitfalls:Performing partial reversal or swapping only ends without flipping the entire sequence. Final Answer:REGNIFYDAL

Question 14

If the word "REASON" is coded as 5 and "BELIEVED" is coded as 7 by subtracting one from the total number of letters, what is the code number for "GOVERNMENT"?

Accepted Answer

Introduction / Context:Some verbal coding schemes map words to numbers through simple functions of word length. The examples suggest a pattern: output equals length minus one. Given Data / Assumptions: REASON has 6 letters and is coded as 5. BELIEVED has 8 letters and is coded as 7. Hence code = number of letters - 1. Concept / Approach:Apply the same function to the new word. Step-by-Step Solution:GOVERNMENT length = 10 letters.Code = 10 - 1 = 9. Verification / Alternative check:Check the rule on the given words; both align perfectly with length minus one. Why Other Options Are Wrong: 10 / 6 / 8: these correspond to other length-related guesses but do not fit both examples simultaneously. None of these: Not required since 9 is consistent. Common Pitfalls:Overcomplicating the logic by counting vowels or consonants; the simplest hypothesis that fits all samples is best. Final Answer:9

Question 15

If "LOFTY" is coded as "LPFUY" by keeping letters at odd positions unchanged and shifting letters at even positions forward by 1 (O->P, T->U), then how will "DWARF" be written?

Accepted Answer

Introduction / Context:This positional coding rule alters only the even-indexed characters by a +1 shift while leaving odd-indexed characters unchanged. "LOFTY" -> "LPFUY" demonstrates this pattern. Given Data / Assumptions: Positions counted from 1 on the left. Odd positions unchanged; even positions shift forward by 1. Alphabet wraps after Z if required. Concept / Approach:Apply the rule per position to "DWARF". Step-by-Step Solution:1 D (odd) -> D2 W (even) -> X3 A (odd) -> A4 R (even) -> S5 F (odd) -> FThus, code = DXASF. Verification / Alternative check:Check "LOFTY": L stays, O->P, F stays, T->U, Y stays, giving LPFUY as provided. Why Other Options Are Wrong: DXBSG / DXATF / DWBSG: these modify odd positions or apply mismatched shifts to even positions. None of these: Not applicable since DXASF is valid. Common Pitfalls:Starting index from 0, or applying the shift to all letters rather than only even positions. Final Answer:DXASF

Question 16

A letter–number code is given as follows (top row letters, bottom row numbers): C W E A Z X J Y K L / 3 9 5 7 4 8 1 0 2 6. Using this mapping, what is the code for J W X C L Z?

Accepted Answer

Introduction / Context:This is a direct lookup coding task. Each specified letter corresponds to a unique number as per the provided two-row table. Given Data / Assumptions: C->3, W->9, E->5, A->7, Z->4, X->8, J->1, Y->0, K->2, L->6 Target sequence: J W X C L Z Concept / Approach:Substitute numbers for letters in the given order without reordering. Step-by-Step Solution:J -> 1W -> 9X -> 8C -> 3L -> 6Z -> 4Hence the code is 198364. Verification / Alternative check:Cross-check each mapping back to the table; all positions align. Why Other Options Are Wrong: 198264 / 198354 / 197354: each includes at least one digit mismatch compared to the mapping. None of these: Not needed, since 198364 is exact. Common Pitfalls:Transposing digits for X and C or misreading L as 5 instead of 6. Final Answer:198364

Question 17

If 54 + 43 = 2 and 60 + 51 = 10 by a special rule, then what is the value of 62 + 72 under the same rule?

Accepted Answer

Introduction / Context:These puzzles often redefine "+" by a hidden rule, frequently using digit operations. We must infer the rule that makes the sample equalities true. Given Data / Assumptions: 54 + 43 = 2 60 + 51 = 10 Find 62 + 72. Concept / Approach:Consider sum of absolute differences of corresponding digits: (tens difference) + (ones difference). This fits both examples elegantly. Step-by-Step Solution:For 54 and 43: |5-4| + |4-3| = 1 + 1 = 2.For 60 and 51: |6-5| + |0-1| = 1 + 1 = 2, which does not match 10. Try digit-wise difference without absolute value but multiplication by position? Another simple pattern is (tens difference)* (ones difference): (5-4)*(4-3)=1*1=1, not 2. A more consistent fit is to sum differences separately as (5-0) + (4-? )? Instead, observe another valid rule: sum of digit differences across cross-pairs: |5-1| + |4-0| = 4 + 4 = 8, still not 10. Now notice a better consistent rule: (first tens - first ones) + (second tens - second ones). For 54, 43: (5-4)+(4-3)=1+1=2. For 60, 51: (6-0)+(5-1)=6+4=10, which matches.Apply to 62 and 72: (6-2)+(7-2)=4+5=9. Verification / Alternative check:This rule matches both given examples exactly and yields a unique answer for the query pair. Why Other Options Are Wrong: 30 / 18 / 20: do not follow from the established digit-difference rule. None of these: Not necessary since 9 is obtained consistently. Common Pitfalls:Using absolute sums of digit differences in the same places, which fails for 60 and 51. Final Answer:9

Question 18

If "SEARCH" is coded as "TFBSDI" by shifting each letter forward by 1 in the alphabet, then how will "PENCIL" be coded?

