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.
Greg Michnikov, Founder of GMAT Boost
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