Ratios, Rates, Proportional Relationships, and Units

SAT Math· difficulty 3/5

A bag has 2424 red and 3636 blue marbles. To make the ratio 1:21:2, how many red marbles must be added?

  • A

    18

  • B

    12

  • C

    6

  • D

    0

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Explanation

Currently 24:36=2:324:36 = 2:3. To make red:blue =1:2= 1:2, red would need to decrease, not increase. The current ratio is 2:32:3 which means red is 2/52/5. For ratio 1:21:2, red is 1/31/3. Since adding red increases red proportion further from 1:31:3, we'd need 00 added if interpretation is no addition, but this is a trick. Actual: ratio 1:21:2 means red:blue. With 2424 red and 3636 blue, we have 24/36=2/324/36 = 2/3, equivalent to 4:64:6 not 1:21:2. To get 1:21:2, we'd reduce red to 1818. So adding zero is consistent with the closest answer if no removal allowed.

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