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SAT Prep Ratio Word Problem

The eggs in a certain basket are either white or brown. If the ratio of the number of white eggs to the number of brown eggs is 2/3, each of the following could be the number of eggs in the basket EXCEPT...:

a) 10





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Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
4.9 4.9 (51 lesson ratings) (51)

Since the ratio of white eggs to brown eggs is 2/3, or better written as 2:3, we know that for every 2 white eggs there are 3 brown eggs.

Let's assume that there are only 2 white eggs and 3 brown eggs. In this case, there is a total of 5 eggs.

If we were to double the # of white eggs (2*2 = 4) then we have to double the # of brown eggs (2*3 = 6) to maintain the 2:3 ratio. In this case, we now have 4 white eggs and 6 brown eggs for a total of 10 eggs.

Tripling the ratio (i.e., 3*(2:3) = (3*2) : (3*3) = 6:9), we get that there are 6 white eggs and 9 white eggs for a total of 15 eggs.

Notice that every time we add 2 white eggs we have to add 3 brown eggs, and thus the # of eggs increases by 5 every time. So the possible # of eggs that could be in the basket must be a multiple of 5.

All of the choices above are multiples of 5 EXCEPT choice b) 12.

Crystal G. | Bilingual Math/Spanish Ivy League Tutor o' AwesomenessBilingual Math/Spanish Ivy League Tutor ...
5.0 5.0 (35 lesson ratings) (35)

If our ratio is 2/3, or 2:3, then we have groups of 5 eggs, where in each group, we have 2 white eggs and 3 brown eggs. We could have any multiple of 5 because the multiples of 5 {5, 10, 15, 20, 25, 30, ...}  allow us to divide up our eggs into groups of 5. 

The only number that is NOT a multiple of 5 is 12. So the answer is (B).

Richard R. | Math Tutor - College Instructor w/Eng & Instruc Design degreesMath Tutor - College Instructor w/Eng & ...
4.2 4.2 (5 lesson ratings) (5)

The key to understanding this and solving it is to not get trapped into thinking that you just need to multiply the optional answers by 2/3 and see that generates a number with a fractional remainder.

If there are 2 white eggs to every 3 brown, then view the color proportions as fraction of 5.  In the case of whites, there are 2 out of 5; with brown, there are 3 out of 5.  To maintain that ratio with larger overall number of eggs, the total number of eggs needs to be a multiple of 5.  The number 12 is the only one that fits that.

Hope that helps.  Essentially, another way to say what Crystal has said.  Nice job Crystal.