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Magoosh Brain Twister: The Smallest Big Change

brain_twister

Welcome back, brave Magooshers! Ready to tackle another brain twisting math challenge? Here we go.

(17 x 19 x 23 x 29)^31 = n

Lowering which of the following numbers by one will result in the least decrease of n?

  1. 17
  2. 19
  3. 23
  4. 29
  5. 31

 

Don’t forget to come back on Thursday for the answer and explanation!

 

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25 Responses to Magoosh Brain Twister: The Smallest Big Change

  1. KedarG December 11, 2014 at 9:54 pm #

    Wow, this is a great question.

  2. priyanka December 11, 2014 at 8:45 pm #

    exponent won’t be the correct answer as it would decrease the amount by a huge product. only tweaking single numbers will cause least change,

    i can write each case as follows:

    1: using 16 inplace of 17 – > (17x19x23x29)^31 -(19x23x29)^31 since 16=(17-1)^31 and using distributive law for products and exponents
    [using A= (17x19x23x29)^31 ]

    similarly
    2: 18: A- (17x23x29)^31
    3: 23: A-(17x19x29)^31
    4:29: A-(17x19x23)^31

    the least product would result in the last case, hence answer is 29

  3. maaj December 11, 2014 at 5:48 pm #

    Hi Chris
    We are sure it isn’t the “31” cause one unit decrease in that means less ” 17*19*23*29″ which is the highest imaginable decrease in the result . by the same procedure we can find out that reducing the biggest number yields to less decrease in the total amount . as an instance :

    1) 17*19*23* 28 means the decrease in the total number by 17*19*23 amount
    2) 17*19*29 * 22 means the decrease in the total number by 17*19*29 amount
    3) 17*23*29 * 18 means the decrease in the total number by 29*17*23 amount
    4) 19*23*29 * 16 means the decrease in the total number by 29*19*23 amount
    as you see the min decrease is for number “1” which has the least size in comparison with other

    • maaj December 11, 2014 at 5:51 pm #

      the answer is 29 by the way!

  4. Bahar December 11, 2014 at 3:53 pm #

    29

  5. Nina December 11, 2014 at 10:56 am #

    29

  6. Nina December 11, 2014 at 10:49 am #

    D. 29

  7. mila December 11, 2014 at 6:12 am #

    A

    • Chris Lele
      Chris Lele December 11, 2014 at 11:01 am #

      The wording is “least decrease”. You might have been thinking “greatest decrease” — though that would be (E).

  8. Prasoon jaya December 11, 2014 at 1:09 am #

    A.17

    • Chris Lele
      Chris Lele December 11, 2014 at 11:02 am #

      Remember it has to be the “least decrease”

  9. kenok December 10, 2014 at 11:17 pm #

    17 answer.
    via common sense

    • Chris Lele
      Chris Lele December 11, 2014 at 11:02 am #

      Remember, the wording: “least decrease”. You might have had it the other way around 🙂

  10. Abu Rasheed December 10, 2014 at 10:36 pm #

    The answer to the brain twister is 31.

    • Chris Lele
      Chris Lele December 11, 2014 at 11:03 am #

      That would result in the greatest decrease. Remember it says “least decrease”.

  11. Sanjay December 10, 2014 at 9:24 pm #

    Ans. A.

    • Chris Lele
      Chris Lele December 11, 2014 at 11:04 am #

      Remember that it has to be least decrease.

  12. Oxana December 10, 2014 at 9:10 pm #

    Lowering of 17 to 16 will result in n*16^31/17^31 = n*(16/17)^31 = n/(1.0625)^31
    Using calculator: (1.0625)^2^2^2^2^2 = (1.0625)^32 = 6.9586 or aprox 7, so lowering of 17 to 16 will result in n decreasing in less then 7 times.
    But lowering of 31 t0 30 will result in n/(17*19*23*29)
    Answer is A

    • Chris Lele
      Chris Lele December 11, 2014 at 11:05 am #

      Oxana,

      What about the other answer choices though?

    • Jun January 1, 2015 at 6:04 pm #

      Nice technique, and applying it to the rest will give us (29/28)^32 as the smallest result hence the least decrease.

  13. Jenil December 8, 2014 at 7:17 pm #

    Wait don’t post the last part, it’s wrong !! 😀

    We have to compare (16)^31 vs (17x19x23x29)^30 and not just (17x19x23x29)

    (16)^31 = (2^4)^31 = (2)^124

    Assuming (17x19x23x29)^30 as (16x18x22x28)^30
    (2^4)^30 * (2)^30 * (3^2)^30 * (2)^30 * (11)^30 * (2^2)^30 * (7^30)

    Simplifying we get,

    2^240 * 3^60 * 11^30 * 7^30

    Clearly the above value is greater : so the value of (17*19*23*29)^30 has to be greater than (16)^31 and will result in greater decrease.

    A is the answer 🙂

    • David December 10, 2014 at 11:30 pm #

      I reckon D, 29, will have the least influence on n.

      1) First of all, we know it will not be D because the exponent has a greater influence on the value of n. Reducing the exponent by one would be the same as dividing n by all the numbers in the brackets.

      2) Then we must compare the terms inside the brackets. Chose the 3 numbers which will produce the smallest product. Changes in the leftover, 4th number will have the least influence on n.

      • Chris Lele
        Chris Lele December 11, 2014 at 11:07 am #

        Wow! You are the only person to answer it correctly–with a perfect explanation to boot.

        Congrats 🙂

      • Oxana December 11, 2014 at 11:26 am #

        Yes, that’s right

    • Chris Lele
      Chris Lele December 11, 2014 at 11:06 am #

      Hmm…remember it says greatest decrease. It looks like you were going for the reverse.


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