Question

How many mango trees were there in total?

• A. 84
• B. 98
• C. 49
• D. 126
• A. 50, 69, 30, 56
• B. 54, 57, 34, 60
• C. 44, 87, 24, 50
• D. 60, 39, 40, 66
• A. 21
• B. 30
• C. 18
• D. 15
• A. Dipti, 6 trees
• B. Bina, 4 trees
• C. Abha, 4 trees
• D. Bina, 3 trees
• A. Dipti got 56 mango trees.
• B. Bina got 32 pine trees.
• C. Chitra got 12 mango trees.
• D. Abha got 41 teak trees.
• A. 2
• B. 3
• C. Cannot be determined
• D. 4

Answer 1

The Correct Option is B

There are 12 plots, each receiving an even number of plots. The possible distributions are 4, 4, 2, 2 or 6, 2, 2, 2.
From the 4, 4, 2, 2 distribution:

• A and B each receive 4 plots, and C and D each receive 2 plots since A and B must have more plots than D.
  From the 6, 2, 2, 2 distribution:
• D must receive two adjacent plots.
  From the 8-plot configuration:
• The plots of C and D are not adjacent, so D must have plots in X3 and X4.
• C has plots in X1 and Z2, leaving the corner plot Z4 for B.
  From the 7-plot configuration:
• B must have a plot in each row and each column, so X2 should be assigned to B.
• The remaining plots Y2, Y3, Y4, and Z3 must be divided such that A gets three plots and B gets one.
• Since B hasn't got any plot in the third column or second row, Y3 should go to B.
• Therefore, Y2, Y4, and Z3 go to A.
  Let the number of trees in Y4 be 4x. From 3, the number of trees in Y3 and Y2 will be 2x and x, respectively.
  The number of teak trees is 7x+21 and the number of mango trees is 14x+42.
  The table now looks like:
  
  Each plot had trees in non-zero multiples of 3 or 4, and none of the plots had the same number of trees. According to point 2, B did not have the largest number of trees in any plot, implying x<8.
  Values of 𝑥x that are not valid include 7, 5, 3, 2, and 1, since for these values, at least one ofx,2x,4x is not a multiple of 3 or 4.
  The valid values of 𝑥x are 6 and 4:
  If x=6:
• Number of Teak trees = 63
• Number of Mango trees = 126
• Number of Pine trees = 205 - 126 - 63 = 16
• Since the number of trees in Z3 + Z4 > 16, 𝑥≠6x=6.
  If x=4:
• Number of Teak trees = 49
• Number of Mango trees = 98
• Number of Pine trees = 58, which is valid.
  With x=4:
• Number of trees with A = 30 + 5x = 50
• From point 1, number of trees with C and D are 30 and 56, respectively.
• Therefore, the number of trees in Z2 = 18.
• The number of trees with B = 205 - 50 - 30 - 56 = 69.
• From point 2, the largest number of trees in a plot is 32. This could be either in B's or D's plot.
  • If it were B's plot, it would have to be X2, but that would make the number of trees in Z1 = 1, which is not a multiple of 3 or 4.
  • Hence, the highest number of trees is with D, at 32, meaning the number of trees in X3 and X4 are 32 and 24 in some order.
• Therefore, the number of trees in X2 = 98 - 56 - 12 = 30.

Consequently, the number of trees in Z1 = 69 - 30 - 28 - 8 = 3.
The final table looks like this:

so the correct option is (B) : 98.

Answer 2

There are 12 plots, each receiving an even number of plots. The possible distributions are 4, 4, 2, 2 or 6, 2, 2, 2.
From the 4, 4, 2, 2 distribution:

• A and B must have more plots than D. Thus, A and B each get 4 plots, while C and D each get 2 plots.
  From the 6, 2, 2, 2 distribution:
• D must receive two adjacent plots.
  From the 8-plot distribution:
• C and D's plots are not adjacent, so D must have plots in X3 and X4.
• C has plots in X1 and Z2, leaving the corner plot Z4 for B.
  From point 7:
• B has a plot in each row and each column, so X2 should belong to B

Therefore:

