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CAT 2020 Slot 3 DILR · Set 5 of 5Logical ReasoningHard DifficultyQ19–Q24 · 6 MCQ

CAT 2020 Slot 3 DILR Set 5: Grids (6 Questions) with Solutions

The Grids set from the official CAT 2020 Slot 3 DILR paper: the caselet, all 6 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 2020 Slot 3 DILR · Questions 19–24
A farmer had a rectangular land containing 205 trees. He distributed that land among his four daughters – Abha, Bina, Chitra and Dipti by dividing the land into twelve plots along three rows (X,Y,Z) and four Columns (1,2,3,4) as shown in the figure below:
The plots in rows X, Y, Z contained mango, teak and pine trees respectively. Each plot had trees in non-zero multiples of 3 or 4 and none of the plots had the same number of trees. Each daughter got an even number of plots. In the figure, the number mentioned in top left corner of a plot is the number of trees in that plot, while the letter in the bottom right corner is the first letter of the name of the daughter who got that plot (For example, Abha got the plot in row Y and column 1 containing 21 trees). Some information in the figure got erased, but the following is known:
1
Abha got 20 trees more than Chitra but 6 trees less than Dipti.
2
The largest number of trees in a plot was 32, but it was not with Abha.
3
The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.
4
Both Abha and Bina got a higher number of plots than Dipti.
5
Only Bina, Chitra and Dipti got corner plots.
6
Dipti got two adjoining plots in the same row.
7
Bina was the only one who got a plot in each row and each column.
8
Chitra and Dipti did not get plots which were adjacent to each other (either in row / column / diagonal).
9
The number of mango trees was double the number of teak trees.
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In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q19. Grids

MCQ · +3 / −1
How many mango trees were there in total?
  1. A) 49
  2. B) 98
  3. C) 126
  4. D) 84
Correct Answer
B) 98
Step-by-step solution
📌 Core Concept
Rows are mango (X), teak (Y) and pine (Z). Clues 3 and 9 tie the three row totals to one unknown, and the total of 205 trees fixes it.
🔢 Step-by-Step Solution
1
Let column 2 have tt teak trees. Clue 3 gives column 3 =2t= 2t and column 4 =4t= 4t. With 21 in column 1, teak total =21+7t= 21+7t.
2
Clue 9 makes mango =2(21+7t)=42+14t= 2(21+7t) = 42+14t.
3
Pine =205−(21+7t)−(42+14t)=142−21t= 205 - (21+7t) - (42+14t) = 142-21t. Row Z already holds 9 and 28, so the two unseen pine plots (Z1 and Z2) sum to 105−21t105-21t.
4
t=1t=1 needs those two plots to sum to 84. The maximum plot is 32, so two plots reach at most 64. Rejected.
5
t=2t=2 needs a sum of 63. Only 32+3132+31 could give it, and 31 is not a multiple of 3 or 4. Rejected.
6
t=3t=3 makes the teak plots 21, 3, 6, 12. But 12 is already the X1 plot, and clue 'none of the plots had the same number of trees' forbids repeating it. Rejected.
7
t=4t=4 gives teak plots 21, 4, 8, 16, which are all distinct. Teak =49=49, and Z1 + Z2 =21=21. Larger tt makes this sum zero or negative.
8
Mango =2×49=98= 2\times 49 = 98.
Quick Check
98+49+58=20598+49+58 = 205, where pine =9+28+21=58=9+28+21=58.
Correct Answer: B

