67.5% of 812 is 15% of what number? Huh?:

by on November 10th, 2009

Really?  First they tell us we can’t use a calculator, then they tell us we should average 2 minutes per question, and then they give us this:

67.5% of 812 is 15% of what number?

This may seem impossible to solve in under two minutes without some outside help. In fact, there are many typical time saving tactics to perform “simple” arithmetic without belaboring the process and taking too long. Keep an eye out for common multiples, common fractions and decimals that seem too hard without a shortcut. For this question, we can convert from “English” to “Math” and ignore the percent signs since they cancel each other out.

67.5 * 812 = 15x

x = 67.5 * 812 / 15

OK, great. But this would be a piece of cake with a calculator, not by hand! However, you may notice that 67.5/15 = 4.5. This is not the most obvious, but the more practice you have with numbers, the more you will begin to notice things like this. Half of 15 is 7.5, so immediately you should recognize this “coincidence” in the stimulus.

Another tip is to not multiply or divide your numbers together until you have set up the whole problem. Had you immediately taken 67.5% of 812, I don’t think you would have gotten 548.1 so easily. Nor do you even need 548.1 to answer the problem!

x = 4.5 * 812

= 4*812 + ½*812

= 3248 + 406

= 3654.

This part shouldn’t take more than one minute.

Furthermore, it helps to approximate. Peek at your answer choices and use your estimation skills to work toward the correct answer. Words like “close to”, “approximately” and “best” are hints that you may want to approximate your calculations.

Give the following question a shot, and stay tuned for a detailed explanation to come later! (Remember, no calculator…)

A particular parking garage is increasing its rates by 15 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?

A. 10%

B. 11%

C. 12%

D. 13%

E. 14%

To be continued……come back tomorrow for the detailed explanation to this question. Until then, good luck!


  • I think the answer is D) 13%

  • 13%

  • 13.33 percent

  • 13%.

    Lets assume that he uses Garage for 30 days and the rent now is 100. So his total cost previoulsy was 3000.
    After 15% increase, rent would be 115 and the number of days he can use to keep his rent same is say 'x'.

    Then 3000=115.x, x~26. Hence his percentage reduction
    ((30-26)/30)*100 which will come close to 13%

  • Current no. of days = x
    Current rate = y

    New Rate = 1.15y
    Nwe no. of days = fx (f is a fraction)

    fx(1.15y) = xy

    f = 100/115
    % reduction = (1-100/115))*100 = 15/115 * 100 = 13.04 %

  • Price X Quantity = 1.15*Price X q*Quantity (means holding the sum constant)

    1 = 1.15 X q

    q = 1/1.15

    1 - q = 13%

  • Let X represent percent increase or decrease.
    So the percentage reduction in the number of days he uses the garage each month is given by,
    substituting, 100*15/100+15 which equals to 13.04%

  • let x be the rate, n be the number of days initially and y be the % reduction in usage days.
    x * n = 1.15x * (1-y)*n
    solving, we get y = .13 i.e. 13%

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