If $d$ is the smallest positive integer such that the range of the remainders obtained when multiples of $3$ are

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Tue Nov 10, 2020 8:17 am

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$P =\{6, 3, 0, d, 4, 14, 9, 2d\}$

If $d$ is the smallest positive integer such that the range of the remainders obtained when multiples of $3$ are divided by $d$ is $3,$ by what percentage is the median of the numbers in $P$ smaller than the mean of the numbers in $P?$

A. $11.1\%$
B. $12.5\%$
C. $16.7\%$
D. $20.0\%$
E. Cannot Be Determined

Answer: C

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Tue Nov 10, 2020 8:17 am

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Re: If $d$ is the smallest positive integer such that the range of the remainders obtained when multiples of $3$ are

by Scott@TargetTestPrep » Tue Nov 17, 2020 2:14 pm

Gmat_mission wrote: ↑
Tue Nov 10, 2020 8:17 am
$P =\{6, 3, 0, d, 4, 14, 9, 2d\}$

If $d$ is the smallest positive integer such that the range of the remainders obtained when multiples of $3$ are divided by $d$ is $3,$ by what percentage is the median of the numbers in $P$ smaller than the mean of the numbers in $P?$

A. $11.1\%$
B. $12.5\%$
C. $16.7\%$
D. $20.0\%$
E. Cannot Be Determined

Answer: C

Solution:

We see that d must be 4 since the smallest remainder when a multiple of 3 is divided by 4 is 0 (for example, 12/4 = 3 R 0) and the largest remainder when a multiple of 3 is divided by 4 is 3 (for example, 3/4 = 0 R 3). Therefore, P = {6, 3, 0, 4, 4, 14, 9, 8} or {0, 3, 4, 4, 6, 8, 9, 14}. We see that the median of the numbers in P is (4 + 6)/2 = 5 and the mean of the numbers in P is (0 + 3 + 4 + 4 + 6 + 8 + 9 + 14)/8 = 48/8 = 6. Since 5 is 1 less than 6, we see that 5 (the median) is 1/6 or 16.7% less than 6 (the mean).

Answer: C

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