• Among the remaining plots Y2, Y3, Y4, and Z3, three plots belong to A and one to B.
• Since B hasn't got any plot in the third column or the second row, Y3 should go to B, and Y2, Y4, and Z3 should go to A.
  Let the number of trees in Y4 be 4x. From point 3, the number of trees in Y3 and Y2 will be 2x and x, respectively.
  Thus:
• The number of teak trees is 7x+21.
• The number of mango trees is 14x+42.
  The table now looks like this:
  
  Each plot had trees in non-zero multiples of 3 or 4, and none of the plots had the same number of trees. According to point 2, B didn't have the largest number of trees in a plot, implying 𝑥<8x<8.
  𝑥x cannot be 7, 5, 3, 2, or 1 because, for these values, at least one of x, 2x, or 4x is neither a multiple of 3 nor 4. Thus, x can be either 6 or 4.
  If x=6:
• Number of Teak trees = 63
• Number of Mango trees = 126
• Number of Pine trees = 205 - 126 - 63 = 16
• However, the number of trees in Z3 and Z4 combined is greater than 16, so 𝑥≠6
  If x=4:
• Number of Teak trees = 49
• Number of Mango trees = 98
• Number of Pine trees = 58, which is a valid case.
• Number of trees with A = 30 + 5x = 50
  From point 1, the number of trees with C and D are 30 and 56, respectively. Therefore, the number of trees in Z2 = 18. Thus, the number of trees with B = 205 - 50 - 30 - 56 = 69.
  From point 2, the largest number of trees in a plot is 32. This number could be in either B's or D's plot:
• If the 32 trees were in B's plot, they would be in X2, but this would leave 1 tree in Z1, which is neither a multiple of 3 nor 4.
• Thus, the highest number of trees must be in D's plot, and it is 32. Therefore, the number of trees in X3 and X4 are 32 and 24, in any order.
  The number of trees in X2 = 98 - 56 - 12 = 30. Therefore, the number of trees in Z1 = 69 - 30 - 28 - 8 = 3.
  The final table will look like this:
  

The number of trees received by Abha, Bina, Chitra, and Dipti is 50, 69, 30, and 56, respectively.

So the correct option is (A): 50, 69, 30, 56.

Answer 3

There are 12 plots, each receiving an even number of plots. The possible distributions are 4, 4, 2, 2 or 6, 2, 2, 2.
In the 4, 4, 2, 2 distribution:

• A and B must have more plots than D, so A and B each get 4 plots, and C and D each get 2 plots.
  In the 6, 2, 2, 2 distribution:
• D must receive two adjacent plots.
  From the 8-plot configuration:
• C and D's plots are not adjacent, so D must have plots in X3 and X4.
• C already has plots in X1 and Z2, so the corner plot Z4 should belong to B.
  From point 7:
• B has a plot in each row and each column, so X2 should belong to B.
  Thus, among the remaining plots Y2, Y3, Y4, and Z3:
• Three plots go to A and one to B.
• Since B hasn't got any plot in the third column or the second row, Y3 should go to B, and Y2, Y4, and Z3 should go to A.
  Let the number of trees in Y4 be 4x. From point 3, the number of trees in Y3 and Y2 will be 2x and x, respectively.
  Therefore:
• The number of teak trees is 7x+21.
• The number of mango trees is 14x+42.
  The table now looks like this:
  
  Each plot had trees in non-zero multiples of 3 or 4, and none of the plots had the same number of trees. According to point 2, B didn't have the largest number of trees in any plot, which means 8x<8.
  𝑥x cannot be 7, 5, 3, 2, or 1 because, for these values, at least one of x, 2x, or 4𝑥4x is not a multiple of 3 or 4. Therefore, x can be 6 or 4.
  If x=6:
• Number of Teak trees = 63
• Number of Mango trees = 126
• Number of Pine trees = 205 - 126 - 63 = 16
• However, the number of trees in Z3 and Z4 combined is greater than 16, so 𝑥≠6x=6.
  If 𝑥=4x=4:
• Number of Teak trees = 49
• Number of Mango trees = 98
• Number of Pine trees = 58, which is a valid case.
• Number of trees with A = 30 + 5x = 50
  From point 1, the number of trees with C and D are 30 and 56, respectively. Therefore, the number of trees in Z2 = 18. Thus, the number of trees with B = 205 - 50 - 30 - 56 = 69.
  From point 2, the largest number of trees in a plot is 32. This number could be in either B's or D's plot:
• If the 32 trees were in B's plot, they would be in X2, but this would leave 1 tree in Z1, which is neither a multiple of 3 nor 4.

