ratio

[sumasajja]

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 could not understand how this is done,,,any1 please explain this problem in detail

[gmatboost]

I like to use a table to record the given info:
(Sorry about the double and triple letters in the table, that was the only way to get the table to sort of line up with out having to draw an image.)

P T S
2 3 ? --->row 1
5 ? 6 --->row 2

To get a combined ratio, I need to make P=10, because in the previous rows it was 2 and 5

PP TT SS
10 ? ? --->row 3

To get T, I multiply row 1 by 5
To get S, I multiply row 2 by 2

PP TT SS
10 15 12 --->row 4

Now, I need to get S to be a multiple of 18, and I need to get T to be a multiple of 12, while maintaining the ratio in row 4

Since S is currently 12 = 2 * 2 * 3, and I need it to be a multiple of 18 = 2 * 3 * 3, I will need to multiply row 4 by the missing component of 18, which is an additional 3

PP TT SS
30 45 36 --->row 5

Since T is now 45 = 3 * 3 * 5, and I need it to be a multiple of 12 = 2 * 2 * 3, I will need to multiply row 5 by the missing component of 12, which is 2*2 = 4

PPP TTT SSS
120 180 144 --->row 6

So, the minimum value of S that satisfies all the conditions is S=144.

Let me know what you think.

[tpr-becky]

A ratio is a part/ part relationship and you can cross cancel units.

they give you 2p/3t as one ratio and 5p/6s as a second ratio. But then they want you to get s/t.

you can flip the second ratio and mulitply to find the ratio of s/t:

2p/3t * 6s/5p = 4s/5t (the p's cancel when you multiply).

Since they want the minimum you could go through the algebra or you could work the ratios starting with the lowest value for S and then determine if the value you find for t is divisible by 12.

36s/t = 4s/5t give you 45= t (not divisible by 12)

72s/t = 4s/5t gives you 90 = t (not divisible by 12)

120s/t = 4s/5t give you t = 150 (not divisible by 12)

144/t = 4s/5t gives you t = 180 (divisible by 12 and this is your answer).

[GMATGuruNY]

The approaches above are great. I also posted a solution here:

https://www.beatthegmat.com/ratio-t86042.html