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28 Oct 2018, 21:21
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Hi applebear,
Your example has a couple of 'problems' with it:
1) It has 9 terms - and there should only be 7 terms
2) You assume that the LARGEST number shows up repeatedly.
Since the average of the 7 terms is 23, we know that the SUM of those terms is 161. That sum is a big 'limiter' in terms of what is possible. The other limiter is that if the smallest number is X, then the largest number is 4X+15 (meaning that the value of the smallest number limits how big the value of the largest number can get).
In these types of situations, to make one number as big as possible, we must make ALL of the other numbers as small as possible (based on the restrictions described in the prompt). We need those three "23s" to get to the solution because that is the smallest that we can make THOSE three values.
GMAT assassins aren't born, they're made,
Rich
Your example has a couple of 'problems' with it:
1) It has 9 terms - and there should only be 7 terms
2) You assume that the LARGEST number shows up repeatedly.
Since the average of the 7 terms is 23, we know that the SUM of those terms is 161. That sum is a big 'limiter' in terms of what is possible. The other limiter is that if the smallest number is X, then the largest number is 4X+15 (meaning that the value of the smallest number limits how big the value of the largest number can get).
In these types of situations, to make one number as big as possible, we must make ALL of the other numbers as small as possible (based on the restrictions described in the prompt). We need those three "23s" to get to the solution because that is the smallest that we can make THOSE three values.
GMAT assassins aren't born, they're made,
Rich
29 Oct 2018, 05:19
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Hello EMPOWERgmatRichC,
Thank you so much for clearing my doubt...however i have one more doubt , why can’t we make the fourth term of the set as “x”? Why 23 ?
Posted from my mobile device
Thank you so much for clearing my doubt...however i have one more doubt , why can’t we make the fourth term of the set as “x”? Why 23 ?
Posted from my mobile device
29 Oct 2018, 12:38
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Hi applebear,
The prompt tells us that the Average of the group is 23 AND the Median of the group is 23. The Median of a group of 7 numbers will the '4th' number (when the numbers are ordered from least to greatest). That is the one value that is 'locked in', so we can't change it.
GMAT assassins aren't born, they're made,
Rich
The prompt tells us that the Average of the group is 23 AND the Median of the group is 23. The Median of a group of 7 numbers will the '4th' number (when the numbers are ordered from least to greatest). That is the one value that is 'locked in', so we can't change it.
GMAT assassins aren't born, they're made,
Rich
