CAT 2020 Slot 3 — DILR Question 19
Answer the next 4 questions based on the information given.
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:
- Abha got 20 trees more than Chitra but 6 trees less than Dipti.
- The largest number of trees in a plot was 32, but it was not with Abha.
- The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4.
- Both Abha and Bina got a higher number of plots than Dipti.
- Only Bina, Chitra and Dipti got corner plots.
- Dipti got two adjoining plots in the same row.
- Bina was the only one who got a plot in each row and each column.
- Chitra and Dipti did not get plots which were adjacent to each other (either in row / column /diagonal).
- The number of mango trees was double the number of teak trees.
How many mango trees were there in total?
Answer & solution
- A
49
- B
126
98
- D
84
The number of teak trees in Column 3 was double of that in Column 2 but was half of that in Column 4. The number of mango trees was double the number of teak trees.
Dipti got two adjoining plots in the same row. Chitra and Dipti did not get plots which were adjacent to each other (either in row / column /diagonal).
∴ Dipti must have got adjacent plots in row X in column 3 and 4.
Bina got a plot in each row and column. Hence, Bina gets last plot in row Z last column.
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Number of plots so far: A = 2, B = 3, C = 2 and D = 2
Since each daughter gets even number of plots and Abha and Bina got more plots than D.
∴ Bina gets one more plot in 2nd column in row X and Abha will get 2 more plots.
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Now, highest trees in a plot is 32 but this plot doesn’t belong to Abha hence, 4x < 32
⇒ x < 8
Also, x should be a multiple of 3 or 4. Hence, x can be 3, 4 or 6.
x cannot be 3 as 4x = 12 but all plots need to have different number of trees.
Also, x cannot be 6 as 2x = 12 but all plots need to have different number of trees.
∴ x = 4.
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Abha got 20 trees more than Chitra but 6 trees less than Dipti.
Abha gets total 21 + 4 + 9 + 16 = 50 tress.
∴ Chitra gets 30 trees
& Dipti gets 56 trees
& Bina will have = 205 – 50 – 30 – 56 = 69 trees
Since Dipti has 56 trees, in the first row B will have 98 – 56 – 12 = 30 trees.
Trees for B = 69 = 30 + 8 + 28 + (trees in row Z first column)
∴ Trees for B in row Z first column = 3
Number of trees for C in row Z = 58 – 3 – 9 – 28 = 18.
Now, highest number of trees in a plot is 32, this must be with D in row X.
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Total number of mango trees is 98.
Hence, option (c).