Directions : Read the given information carefully and answer the questions…
2023
Directions : Read the given information carefully and answer the questions based on it:
There is a matrix contains 4 rows (I, II, III and IV) top to bottom and 4 columns (I, II, III and IV) left to right.
Meaningful Word will be formed only when we go left to right in row and top to bottom in column.
Condition:
• No letters are repeated more than twice.
• Alphabets are coded as A-1, B-2, C-3, D-4, E-5, F-1, G-2, H-3, I-4…………. Y-5, Z-1.
• Place value of column and row are added to get cell value of particular row or column.
• If a column/row has one letter then the entire column/row should not have that letter. For ex- if row 1
and column 1 has ‘M’ letter then that letter should not be repeated in entire row 1 and column 1.
4 letter meaningful word has to be formed in each column:
In column I: I, II, IV positions contain letter V, A, T respectively.
In column II: III, IV positions contain letter H, O respectively.
In column III: II position contain letter R.
In column IV: I, III, IV position contain letter N, T, S respectively.
What is the difference between the total value of column III and total value of row 1?
- A.
1
- B.
3
- C.
4
- D.
2
- E.
None of the above
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
This is a matrix word-building puzzle. Each 4-letter column (read top to bottom) and each 4-letter row (read left to right) must spell a valid English word, while every cell also carries a numeric code under a repeating A–E = 1–5 cycle (A1, B2, C3, D4, E5, F1, G2 …, so the code of a letter is its position modulo 5). The "value" of a row or column is the sum of the codes of its four letters. To answer, first reconstruct the whole grid from the word constraints, then add up the codes.
Step 1 — Reconstruct the grid
Fill each column so it forms a meaningful word, checking that every crossing row also spells a word and that no letter repeats inside any single row or column:
Column I has V, A, _, T → the only word is VAST, so cell (III, I) = S.
Column II ends in _, _, H, O → ECHO, so (I, II) = E and (II, II) = C.
Column IV is N, _, T, S → NETS, so (II, IV) = E.
Row II is now A, C, R, E → ACRE, which fixes (II, III) = R (matching the given R).
Row I is V, E, _, N → VEIN, so (I, III) = I.
Column III is I, R, _, _ and Row III is S, H, _, T → IRON down and SHOT across give (III, III) = O and (IV, III) = N.
Row IV is T, O, N, S → TONS. The grid is complete.
The completed grid (with each letter's code in brackets):
Col I | Col II | Col III | Col IV | |
|---|---|---|---|---|
Row I | V (2) | E (5) | I (4) | N (4) |
Row II | A (1) | C (3) | R (3) | E (5) |
Row III | S (4) | H (3) | O (5) | T (5) |
Row IV | T (5) | O (5) | N (4) | S (4) |
Validity check: no letter appears more than twice anywhere, and no letter repeats within any single row or column, so all conditions hold.
Step 2 — Add the required codes
Total value of Column III (IRON) = I(4) + R(3) + O(5) + N(4) = 16.
Total value of Row I (VEIN) = V(2) + E(5) + I(4) + N(4) = 15.
Difference = 16 − 15 = 1.
Cross-check
Re-deriving Column III independently from its word IRON (4+3+5+4 = 16) and Row I from VEIN (2+5+4+4 = 15) gives the same totals, so the difference is firmly 1.
Required difference = 1.