NIMCET 2008 Reasoning PYQ — Substitute digits for the letters to make the following relation … | Mathem Solvex | Mathem Solvex
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NIMCET 2008 — Reasoning PYQ
NIMCET | Reasoning | 2008
Substitute digits for the letters to make the following relation true.
S T I L L
+W I T H I N
Note: The leftmost letter can’t be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g., if you substitude 3 for the letters S, no other letter can be 3 and all other S in the puzzle must be 3.
Choose the correct answer:
A.
98533+258056=356589
(Correct Answer)
B.
41211+527013=938224
C.
98533+158056=256589
D.
47166+517013=614179
Correct Answer:
98533+258056=356589
Explanation
1. Check Option (a):98533+258056=356589
Words:STILL=98533, WITHIN=258056, LIMITS=356589
Mapping Check:
L=3 (from STILL)
L=3 (from LIMITS) — Matches.
I=5 (from STILL)
I=5 (from WITHIN and LIMITS) — Matches.
Sum Check:98533+258056=356589. — Correct.
Constraint Check: All letters have unique digits.
2. Check Option (b):41211+527013=938224
Mapping Check:L=1 in STILL, but L=9 in LIMITS.
Result:Invalid (One letter cannot represent two different digits).
3. Check Option (c):98533+158056=256589
Sum Check:98533+158056=256589. — Correct.
Mapping Check:
In STILL, S=9 and T=8.
In LIMITS, S=9 and T=8. — Matches.
However, compare STILL (98533) and WITHIN (158056):
I=5 (in STILL)
I=5 (in WITHIN) — Matches.
Wait: Let's look at the mapping for L. In STILL, L=3. In LIMITS, L=2.
Result:Invalid (L must be the same digit).
4. Check Option (d):47166+517013=614179
Mapping Check:L=6 in STILL, but L=6 is not the starting digit of LIMITS (which starts with 6, meaning L=6).
Sum Check:47166+517013=564179, not 614179.
Result:Invalid.
Final Answer:
The only option that satisfies the sum and the one-to-one letter-to-digit mapping is (a).
Correct Option: (a)
Explanation
1. Check Option (a):98533+258056=356589
Words:STILL=98533, WITHIN=258056, LIMITS=356589
Mapping Check:
L=3 (from STILL)
L=3 (from LIMITS) — Matches.
I=5 (from STILL)
I=5 (from WITHIN and LIMITS) — Matches.
Sum Check:98533+258056=356589. — Correct.
Constraint Check: All letters have unique digits.
2. Check Option (b):41211+527013=938224
Mapping Check:L=1 in STILL, but L=9 in LIMITS.
Result:Invalid (One letter cannot represent two different digits).
3. Check Option (c):98533+158056=256589
Sum Check:98533+158056=256589. — Correct.
Mapping Check:
In STILL, S=9 and T=8.
In LIMITS, S=9 and T=8. — Matches.
However, compare STILL (98533) and WITHIN (158056):
I=5 (in STILL)
I=5 (in WITHIN) — Matches.
Wait: Let's look at the mapping for L. In STILL, L=3. In LIMITS, L=2.
Result:Invalid (L must be the same digit).
4. Check Option (d):47166+517013=614179
Mapping Check:L=6 in STILL, but L=6 is not the starting digit of LIMITS (which starts with 6, meaning L=6).
Sum Check:47166+517013=564179, not 614179.
Result:Invalid.
Final Answer:
The only option that satisfies the sum and the one-to-one letter-to-digit mapping is (a).