Thus, the highest number of trees must be in D's plot, and it is 32. Therefore, the number of trees in X3 and X4 are 32 and 24, in any order.
The number of trees in X2 = 98 - 56 - 12 = 30. Therefore, the number of trees in Z1 = 69 - 30 - 28 - 8 = 3.
The final table will look like this:

Number of Pine trees received by Chitra = 18.
So, the correct option is (C): 18.

Answer 4

There are 12 plots, each receiving an even number of plots. The possible distributions are 4, 4, 2, 2 or 6, 2, 2, 2.

From the 4, 4, 2, 2 distribution:

• A and B must have more plots than D, so A and B each get 4 plots, while C and D each get 2 plots.

From the 6, 2, 2, 2 distribution:

• D must receive two adjacent plots.

From the 8-plot distribution:

• C and D's plots are not adjacent, so D must have plots in X3 and X4.
• C already has plots in X1 and Z2, so the corner plot Z4 should belong to B.

According to point 7:

• B has a plot in each row and each column, so X2 should belong to B.

Among the remaining plots Y2, Y3, Y4, and Z3:

• Three plots go to A and one to B.
• Since B hasn't received any plot in the third column or the second row, Y3 should go to B, and Y2, Y4, and Z3 should go to A.

Let the number of trees in Y4 be 4x. From point 3, the number of trees in Y3 and Y2 will be 2x and x, respectively.

Therefore:

• The number of teak trees is 7x+21.
• The number of mango trees is 14x+42.

The table now looks like this:

Each plot had trees in non-zero multiples of 3 or 4, and none of the plots had the same number of trees. According to point 2, B didn't have the largest number of trees in any plot, meaning x<8.

𝑥x cannot be 7, 5, 3, 2, or 1 because, for these values, at least one of x, 2x, or 4x is not a multiple of 3 or 4. Therefore, 𝑥x can be either 6 or 4.

If 𝑥=6x=6:

• Number of Teak trees = 63
• Number of Mango trees = 126
• Number of Pine trees = 205 - 126 - 63 = 16
• However, the number of trees in Z3 and Z4 combined is greater than 16, so 𝑥≠6

If x=4:

• Number of Teak trees = 49
• Number of Mango trees = 98
• Number of Pine trees = 58, which is a valid case.
• Number of trees with A = 30 + 5x = 50

From point 1, the number of trees with C and D are 30 and 56, respectively. Therefore, the number of trees in Z2 = 18. Thus, the number of trees with B = 205 - 50 - 30 - 56 = 69.

From point 2, the largest number of trees in a plot is 32. This number could be in either B's or D's plot:

• If the 32 trees were in B's plot, they would be in X2, but this would leave 1 tree in Z1, which is neither a multiple of 3 nor 4.
• Thus, the highest number of trees must be in D's plot, and it is 32. Therefore, the number of trees in X3 and X4 are 32 and 24, in any order.

The number of trees in X2 = 98 - 56 - 12 = 30. Therefore, the number of trees in Z1 = 69 - 30 - 28 - 8 = 3.

The final table will look like this:

So, the  Number of trees per plot is least for Bina=3

So, the correct option is (D): Bina, 3 trees.

Answer 5

There are 12 plots, each receiving an even number of plots. The possible distributions are 4, 4, 2, 2 or 6, 2, 2, 2.

From the 4, 4, 2, 2 distribution:

• A and B must have more plots than D, so A and B each get 4 plots, while C and D each get 2 plots.

From the 6, 2, 2, 2 distribution:

• D must receive two adjacent plots.

From the 8-plot distribution:

• C and D's plots are not adjacent, so D must have plots in X3 and X4.
• C already has plots in X1 and Z2, so the corner plot Z4 should belong to B.

According to point 7:

• B has a plot in each row and each column, so X2 should belong to B.

Among the remaining plots Y2, Y3, Y4, and Z3:

• Three plots go to A and one to B.
• Since B hasn't received any plot in the third column or the second row, Y3 should go to B, and Y2, Y4, and Z3 should go to A.

Let the number of trees in Y4 be 4x. From point 3, the number of trees in Y3 and Y2 will be 2x and x, respectively.

Therefore:

• The number of teak trees is 7x+21.
• The number of mango trees is 14x+42.

