CAT 2020 Question Paper | CAT LR DI Slot 3

CAT Questions

Looking for a place to start your DILR preparation? Solving CAT Previous Year Paper questions is the best way to go about it! Start right away with this beautiful question from CAT 2020 Question Paper. Check the text and video solutions provided to see if you get to the right answer.

CAT DILR : CAT 2020 Question Paper Slot 3

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.

Question 4 : Who got the plot with the smallest number of trees and how many trees did that plot have?

1. Abha, 4 trees
2. Dipti, 6 trees
3. Bina, 3 trees
4. Bina, 4 trees

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Video Explanation

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Explanatory Answer

1. Abha got 20 trees more than Chitra but 6 trees less than Dipti – C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
4. Both Abha and Bina got a higher number of plots than Dipti. Dipti gets at least 2, A and B get at least 4. These add up to at least 10. Or, C also gets 2.
9. The number of mango trees was double the number of teak trees. Number of teak trees = 7m + 21, Mango trees = 14m + 42. Adding up to 21m + 63.
This is the most interesting. We know that each plot has non-zero multiples of 3 or 4. So, m has to be 3, 4, 6 or something like that.
If m were 3, then the 21m + 63 would be 126
If m were 4, then 21m + 63 would be 147
If m were 6, then 21m + 63 would be 189.
We know that there are more than 37 pine trees. So, m cannot be 6 or more as there are only 205 trees in total. So, m = 3 or 4.
Now, let us look at the other constraints

1. C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
2. The largest number of trees in a plot was 32, but it was not with Abha.
4. A and B got 4 plots each, C and D got 2 each.
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) – What does this tell us?
9. The number of mango trees was double the number of teak trees.

1. C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
2. The largest number of trees in a plot was 32, but it was not with Abha.
4. A and B got 4 plots each, C and D got 2 each.
5. Only Bina, Chitra and Dipti got corner plots.
6. Dipti got 2 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) – D should have got Mango tree plots in columns 3 and 4
9. The number of mango trees was double the number of teak trees.


1. C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
2. The largest number of trees in a plot was 32, but it was not with Abha.
4. A and B got 4 plots each, C and D got 2 each.
5. Only Bina, Chitra and Dipti got corner plots.
7. Bina was the only one who got a plot in each row and each column. – What does this give us now?
8. D should have got Mango tree plots in columns 3 and 4
9. The number of mango trees was double the number of teak trees.

1. C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
2. The largest number of trees in a plot was 32, but it was not with Abha.
4. A and B got 4 plots each, C and D got 2 each.
5. Only Bina, Chitra and Dipti got corner plots.
7. Bina was the only one who got a plot in each row and each column. – Pine column 4 is B.
8. D should have got Mango tree plots in columns 3 and 4
9. The number of mango trees was double the number of teak trees.

1. C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
2. The largest number of trees in a plot was 32, but it was not with Abha.
4. A and B got 4 plots each, C and D got 2 each.
5. Only Bina, Chitra and Dipti got corner plots.
7. Bina was the only one who got a plot in each row and each column. – Pine column 4 is B.Teak Column 3 should also be B. And so, Mango Column 2 should also be B

1. C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
2. The largest number of trees in a plot was 32, but it was not with Abha.
9. Now we are back to our question with respect to m. Should m be 3 or 4? Let us fill both.
A gets 5m + 30 trees totally. If m were 3, A would get 45 trees totally, C should get 25 trees totally. C gets 12 trees in one plot and so would have to get 13 in another. This is not possible. So, m = 4.


1. C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
2. The largest number of trees in a plot was 32, but it was not with Abha.
Total number of teak trees = 49. Total number of Mango trees = 98. These two add up to 147. So, total number of Pine trees = 58.
So, column 1 Pine tree number should be 3.

1. C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
2. The largest number of trees in a plot was 32, but it was not with Abha.
A gets 50 trees totally. C gets 30, D gets 56. A + C + D = 136, so B gets 69. Column 2 Mango trees belong to B. B has a total of 69 trees. So, Column 2 B should be 69 – 3 – 8 – 28 = 30.

1. C gets p trees, A gets p + 20, D gets p + 26. Adding up to 3p + 46.
2. The largest number of trees in a plot was 32, but it was not with Abha. We have filled everything else. D should have 32 trees in a plot. So, D has 24 and 32 trees in her two plots.

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The question is " Who got the plot with the smallest number of trees and how many trees did that plot have? "

Hence, the answer is 'Bina, 3 trees'

Choice C is the correct answer.

 

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