ACT and SAT Math Tips: Ratio Rationale

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Ratio questions on Socksthe ACT and SAT often cause panic among test takers. You know the ones. They ask how much cinnamon is needed in a larger recipe or how many yellow beads must be added to inventory in order to satisify certain proportions. But there is no need to fear these ratio questions--many are quite basic and can be solved in seconds if you know some PowerScore tricks.

One type of ratio question like this requires you to find a possible total number of items given a ratio of parts:
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You can solve this question in three seconds, without picking up your calculator! The answer for these questions must always be a multiple of the sum of the ratio:

        White : Brown
            3        :     8            White + Brown = Sum   →   3 + 8 = 11

The only multiple of 11 is 44, answer choice (E).

Well, that was easy! To see why this is true, return to the fractional representation:

        White : Brown
            3        :     8            White + Brown = Sum   →   3 + 8 = 11

          3/11      8/11          3/11 of the socks are white, 8/11 of the socks are brown

If the total number of socks is 44, the number of white and brown socks is a whole number:

        Total number of white socks = 3/11 of 44   OR   3/11 x 44 = 12 white socks

        Total number of brown socks = 8/11 of 44   OR   8/11 x 44 = 32 white socks

But if the total number of socks is not a multiple of 11, then the number of white and brown socks is not an whole number. Say the number of socks is 40:

        Total number of white socks = 3/11 of 40   OR   3/11 x 40 = 10.9 white socks

        Total number of brown socks = 8/11 of 40   OR   8/11 x 40 = 29.1 white socks

You cannot have 10.9 white socks! The answer must be a whole number.

These types of ratio questions will always use items that can’t be divided, such as socks, marbles, or people. Items that can be divided, such as sugar, bird seed, or dirt, will be used in other types of ratio questions.

If you need more help with ratios or want to see what other time-saving shortcuts exist on the ACT Math section, check out our ACT courses and services.

Photo: My Sock Drawer, courtesy of Mr.TinDC