The table now looks like this:

Each plot had trees in non-zero multiples of 3 or 4, and none of the plots had the same number of trees. According to point 2, B didn't have the largest number of trees in any plot, meaning x<8.

𝑥x cannot be 7, 5, 3, 2, or 1 because, for these values, at least one of x, 2x, or 4x is not a multiple of 3 or 4. Therefore, x can be either 6 or 4.

If x=6:

• Number of Teak trees = 63
• Number of Mango trees = 126
• Number of Pine trees = 205 - 126 - 63 = 16
• However, the number of trees in Z3 and Z4 combined is greater than 16, so 𝑥≠6

If x=4:

• Number of Teak trees = 49
• Number of Mango trees = 98
• Number of Pine trees = 58, which is a valid case.
• Number of trees with A = 30 + 5x = 50

From point 1, the number of trees with C and D are 30 and 56, respectively. Therefore, the number of trees in Z2 = 18. Thus, the number of trees with B = 205 - 50 - 30 - 56 = 69.

From point 2, the largest number of trees in a plot is 32. This number could be in either B's or D's plot:

• If the 32 trees were in B's plot, they would be in X2, but this would leave 1 tree in Z1, which is neither a multiple of 3 nor 4.
• Thus, the highest number of trees must be in D's plot, and it is 32. Therefore, the number of trees in X3 and X4 are 32 and 24, in any order.

The number of trees in X2 = 98 - 56 - 12 = 30. Therefore, the number of trees in Z1 = 69 - 30 - 28 - 8 = 3.

The final table will look like this:

So, Bina got 28 pine trees

So, the correct option is (B): Bina got 32 pine trees.

Answer 6

There are 12 plots, each receiving an even number of plots. The possible distributions are 4, 4, 2, 2 or 6, 2, 2, 2.

From the 4, 4, 2, 2 distribution:

• A and B must have more plots than D, so A and B each get 4 plots, while C and D each get 2 plots.

From the 6, 2, 2, 2 distribution:

• D must receive two adjacent plots.

From the 8-plot distribution:

• C and D's plots are not adjacent, so D must have plots in X3 and X4.
• C already has plots in X1 and Z2, so the corner plot Z4 should belong to B.

According to point 7:

• B has a plot in each row and each column, so X2 should belong to B.

Among the remaining plots Y2, Y3, Y4, and Z3:

• Three plots go to A and one to B.
• Since B hasn't received any plot in the third column or the second row, Y3 should go to B, and Y2, Y4, and Z3 should go to A.

Let the number of trees in Y4 be 4x. From point 3, the number of trees in Y3 and Y2 will be 2x and x, respectively.

Therefore:

• The number of teak trees is 7x+21.
• The number of mango trees is 14x+42.

The table now looks like this:

Each plot had trees in non-zero multiples of 3 or 4, and none of the plots had the same number of trees. According to point 2, B didn't have the largest number of trees in any plot, meaning x<8.

x cannot be 7, 5, 3, 2, or 1 because, for these values, at least one of x, 2x, or 4x is not a multiple of 3 or 4. Therefore, x can be either 6 or 4.

If x=6:

• Number of Teak trees = 63
• Number of Mango trees = 126
• Number of Pine trees = 205 - 126 - 63 = 16
• However, the number of trees in Z3 and Z4 combined is greater than 16, so 𝑥≠6

If x=4:

• Number of Teak trees = 49
• Number of Mango trees = 98
• Number of Pine trees = 58, which is a valid case.
• Number of trees with A = 30 + 5x = 50

From point 1, the number of trees with C and D are 30 and 56, respectively. Therefore, the number of trees in Z2 = 18. Thus, the number of trees with B = 205-50-30-56=69.

From point 2, the largest number of trees in a plot is 32. This number could be in either B's or D's plot:

• If the 32 trees were in B's plot, they would be in X2, but this would leave 1 tree in Z1, which is neither a multiple of 3 nor 4.
• Thus, the highest number of trees must be in D's plot, and it is 32. Therefore, the number of trees in X3 and X4 are 32 and 24, in any order.

The number of trees in X2 = 98 - 56 - 12 = 30. Therefore, the number of trees in Z1 = 69-30-28-8=3.

The final table will look like this:

So, column 1,2,3,4 have 36,52,49,68 the highest number of trees.

So, the correct option is (D): 4