I came across the following question

The average of four numbers is 36. Which is greater Sum of same four numbers or $140$

Now the answer states (a- The sum of same four numbers). How did they determine the minimum and the maximum value of the numbers from the average equation ?

$\frac{a+b+c+d}{4} = 36$ or $ a+b+c+d = 144 $

  • $\begingroup$ They didn't. Why would they need to determine the min. or max. of the numbers? $\endgroup$ – copper.hat Aug 2 '12 at 4:46
  • $\begingroup$ Clearly, the sum(=144) is > 140 $\endgroup$ – lab bhattacharjee Aug 2 '12 at 4:47
  • $\begingroup$ I take it you know why the sum of the four is $144$. You cannot find the individual numbers from the information, but if you know they are all positive integers, not necessarily distinct, then the smallest possible value of one of the numbers is $1$, and the biggest possible value is $141$ ($1+1+1+141=144$). If you know they are distinct positive integers, the largest possible entry is $138$ ($1+2+3+138=144$). $\endgroup$ – André Nicolas Aug 2 '12 at 4:47
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    $\begingroup$ @MistyD: Yes, you seem to be misinterpreting the question. The answer by Sidd explains things. Suppose that your average grade in $4$ tests (each out of $100$) is $75$. If you tell someone this, they will know your $4$ grades must have added up to $300$, without knowing any of the actual grades on the individual tests. $\endgroup$ – André Nicolas Aug 2 '12 at 4:55
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    $\begingroup$ In this case same is unnecessary. $\endgroup$ – copper.hat Aug 2 '12 at 4:55

The minimum and the maximum aren't needed to find which is higher. The "sum" refers to a+b+c+d. You don't need to worry about those individual elements, but just that expression as a whole. You already showed how a+b+c+d is 144, which is greater than 140, therefore the sum of the four numbers is greater.

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  • $\begingroup$ Thank you for the answer. But it says the sum of $same$ four numbers in this case it might be a+a+a+a or d+d+d+d $\endgroup$ – MistyD Aug 2 '12 at 4:53
  • $\begingroup$ Same means the same collection of four numbers. $\endgroup$ – copper.hat Aug 2 '12 at 4:54
  • $\begingroup$ Oh okay.. that makes sense $\endgroup$ – MistyD Aug 2 '12 at 4:55
  • $\begingroup$ I think "same four numbers" referred to the four numbers in "average of four numbers", I don't think it means that the numbers are all the same. $\endgroup$ – Sidd Singal Aug 2 '12 at 4:56

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