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04 May 2020, 06:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (03:04) correct
69%
(02:59)
wrong
based on 120
sessions
History
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Not Attempted Yet
Pea, tomato, and spinach plants are planted in a field. For every 2 pea plants, there are 3 tomato plants, and for every 5 pea plants, there are 6 spinach plants. Spinach is sown 18 plants to a row and tomatoes 12 plants to a row, with no partial or mixed-crop rows. What is the minimum number of spinach plants in the field?
(A) 36
(B) 72
(C) 120
(D) 144
(E) 180
(A) 36
(B) 72
(C) 120
(D) 144
(E) 180
04 May 2020, 08:25
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P:T = 2:3 = 10:15.
P:S = 5:6 = 10:12.
Now that P=10 in each ratio, the ratios can be combined:
P:T:S = 10:15:12.
We need to determine the minimum factor by which all the values in the ratio above must be multiplied.
Since T=15, and the tomato plants are planted 12 to a row, the minimum number of tomato plants must be a multiple both of 15 and of 12.
The LCM of 15 and 12 is 60.
Since 60/T = 60/15 = 4, all the values in the ratio above must be multiplied at least by a factor of 4.
Since S=12, and the spinach plants are planted 18 to a row, the minimum number of spinach plants must be a multiple both of 12 and of 18.
The LCM of 12 and 18 is 36.
Since 36/S = 36/12 = 3, all the values in the ratio above must be multiplied at least by a factor of 3.
Thus, all the values in the ratio above must be multiplied by 4*3 = 12.
12 * (10:15:12) = 120:180:144.
Thus, S=144.
correct answer D
P:S = 5:6 = 10:12.
Now that P=10 in each ratio, the ratios can be combined:
P:T:S = 10:15:12.
We need to determine the minimum factor by which all the values in the ratio above must be multiplied.
Since T=15, and the tomato plants are planted 12 to a row, the minimum number of tomato plants must be a multiple both of 15 and of 12.
The LCM of 15 and 12 is 60.
Since 60/T = 60/15 = 4, all the values in the ratio above must be multiplied at least by a factor of 4.
Since S=12, and the spinach plants are planted 18 to a row, the minimum number of spinach plants must be a multiple both of 12 and of 18.
The LCM of 12 and 18 is 36.
Since 36/S = 36/12 = 3, all the values in the ratio above must be multiplied at least by a factor of 3.
Thus, all the values in the ratio above must be multiplied by 4*3 = 12.
12 * (10:15:12) = 120:180:144.
Thus, S=144.
correct answer D
04 May 2020, 08:44
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T:P=3:2 ; P:S=5:6 so T:P:S=15:10:12
Spinach--18 plants/row-Let a rows so 18a
Tomato---12 plants/row-Let b rows so 12b
T:P:S=15:10:12
so let tomato plants, pea and spinach plants be 15k, 10k, 12k respectively.
18a=12k--a=2k/3--k and a should be intrgers
12b=15k--b=5k/4 Here also b, k should be intrgers. Lcm of b, a is 12 so least value of k is 12 .
So min no. of Spinach plants are 12k=12*12=144
Posted from my mobile device
Spinach--18 plants/row-Let a rows so 18a
Tomato---12 plants/row-Let b rows so 12b
T:P:S=15:10:12
so let tomato plants, pea and spinach plants be 15k, 10k, 12k respectively.
18a=12k--a=2k/3--k and a should be intrgers
12b=15k--b=5k/4 Here also b, k should be intrgers. Lcm of b, a is 12 so least value of k is 12 .
So min no. of Spinach plants are 12k=12*12=144
Posted from my mobile device