Q20. Grids

MCQ · +3 / −1
Which of the following is the correct sequence of trees received by Abha, Bina, Chitra and Dipti in that order?
  1. A) 60, 39, 40, 66
  2. B) 50, 69, 30, 56
  3. C) 44, 87, 24, 50
  4. D) 54, 57, 34, 60
Correct Answer
B) 50, 69, 30, 56
Step-by-step solution
📌 Core Concept
Clues 3 and 9 fix the teak and mango totals. The 205-tree total then fixes the pine total, and the plot-count clues pin down each daughter's plots.
🔢 Step-by-Step Solution
1
Clue 3 gives teak (row Y) in columns 2, 3, 4 as a,2a,4aa, 2a, 4a. Y4 is at most 32, and 32 is not allowed because Y4 is Abha's and clue 2 says the largest plot is not hers. So a≤7a\le 7 and aa is 3, 4 or 6. For a=3a=3 the plots are 3, 6, 12, and 12 repeats X1. For a=6a=6 the plots are 6, 12, 24, and 12 repeats again. So a=4a=4 and row Y is 21, 4, 8, 16, which totals 49.
2
Clue 9 gives mango =98=98. The pine total is 205−49−98=58205-49-98=58. So Z1 + Z2 =58−9−28=21=58-9-28=21.
3
Mango: X2 + X3 + X4 =98−12=86=98-12=86. Without 32 the three largest allowed values, 30, 27 and 24, total only 81. With 32 the other two must total 54, and 30 + 24 is the only valid pair, since 27 + 27 repeats and 28 is already used. So X2, X3, X4 are 32, 30, 24 in some order.
4
Plot counts: each daughter has an even number of plots. Dipti has at least 2, and clue 4 makes Abha and Bina strictly more, so each has at least 4. Chitra already has X1 and Z2, so she has at least 2. The total of 12 forces Abha 4, Bina 4, Chitra 2, Dipti 2. Chitra's plots are exactly X1 and Z2, so Chitra =12+Z2=12+\text{Z2}.
5
Z1 + Z2 =21=21 with values not yet used (9, 12 and 21 are taken), each a multiple of 3 or 4, gives Z2 as 3, 6, 15 or 18. Then Chitra is 15, 18, 27 or 30, and by clue 1 Abha == Chitra +20+20 is 35, 38, 47 or 50.
6
Abha already has Y1 + Y4 =37=37. So 35 is impossible, and 38 would need two more plots totalling 1, which cannot be done. For 47 the two extra plots must total 10. Abha has no corners (clue 5) and cannot hold Z2 (Chitra's) or 32 (clue 2). The free plots are Y2 = 4, Y3 = 8, Z3 = 9 and X2/X3 (24 or 30). No pair of these totals 10 (4 + 8 = 12, 4 + 9 = 13, 8 + 9 = 17). For 50 the extra plots total 13, which is Y2 + Z3 = 4 + 9. So Abha =50=50, Chitra =30=30 (Z2 = 18, Z1 = 3) and Dipti =56=56.
7
Bina =205−50−30−56=69=205-50-30-56=69.
8
Clue 6 gives Dipti two adjoining mango plots totalling 56, which is 32 + 24. Dipti cannot take X2 because it is adjacent to Chitra's X1 (clue 8). So Dipti has X3 and X4 and Bina has X2 = 30. Bina's plots are then X2 = 30, Y3 = 8, Z1 = 3 and Z4 = 28. They cover every row and column (clue 7) and total 69.
Why Not the Others
Chitra's total must be one of 15, 18, 27 or 30.
A has Chitra 40, which is not in that set.
C has Chitra 24, which is not in that set.
D has Chitra 34, which is not in that set.
Quick Check
50+69+30+56=20550+69+30+56=205.
Correct Answer: B

Q21. Grids

MCQ · +3 / −1
How many pine trees did Chitra receive?
  1. A) 18
  2. B) 15
  3. C) 21
  4. D) 30
Correct Answer
A) 18
Step-by-step solution
📌 Core Concept
Chitra's pine plots lie in row Z. Her plot count and the 20-tree gap in clue 1 pin down Z2.
🔢 Step-by-Step Solution
1
The teak row is 21, 4, 8, 16 (total 49), the mango total is 98, and Z3 =9=9, Z4 =28=28, so Z1 + Z2 =21=21. Z1 belongs to Bina and Z2 to Chitra.
2
The plot-count clues give Abha 4, Bina 4, Chitra 2, Dipti 2. So Chitra owns only X1 (12) and Z2.
3
Abha owns Y1 and Y4 (37 trees) plus two more plots. The only available pair is 9+49+4 (Z3 and Y2), so Abha has 50 trees.
4
Clue 1 gives Chitra =50−20=30=50-20=30. So Z2 =30−12=18=30-12=18.
5
Z1 =21−18=3=21-18=3. Chitra's only pine plot is Z2, so she has 18 pine trees.
Quick Check
Chitra: 12+18=30=50−2012+18=30 = 50-20.
Correct Answer: A

