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CAT 2019 Slot 2 DILR · Set 2 of 8Logical ReasoningModerate DifficultyQ5–Q8 · 0 MCQ + 4 TITA

CAT 2019 Slot 2 DILR Set 2: Grids (4 Questions) with Solutions

The Grids set from the official CAT 2019 Slot 2 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 2 DILR · Questions 5–8
Three pouches (each represented by a filled circle) are kept in each of the nine slots in a 3×33 \times 3 grid, as shown in the figure. Every pouch has a certain number of one-rupee coins. The minimum and maximum amounts of money (in rupees) among the three pouches in each of the nine slots are given in the table. For example, we know that among the three pouches kept in the second column of the first row, the minimum amount in a pouch is Rs. 6 and the maximum amount is Rs.
8
There are nine pouches in any of the three columns, as well as in any of the three rows. It is known that the average amount of money (in rupees) kept in the nine pouches in any column or in any row is an integer. Hence the sum of nine pouches in any row or column should be a multiple of 9. It is also known that the total amount of money kept in the three pouches in the first column of the third row is Rs.
4
![Figure 1 - CAT 2019 Slot 2](/images/questions/cat-2019-s2-dilr-ld8AksUcxLgW4hI.webp)
Figure 2 - CAT 2019 Slot 2 Figure 2 - CAT 2019 Slot 2

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

Q5. Grids

TITA · +3 / 0
What is the total amount of money (in rupees) in the three pouches kept in the first column of the second row?
Correct Answer
13
Step-by-step solution
📌 Core Concept
Each slot's (min, max) pair limits its total to a short range. The multiple-of-9 condition on every row and column sum then fixes each total.
🔢 Step-by-Step Solution
1
For a slot with minimum aa and maximum bb, the total lies between 2a+b2a+b and a+2ba+2b. The ranges are: R1 = 8-10, 20–22, 5–7. R2 = 11–13, 3, 32–46. R3 = 4, 4–5, 9–12.
2
The slot (1, 1) means all three pouches hold Re 1, so the total is 3. The given total of 4 in R3C1 fits (1, 1, 2).
3
Row 1 sums to between 33 and 39, so it is 36. Row 2 sums to between 46 and 62, so it is 54. Row 3 sums to between 17 and 21, so it is 18.
4
Column 1 sums to between 23 and 27, so it is 27. Column 2 sums to between 27 and 30, so it is 27.
5
Row 3 gives 4+x+y=184 + x + y = 18, where xx is the R3C2 total (4 or 5) and yy is the R3C3 total (9 to 12). Column 2 gives R1C2 =27−3−x=24−x= 27 - 3 - x = 24 - x. This must be at least 20, so x=4x = 4 and R1C2 =20= 20.
6
Column 1 gives R1C1 + R2C1 =27−4=23= 27 - 4 = 23. With R1C1 in 8-10 and R2C1 in 11-13, the only pair is 10+1310 + 13. So R2C1 =13= 13, and the pouches are (3, 5, 5).
Quick Check
Row 1 gives R1C3 =36−10−20=6= 36 - 10 - 20 = 6. Row 2 gives R2C3 =54−13−3=38= 54 - 13 - 3 = 38. Column 3 gives 6+38+10=546 + 38 + 10 = 54, a multiple of 9.
Correct Answer: 13

