Question

If in a certain code CRYSTAL is written as DTJSXFR, then in the same code how is QUANTUM written?

• A. WRDNXZS
• B. RWDNYZS
• C. RWDNXZS
• D. RWNDXZS

Hint:

For coding sequences, look for a fixed per-position shift pattern by comparing the sample input and output letter by letter.

Answer 1

The Correct Option is C

Step 1: Decode the rule from the example.
From \(\text{CRYSTAL} \rightarrow \text{DTJSXFR}\), each position is shifted by a fixed amount (mod 26):
1st \(+1\), 2nd \(+2\), 3rd \(+3\), 4th \(+0\), 5th \(+4\), 6th \(+5\), 7th \(+6\). (These are forward shifts in the alphabet, wrapping around after \(Z\).) Step 2: Apply the same position-wise shifts to QUANTUM.
\[ \begin{aligned} \text{Q}(+1) &\Rightarrow \text{R},
\text{U}(+2) &\Rightarrow \text{W},
\text{A}(+3) &\Rightarrow \text{D},
\text{N}(+0) &\Rightarrow \text{N},
\text{T}(+4) &\Rightarrow \text{X},
\text{U}(+5) &\Rightarrow \text{Z},
\text{M}(+6) &\Rightarrow \text{S}. \end{aligned} \] Thus, \(\text{QUANTUM} \Rightarrow \boxed{\text{RWDNXZS}}\).