CSAT Solved Papers/ 2022/Q16

2022 CSAT — Q16

Quant Logical & quantitative reasoning 2.5 marks Easy

If the order of the letters in the English alphabet is reversed and each letter represents the letter whose position it occupies, then which one of the following represents ‘LUCKNOW’?

A OGXPMLD
B OGXQMLE
C OFXPMLE
D OFXPMLD Answer

Worked rationale

Reversing the alphabet maps each letter to its complement: position $k \mapsto 27 - k$ , i.e. $A\leftrightarrow Z,\ B\leftrightarrow Y,\ \dots,\ M\leftrightarrow N$ .

Encode LUCKNOW letter by letter:

$L\,(12) \to 27-12 = 15 = O$
$U\,(21) \to 6 = F$
$C\,(3) \to 24 = X$
$K\,(11) \to 16 = P$
$N\,(14) \to 13 = M$
$O\,(15) \to 12 = L$
$W\,(23) \to 4 = D$

Reading off: $\mathbf{OFXPMLD}$ .

Answer: (d) OFXPMLD.

Why the other options miss

A

an arithmetic slip: maps $U\,(21) \to G$ instead of $F$ (uses $27-20$ , an off-by-one on $U$ ‘s position).
B

an arithmetic slip: two slips ( $U\to G$ , $K\to Q$ , $W\to E$ ) compounding the position arithmetic.
C

an arithmetic slip: correct except $W\,(23)\to D$ is mis-set to $E\,(=27-22)$ .

Specialist insight

Use the single rule $k \mapsto 27 - k$ and lock the easy anchors first: $M\leftrightarrow N$ is the centre, and $A\leftrightarrow Z$ the ends. The distractors are engineered as one-letter slips (especially $U\to F$ vs $G$ and $W\to D$ vs $E$ ), so verify the two trickiest letters ( $U, W$ ) rather than the obvious ones. $27 - 21 = 6 = F$ and $27 - 23 = 4 = D$ settle it.

The trap, in one line

$k\mapsto 27-k$ : $U\to F$ (not $G$ ) and $W\to D$ (not $E$ ) decide it $\Rightarrow$ OFXPMLD $=$ (d).

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