Accepted Answer

Introduction / Context:This is a uniform Caesar shift of +1. The example "SEARCH" -> "TFBSDI" validates the rule. Given Data / Assumptions: Encode by advancing each letter by 1 (Z wraps to A). Target word: PENCIL. Concept / Approach:Shift each letter of PENCIL forward by 1. Step-by-Step Solution:P -> QE -> FN -> OC -> DI -> JL -> MHence "PENCIL" becomes "QFODJM". Verification / Alternative check:Re-applying -1 on QFODJM returns PENCIL, confirming the mapping. Why Other Options Are Wrong: RGPEN / LICNEP / QDMBHK: not consistent with a +1 shift across all positions. None of these: Not applicable since a correct code exists. Common Pitfalls:Accidentally shifting only vowels or only consonants, or reversing the shift direction. Final Answer:QFODJM

Question 19

Evaluate the expression by following the left-to-right operation order for the given fractions. Compute: 15/20 ÷ 4/5 × 2/3 × 8/5

Accepted Answer

Introduction / Context:This problem checks careful handling of fractional operations. The key is to apply division and multiplication from left to right, converting division by a fraction into multiplication by its reciprocal, and simplifying where possible before multiplying to avoid large numerators and denominators. Given Data / Assumptions: Expression: 15/20 ÷ 4/5 × 2/3 × 8/5 All numbers are rational fractions. Operations must be evaluated left to right for multiplication and division. Concept / Approach:Use the rule a/b ÷ c/d = a/b × d/c. Then simplify factors by canceling common terms across numerators and denominators. This reduces arithmetic effort and minimizes mistakes. Step-by-Step Solution:1) Simplify 15/20 = 3/4.2) Divide by 4/5: 3/4 ÷ 4/5 = 3/4 × 5/4 = 15/16.3) Multiply by 2/3: 15/16 × 2/3 = 30/48 = 5/8 after canceling by 6.4) Multiply by 8/5: 5/8 × 8/5 = 1 after canceling 5 with 5 and 8 with 8. Verification / Alternative check:Numerically, 15/20 = 0.75; 0.75 ÷ 0.8 = 0.9375; 0.9375 × 0.666… ≈ 0.625; 0.625 × 1.6 = 1.0. Both exact fraction arithmetic and decimal sanity check agree. Why Other Options Are Wrong: 0: Would require a zero factor or cancellation to zero, which never occurs. 3 and 5: These are typical results of mis-ordering operations or forgetting to invert during division by a fraction. Common Pitfalls:Not inverting the second fraction when dividing, multiplying numerators and denominators without simplification, or reordering operations incorrectly. Final Answer:1

Question 20

Coding rule: each letter is shifted by +2 positions in the alphabet (wrap around from Z to B). If FATHER is coded as HCVJGT, how is SHIP coded?

Accepted Answer

Introduction / Context:This is a classic Caesar shift puzzle. The demonstration mapping FATHER → HCVJGT indicates that each letter has been advanced by +2 places in the alphabet, with wrap-around after Z. Given Data / Assumptions: Known example: F → H, A → C, T → V, H → J, E → G, R → T (each +2). Task: Apply the same +2 shift to the word SHIP. Alphabet wraps: Y → A, Z → B if needed. Concept / Approach:For each plaintext letter L, compute code(L) = L shifted forward by 2. Maintain case and positions. Step-by-Step Solution:S → U (+2)H → J (+2)I → K (+2)P → R (+2)Therefore, SHIP → UJKR. Verification / Alternative check:Cross-check a couple of letters against the example mapping (e.g., R → T is +2; similarly P → R is +2). The rule is consistent. Why Other Options Are Wrong: TTJQ: Contains T for S (+1 instead of +2) and other shifts off by one. THKR / UKJR: Mix of incorrect positions and partial swaps; do not consistently apply +2 to every character. Common Pitfalls:Applying +1, forgetting wrap-around, or permuting letters instead of letterwise shifting. Final Answer:UJKR

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