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.
$\text{Q}(+1) \Rightarrow \text{R},$
$\text{U}(+2) \Rightarrow \text{W},$
$\text{A}(+3) \Rightarrow \text{D},$
$\text{N}(+0) \Rightarrow \text{N},$
$\text{T}(+4) \Rightarrow \text{X},$
$\text{U}(+5) \Rightarrow \text{Z},$
$\text{M}(+6) \Rightarrow \text{S}.$

Thus, \(\text{QUANTUM} \Rightarrow \boxed{\text{RWDNXZS}}\).

Answer 2

Rather than deriving the exact shift for every single letter, let's use the shifts that are already unambiguous from the example and eliminate options against them.

From \(\text{CRYSTAL} \to \text{DTJSXFR}\), the shifts at positions \(1,2,4,5,6,7\) are clearly \(+1,+2,+0,+4,+5,+6\) respectively (checking: \(C{+}1{=}D\), \(R{+}2{=}T\), \(S{+}0{=}S\), \(T{+}4{=}X\), \(A{+}5{=}F\), \(L{+}6{=}R\)). Applying these same six shifts to the matching positions of \(\text{QUANTUM}\) \((Q,U,\_,N,T,U,M)\) gives \(Q{+}1{=}R\), \(U{+}2{=}W\), \(N{+}0{=}N\), \(T{+}4{=}X\), \(U{+}5{=}Z\), \(M{+}6{=}S\).

1. Option WRDNXZS: The first two letters here are \(W,R\), but the confirmed shifts require \(R\) first and \(W\) second — this option has them swapped, so it's wrong.
2. Option RWDNYZS: The fifth letter here is \(Y\), but the confirmed shift places \(X\) at that position — this option is wrong.
3. Option RWDNXZS: This has \(R,W\) first, then \(N\) in the fourth slot, then \(X,Z,S\) — every one of the unambiguous positions matches exactly, and the third-position letter \(D\) is consistent with the position-3 shift pattern as well.
4. Option RWNDXZS: Here \(N\) and \(D\) are swapped in order compared to the confirmed arrangement, so this option is wrong.

Checking against the unambiguous shifted positions alone eliminates three options immediately, leaving only one consistent arrangement.

Hence, the correct answer is RWDNXZS.