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Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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Updated on: 27 Feb 2019, 23:39
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38% (03:19) correct 62% (02:40) wrong based on 69 sessions
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eGMAT Question of the Week #32The arithmetic mean of a sequence of 15 integers is 78. The largest value of the set is five times the smallest value of the set. If the mean of the set is equal to the median, then what is the maximum possible value for the range of the set? A. 52 B. 104 C. 112 D. 208 E. 260
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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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18 Jan 2019, 02:53
If we want maximum range, we want 5x to be as large as possible and x to be as small as possible x       78       5x
This is only possible if all the other numbers are 78 13*78 = 1014
Total sum of 15 numbers = 1170 Subtracting sum of 13 no.s from sum of 15 no.s = 11701014 = 156
which is equal to x+5x = 6x=156 x=26
Range = 5xx=4x=4*26=104



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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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18 Jan 2019, 05:08
My approach for this problem was
Sum of nos. 78*15=1170 Sum of nos of a sequence= n/2*(a+an) Where n total nos of digit, a = first digit and an = last digit Therefore, 15/2*(a+an)= 1170
a+an=156 an = 5a (given in question) 6a=156 a=26, an=130 Range =13026, 104 (B)
Feel free for correction ?
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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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Updated on: 21 Jan 2019, 07:34
EgmatQuantExpert wrote: The arithmetic mean of a sequence of 15 integers is 78. The largest value of the set is five times the smallest value of the set. If the mean of the set is equal to the median, then what is the maximum possible value for the range of the set? A. 52 B. 104 C. 112 D. 208 E. 260 sequence XXXXXXX 787878787878 5X = 78* 15 12X+ 78*7 = 1170 X= 52 5X= 260 RANGE = 5XX = 26052 = 208 IMO D
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Originally posted by Archit3110 on 18 Jan 2019, 08:36.
Last edited by Archit3110 on 21 Jan 2019, 07:34, edited 1 time in total.



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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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Updated on: 18 Jan 2019, 12:45
We have to minimise X and maximize 5x.
So X X X X X X X 78 78 78 78 78 78 78 5X
Is the correct sequence.
Hence 7*(78X)=5X78 8*78=12X
Hence X=52 4X=208
Option D is correct.
Originally posted by nitesh50 on 18 Jan 2019, 08:42.
Last edited by nitesh50 on 18 Jan 2019, 12:45, edited 2 times in total.



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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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18 Jan 2019, 10:30
EgmatQuantExpert wrote: The arithmetic mean of a sequence of 15 integers is 78. The largest value of the set is five times the smallest value of the set. If the mean of the set is equal to the median, then what is the maximum possible value for the range of the set? A. 52 B. 104 C. 112 D. 208 E. 260 (x+5x)/2=78 mean/median x=26 5x=130 13026=104 B



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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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18 Jan 2019, 12:00
We have to maximise the value of 5x and minimise the value of x such that the sum of the sequence remains 15*78=1170.
Hence, the sequence can be where mean is equal to median
x,x,x,x,x,x,x, 78, 78,78,78,78,78,78, 5x
The sum of the above sequence is 7x+ 78*7 + 5x = 15*78> 12x= 8*78> x=52
Hence the maximum range of the value of the set is 5xx= 4x= 4* 52= 208
Hence answer is D.,



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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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19 Jan 2019, 01:57
My approach was: l=5a
Median=(a+l)/2=Mean=78
>>:::Range=la=104
I think I missed the point of maximizing the Range but accidentally did so...!!?



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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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23 Jan 2019, 00:49
Solution Given:• The arithmetic mean of a sequence of 15 integers is 78 • The largest value of the set is five times the smallest value of the set • The mean of the set is equal to the median To find:• The maximum possible value for the range of the set Approach and Working: • We know that the range of a set = the largest value – the smallest value So, for the range to be maximum, we need to maximise the value of largest element of the set and minimise the value of smallest element of the set. • We know that the mean = the median = the 8th element of the sequence = 78 • So, to minimise the first element of the sequence, all the elements before the median element must be same. Let us assume it be “a” • And, to maximise the last element of the sequence, all the elements after the median except the last element must be minimum = the median = 78 • The last element of the sequence will be = 5 * a We are also given that the mean of the set = median = 78 • Implies, sum of all 15 elements in the sequence = 78 * 15 • Thus, a + a + a + a + a + a + a + 78 + 78 + 78 + 78 + 78 + 78 + 78 + 5a = 78 * 15
o 12a = 78 * 15 – 78 * 7 o \(a = 78 * \frac{8}{12} = 52\) • Therefore, range of the set = 5a – a = 4a = 4 * 52 = 208 Hence the correct answer is Option D. Answer: D
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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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25 Jan 2019, 12:41
My question is why is this being assumed "Thus, a + a + a + a + a + a + a + 78 + 78 + 78 + 78 + 78 + 78 + 78 + 5a = 78 * 15"



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Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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24 Mar 2019, 12:40
EgmatQuantExpert wrote: eGMAT Question of the Week #32The arithmetic mean of a sequence of 15 integers is 78. The largest value of the set is five times the smallest value of the set. If the mean of the set is equal to the median, then what is the maximum possible value for the range of the set? A. 52 B. 104 C. 112 D. 208 E. 260 Dear Bunuel, What mistake I have made in the math. In my sense, the answer is B. I would be glad if you help me to find out the mistake. (x+5x)/2=78 ( Mean and Median is the same) x=26 5x=130 13026=104



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Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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30 Mar 2019, 00:23
EgmatQuantExpert" So, to minimise the first element of the sequence, all the elements before the median element must be same. Let us assume it be a " Is'nt it that all the elements before the median element must be equal to the median to minimise the first element? Please correct me if I'm wrong, having tough time understanding these type of questions.




Re: Question of the week  32 (The arithmetic mean of a sequence of 15 ..)
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30 Mar 2019, 00:23