Q6. Grids

TITA · +3 / 0
How many pouches contain exactly one coin?
Correct Answer
8
Step-by-step solution
📌 Core Concept
The (min, max) ranges together with the multiple-of-9 row and column sums fix every slot total. The totals then show which pouches must hold exactly one coin.
🔢 Step-by-Step Solution
1
Slot totals lie in these ranges: R1 = 8–10, 20–22, 5–7. R2 = 11–13, 3, 32–46. R3 = 4, 4–5, 9–12.
2
Row sums must be 36, 54 and 18. Column 1 must sum to 27 and column 2 to 27.
3
Row 3 and column 2 together force R3C2 =4= 4 and R1C2 =20= 20. Column 1 then forces R1C1 =10= 10 and R2C1 =13= 13. Row 1 gives R1C3 =6= 6.
4
Now count the pouches holding exactly one coin slot by slot.
R1C1 has minimum 2, so none.
R1C2 has minimum 6, so none.
R1C3 has (min, max) = (1, 3) and total 6, so the pouches are (1, 2, 3). That gives 1.
R2C1 has minimum 3, so none.
R2C2 has (1, 1), so all three pouches hold Re 1. That gives 3.
R2C3 has minimum 6, so none.
R3C1 has total 4 with (1, 2), so the pouches are (1, 1, 2). That gives 2.
R3C2 has total 4 with (1, 2), so the pouches are (1, 1, 2). That gives 2.
R3C3 has minimum 2, so none.
5
The count is 1+3+2+2=81 + 3 + 2 + 2 = 8.
Correct Answer: 8

Q7. Grids

TITA · +3 / 0
What is the number of slots for which the average amount (in rupees) of its three pouches is an integer?
Correct Answer
2
Step-by-step solution
📌 Core Concept
The average of a slot's three pouches is an integer exactly when the slot total is a multiple of 3. So the task is to find all nine slot totals.
🔢 Step-by-Step Solution
1
The (min, max) pairs give total ranges: R1 = 8–10, 20–22, 5–7. R2 = 11–13, 3, 32–46. R3 = 4, 4–5, 9–12.
2
Row sums must be 36, 54 and 18, and column 1 and column 2 must each sum to 27.
3
Row 3 gives x+y=14x + y = 14 for R3C2 and R3C3. Column 2 gives R1C2 =24−x= 24 - x, which must be at least 20. So R3C2 =4= 4, R1C2 =20= 20 and R3C3 =10= 10.
4
Column 1 gives R1C1 + R2C1 =23= 23, which forces 10+1310 + 13. Row 1 gives R1C3 =36−30=6= 36 - 30 = 6. Row 2 gives R2C3 =54−16=38= 54 - 16 = 38.
5
The slot totals are: R1 = 10, 20, 6. R2 = 13, 3, 38. R3 = 4, 4, 10.
6
Only 6 and 3 are multiples of 3. These are R1C3 and R2C2.
Quick Check
Column 3 gives 6+38+10=546 + 38 + 10 = 54, which is a multiple of 9.
Correct Answer: 2

Q8. Grids

TITA · +3 / 0
The number of slots for which the total amount in its three pouches strictly exceeds Rs. 10 is
Correct Answer
3
Step-by-step solution
📌 Core Concept
Each slot's (min, max) pair limits its total, and the multiple-of-9 row and column sums then fix every total exactly. The totals can then be compared with 10.
🔢 Step-by-Step Solution
1
The total ranges are: R1 = 8–10, 20–22, 5–7. R2 = 11–13, 3, 32–46. R3 = 4, 4–5, 9–12.
2
Row sums must be 36, 54 and 18. Column 1 and column 2 must each sum to 27.
3
Row 3 gives x+y=14x + y = 14 for R3C2 and R3C3. Column 2 gives R1C2 =24−x= 24 - x, which must be at least 20. So R3C2 =4= 4, R1C2 =20= 20 and R3C3 =10= 10.
4
Column 1 gives R1C1 + R2C1 =23= 23, which forces 10+1310 + 13. Row 1 then gives R1C3 =6= 6, and row 2 gives R2C3 =38= 38.
5
The totals are: R1 = 10, 20, 6. R2 = 13, 3, 38. R3 = 4, 4, 10.
6
The totals strictly above 10 are 20, 13 and 38. The two slots with total exactly 10 do not count.
7
The count is 3.
Correct Answer: 3
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CAT 2019 Slot 2 DILR at a Glance

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

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