Q22. Grids

MCQ · +3 / −1
Who got the plot with the smallest number of trees and how many trees did that plot have?
  1. A) Bina, 3 trees
  2. B) Dipti, 6 trees
  3. C) Abha, 4 trees
  4. D) Bina, 4 trees
Correct Answer
A) Bina, 3 trees
Step-by-step solution
📌 Core Concept
Once every plot is known, the smallest plot and its owner can be read off. The totals follow from the tree-count and plot-count clues.
🔢 Step-by-Step Solution
1
Teak plots are 21, 4, 8, 16. Pine plots are Z1, Z2, 9, 28 with Z1 + Z2 =21=21. Chitra has two plots (X1 and Z2), and Abha has 50 trees, so Chitra has 30. This gives Z2 =18=18 and Z1 =3=3.
2
Z1 is Bina's plot (given in the figure), so a 3-tree plot is Bina's.
3
The mango plots are 12 and three plots that sum to 86 with a maximum of 32. These are 32, 30 and 24, all well above 3.
4
The only values below 3 or 4 are excluded, since each plot holds a non-zero multiple of 3 or 4. The smallest plot is therefore 3, held by Bina.
Why Not the Others
Dipti, 6: no plot has 6 trees.
Abha, 4: her Y2 plot has 4, but 3 is smaller.
Bina, 4: Bina's smallest plot is 3, not 4.
Correct Answer: A

Q23. Grids

MCQ · +3 / −1
Which of the following statements is NOT true?
  1. A) Bina got 32 pine trees
  2. B) Dipti got 56 mango trees
  3. C) Chitra got 12 mango trees
  4. D) Abha got 41 teak trees
Correct Answer
A) Bina got 32 pine trees
Step-by-step solution
📌 Core Concept
With the full grid known, each statement can be tested against the plots each daughter owns.
🔢 Step-by-Step Solution
1
Teak is 21, 4, 8, 16. Pine is Z1 =3=3, Z2 =18=18, Z3 =9=9, Z4 =28=28. Mango is X1 =12=12 with X2, X3, X4 a permutation of 30, 32, 24.
2
Abha owns Y1, Y2, Y4 and Z3, which total 50. Chitra owns X1 and Z2, a total of 30. Dipti has two adjoining mango plots, 32 and 24, totalling 56. Bina has X2 =30=30, Y3 =8=8, Z1 =3=3 and Z4 =28=28, a total of 69. Bina is the only one with a plot in every row and every column.
3
Option A: Bina's pine plots are Z1 and Z4, so 3+28=313+28=31, not 32. This is false.
4
Option B: Dipti's mango plots are 32 and 24, so 56 is true.
5
Option C: Chitra's mango plot is X1 =12=12, which is true.
6
Option D: Abha's teak plots are Y1, Y2, Y4, so 21+4+16=4121+4+16=41, which is true.
Why Not the Others
B, C and D are all true, so they cannot be the 'NOT true' statement.
Correct Answer: A

Q24. Grids

MCQ · +3 / −1
Which column had the highest number of trees?
  1. A) 2
  2. B) 4
  3. C) 3
  4. D) Cannot be determined
Correct Answer
B) 4
Step-by-step solution
📌 Core Concept
The column totals are found from the completed grid. Column 4 wins whichever way the two Dipti plots are ordered.
🔢 Step-by-Step Solution
1
Row X is 12 in X1 and X2, X3, X4 as 30, 32, 24. Clue 6 puts Dipti's adjoining plots in row X as X3 and X4, which hold 32 and 24, and Bina takes X2 =30=30. Row Y is 21, 4, 8, 16. Row Z is 3, 18, 9, 28.
2
Column 1: 12+21+3=3612+21+3=36.
3
Column 2: 30+4+18=5230+4+18=52.
4
Column 3: X3 +8+9=X3+17+8+9 = \text{X3}+17. Column 4: X4 +16+28=X4+44+16+28=\text{X4}+44.
5
X3 + X4 =56=56. If X3 =32=32, column 3 is 49 and column 4 is 68. If X3 =24=24, column 3 is 41 and column 4 is 76.
6
Column 4 exceeds 52 and column 3 in both cases, so the answer does not depend on the order.
Why Not the Others
Column 2 has 52, which is lower than column 4.
Column 3 has at most 49.
The answer can be determined, so D is wrong.
Correct Answer: B
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CAT 2020 Slot 3 DILR at a Glance

Sets in this section5
Questions in this section24
Section time40 minutes
Convenor IIMIIM Indore

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