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CAT 2019 Slot 1 DILR · Set 1 of 8Logical ReasoningEasy DifficultyQ1–Q4 · 0 MCQ + 4 TITA

CAT 2019 Slot 1 DILR Set 1: Coding/Decoding (4 Questions) with Solutions

The Coding/Decoding set from the official CAT 2019 Slot 1 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2019 Slot 1 DILR · Questions 1–4
The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.
Official Reference Chart - CAT 2019 Slot 1 Official Reference Chart - CAT 2019 Slot 1

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q1. Coding/Decoding

TITA · +3 / 0
Which digit does the letter A represent?
Correct Answer
1
Step-by-step solution
📌 Core Concept
Column-wise addition with carries. The units column fixes FF, and the leftmost columns then fix BB and AA.
🔢 Step-by-Step Solution
1
Units column: F+FF+F ends in FF, so F=0F=0 and no carry goes to the tens column.
2
Tens column: G+KG+K ends in AA. Call the carry out of it c2c_2.
3
Hundreds column: A+F+c2A+F+c_2 ends in CC, which means A+c2A+c_2 ends in CC. Since A≠CA\ne C, c2=1c_2=1. Then C=A+1C=A+1 with no carry. (A=9A=9 would give C=0=FC=0=F, which is not allowed.)
4
Ten-thousands column: H+H+c4H+H+c_4 ends in F=0F=0, so 2H+c4=102H+c_4=10. This gives H=5H=5, c4=0c_4=0, and a carry of 1.
5
Hundred-thousands column: B+A+1B+A+1 ends in AA, so B+1=10B+1=10 and B=9B=9, with a carry of 1.
6
The seventh digit of the sum is just this carry. It is the leading AA, so A=1A=1.
Quick Check
Then C=2C=2. The leading AA in the sum is 1, which matches the carry from the top column.
Correct Answer: 1

Q2. Coding/Decoding

TITA · +3 / 0
Which digit does the letter B represent?
Correct Answer
9
Step-by-step solution
📌 Core Concept
Column-wise addition with carries. The units column fixes FF, and the top columns then fix BB.
🔢 Step-by-Step Solution
1
Units column: F+FF+F ends in FF, so F=0F=0 with no carry.
2
Hundreds column: A+0+c2A+0+c_2 ends in CC with C≠AC\ne A, so the carry from the tens column is c2=1c_2=1 and C=A+1C=A+1. There is no carry out of this column, because A=9A=9 would force C=0=FC=0=F.
3
Ten-thousands column: 2H+c42H+c_4 ends in 0, so H=5H=5 and c4=0c_4=0. This column sends a carry of 1 to the next one.
4
Hundred-thousands column: B+A+1B+A+1 must end in AA, so B+1=10B+1=10 and B=9B=9.
5
The carry out of this column forms the leading digit of the sum, so it is 1. That leading digit is AA, so A=1A=1 and the numbers are consistent.
Correct Answer: 9

Q3. Coding/Decoding

TITA · +3 / 0
Which among the digits 3, 4, 6 and 7 cannot be represented by the letter D?
Correct Answer
7
Step-by-step solution
📌 Core Concept
Solve the fixed letters first, then list every assignment of the leftover digits that satisfies the tens and thousands columns.
🔢 Step-by-Step Solution
1
The units column gives F=0F=0. The hundreds and ten-thousands columns give C=A+1C=A+1 and H=5H=5. The top columns give B=9B=9 and A=1A=1, so C=2C=2.
2
Tens column: G+K=A+10=11G+K=A+10=11.
3
Thousands column: A+J+c3=GA+J+c_3=G. We have c3=0c_3=0 and no carry out, since c4=0c_4=0. So G=J+1G=J+1.
4
The digits 0, 1, 2, 5, 9 are already used, so GG, JJ, KK come from {3,4,6,7,8}\{3,4,6,7,8\}. Check (J,G,K)(J,G,K):
J=3J=3, G=4G=4, K=7K=7 works. DD and EE are then 6 and 8.
J=6J=6, G=7G=7, K=4K=4 works. DD and EE are then 3 and 8.
J=7J=7, G=8G=8, K=3K=3 works. DD and EE are then 4 and 6.
J=4J=4 gives G=5G=5, which is taken by HH. J=8J=8 gives G=9G=9, which is taken by BB.
5
So DD can be 6, 8, 3 or 4. The digit 7 is used by KK or GG in every valid case, so it can never go to DD.
Correct Answer: 7

Q4. Coding/Decoding

TITA · +3 / 0
Which among the digits 4, 6, 7 and 8 cannot be represented by the letter G?
Correct Answer
6
Step-by-step solution
📌 Core Concept
Solve the fixed letters first, then list every assignment of the leftover digits that satisfies the tens and thousands columns.
🔢 Step-by-Step Solution
1
The units column gives F=0F=0. The hundreds and ten-thousands columns give C=A+1C=A+1 and H=5H=5. The top columns give B=9B=9 and A=1A=1, so C=2C=2.
2
Tens column: G+K=A+10=11G+K=A+10=11.
3
Thousands column: A+J=GA+J=G with no carry, so G=J+1G=J+1.
4
GG, JJ, KK come from {3,4,6,7,8}\{3,4,6,7,8\} because 0, 1, 2, 5, 9 are already used. Check (J,G,K)(J,G,K):
(3,4,7)(3,4,7) works.
(6,7,4)(6,7,4) works.
(7,8,3)(7,8,3) works.
J=4J=4 gives G=5G=5, which is taken by HH. J=8J=8 gives G=9G=9, which is taken by BB.
5
GG can therefore be 4, 7 or 8. Among 4, 6, 7 and 8, the digit 6 is the one GG can never take. G=6G=6 would need J=5J=5, which is taken by HH.
Correct Answer: 6
Timed Practice

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CAT 2019 Slot 1 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Kozhikode

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