Solutions

  1. To convert a decimal to a fraction, write it over the appropriate power of 10 and simplify:

  2. To convert a percent to a fraction, write it over a denominator of 100 and simplify:

  3. To convert a fraction to a decimal, divide the numerator by the denominator:

    It often helps to simplify the fraction before you divide:

  4. To convert a mixed number to a decimal, simplify the mixed number first, if needed:

  5. To convert a fraction to a percent, rewrite the fraction with a denominator of 100:

    Alternatively, you can convert the fraction to a decimal and shift the decimal point two places to the right and add a percent symbol:

  6. To convert a decimal to a percent, shift the decimal point two places to the right and add a percent symbol:

    80.4 = 8,040%
    0.0007 = 0.07%

  7. To order from least to greatest, express all the terms in the same form:




    Alternatively, you can use FDP logic and Benchmark Values to solve this problem: . 40% is 10% less than . Since is a smaller piece away from it is closer to and therefore larger than 40%. Thus, 0.8 is clearly greater than . Therefore,

  8. To order from least to greatest, express all the terms in the same form:



  9. To order from least to greatest, express all the terms in the same form:


    Alternatively, you can use FDP logic and Benchmark Values to solve this problem: 2400% is 24, which is clearly the largest value. Then, you can use Benchmark Values to compare and 2.401. Because the whole number portion, 2, is the same, just compare the fraction parts. is greater than . Thus, 0.401 is less than . Therefore,  must be greater than 2.401. So, .

  10. To order from least to greatest, express all the terms in the same form:

    (Note that, because x2 is a positive term common to all the terms you are comparing, you can ignore its presence completely. If the common term were negative, then the order would be reversed.)


    		You can find the first few digits of the decimal by long division.

    Alternatively, you can use FDP logic and Benchmark Values to solve this problem: 3.10% is 0.0310, which is clearly the smallest value. Then, compare 2.9 and to see which one is closer to 3: 2.9 is away from 3 and is away from 3. Because  is smaller than is closest to 3; therefore, it is larger. So, .

  11. To order from least to greatest, express all the terms in the same form:



    		 You can find the first few digits of the decimal by long division.

    Alternatively, you can use FDP logic and Benchmark Values to solve this problem: 248,000% = 2,480, which is clearly the largest value. The fraction is approximately , or , which is 2.5. This is clearly less than 2.9002003. Therefore, < 2.9002003 < 248,000%.

  12. 120

    This is best handled as a percent-to-decimal conversion problem. If you simply recognize that this problem will become much easier: . Multiplying 0.625 × 240 will take much longer to complete, unless you use a calculator.

  13. 1,250

    This is best handled as a percent-to-decimal conversion problem. If you simply recognize that this problem will become much easier:

    . Dividing out 200 ÷ 0.16 would likely take longer to complete.

  14. You can use decimal equivalents. X percent is and you simply need to multiply by Y.

    Alternatively, you can set up a table and solve for the unknown (in this case, call it Z):

    PART Z X
    WHOLE Y 100

  15. You can use decimal equivalents. X equals some unknown percent of Y (call it Z percent),

    so , and then simply solve for Z :

    Alternatively, you can set up a table and solve for the unknown Z:

    PART X Z
    WHOLE Y 100
  16. (C)

    Simplify Quantity A. You can divide the number of action figures by the total number of toys to find the percentage of action figures:

         Quantity A      Quantity B
    Percent of toys sold that
    are action figures =
    		33.7%

    A percentage is defined as being out of 100, so reduce the fraction until the denominator is 100:

         Quantity A      Quantity B
    33.7%

    Because the denominator is 100, the number in the numerator is the percent. So action figures are 33.7% of the total number of toys. The two quantities are equal.

  17. (B)

    Take a close look at the expression in Quantity A: 0.002 is first divided by 10−3, and then multiplied by 10−3. The net effect is the same as multiplying by 1. The two 10−3 terms cancel out:

         Quantity A      Quantity B
    0.02

    Therefore, Quantity B is larger.

  18. (B)

    Because all bills have the same height, you can compare the number of bills in each stack directly to determine the percent increase in height. The number of $20 bills in a stack with a value of $1,600 is:

    1600/20 = 80

    The number of $10 bills in a stack with a value of $1,050 is

    1,050/10 = 105

    Plug these values into the percent change formula to evaluate Quantity A:

    Quantity A Quantity B
    The percent by which the height
    of the stack of $10 bills is greater
    than that of the stack of $20    		 33.5%
    bills =

    Now compare the two quantities. , so Quantity A must be less than . Recall that is 33.% as a percent, so 33.5% is slightly larger than . Therefore, the value in Quantity A must be less than 33.5%.

    Thus, Quantity B is greater.