CSAT Solved Papers/ 2021/Q56

2021 CSAT — Q56

Quant Logical & quantitative reasoning 2.5 marks Medium

In a code language ‘MATHEMATICS’ is written as ‘LBSIDNZUHDR’. How is ‘CHEMISTRY’ written in that code language?

A DIDLHRSSX
B BIDNHTSSX Answer
C BIDLHTSSX
D DGFLIRUQZ

Worked rationale

Compare each letter of MATHEMATICS to its code, using alphabet positions ( $A=1,\dots,Z=26$ ), and read the shift per position:

pos	1	2	3	4	5	6	7	8	9	10	11
plain	M	A	T	H	E	M	A	T	I	C	S
code	L	B	S	I	D	N	Z	U	H	D	R
shift	$-1$	$+1$	$-1$	$+1$	$-1$	$+1$	$-1$	$+1$	$-1$	$+1$	$-1$

The rule is $-1$ on odd positions, $+1$ on even positions (with wrap-around, e.g. position $7$ : $A\to Z$ ). Apply it to CHEMISTRY ( $9$ letters):

pos	1	2	3	4	5	6	7	8	9
plain	C	H	E	M	I	S	T	R	Y
shift	$-1$	$+1$	$-1$	$+1$	$-1$	$+1$	$-1$	$+1$	$-1$
code	B	I	D	N	H	T	S	S	X

So CHEMISTRY $\to$ BIDNHTSSX.

Answer: (b) BIDNHTSSX.

Why the other options miss

A

the parity flipped backwards: flips the parity (uses $+1$ on odds, $-1$ on evens) at the start, giving $C\to D$ , $M\to L$ .
C

an arithmetic slip: correct rule but slips on position $4$ ( $M\to L$ instead of $N$ ), one letter off.
D

the wrong rule applied: applies a uniform shift (all $+1$ or a Caesar-style constant) instead of the alternating $\mp 1$ .

Specialist insight

The decode is not a single Caesar shift — the shift alternates with position parity ( $-1,+1,-1,+1,\dots$ ). Recover it by tabulating plain-vs-code differences before touching the target word; the clean $\mp1$ pattern (and the $A\to Z$ wrap at an odd slot) confirms the rule. Then it’s mechanical, but watch the even slots ( $+1$ : $H\to I$ , $M\to N$ , $S\to T$ , $R\to S$ ) where the off-by-one distractor (c) is planted.

The trap, in one line

Shift is $-1$ on odd positions, $+1$ on even; CHEMISTRY $\to$ BIDNHTSSX $\Rightarrow$ (b).

← All 2021 CSAT questions