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A set consists of 5 distinct positive integers a, b, c, d, e, ........

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A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

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New post 09 Jan 2019, 01:24
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A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

    A. 16
    B. 17
    C. 18
    D. 19
    E. 20


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A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

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New post Updated on: 09 Jan 2019, 02:41
given
b is least integer and d is highest no
and sum of a,b,c= 24
mean of b+24+d/5 =8.8
b+d=20
since d is the highest no it can be 19 and b is least can be 1
so 19-1= 18
IMO C


EgmatQuantExpert wrote:
A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

    A. 16
    B. 17
    C. 18
    D. 19
    E. 20


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Originally posted by Archit3110 on 09 Jan 2019, 02:13.
Last edited by Archit3110 on 09 Jan 2019, 02:41, edited 1 time in total.
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A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

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New post 09 Jan 2019, 02:38
Archit3110 wrote:
given
b is least integer and d is highest no
and sum of a,b,c= 24
mean of b+24+d/5 =8.8
b+d=20
since d is the highest no it can be 20 and b is least can be 0
so 20-0 = 20
IMO E


EgmatQuantExpert wrote:
A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

    A. 16
    B. 17
    C. 18
    D. 19
    E. 20


To read all our articles:Must read articles to reach Q51

Image



Hi Archit3110,

Please note that a, b, c, d and e are positive integers

Regards,
_________________








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A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

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New post 09 Jan 2019, 02:40
EgmatQuantExpert

there is a confusion regarding usage of 0 ;
what i know is that 0 is neither +ve or -ve integer

if a statement says n is a set of +ve integers then we begin set n from (1,2,3...)

and if statement says n is a set of non negative integer then we begin set from ( 0,1,2,3,..)

will 0 be considered in set of +ve even integers? i.e (0,2,4,6,.) or not?

EgmatQuantExpert
in that case b =1 and d = 19
and d-b = 18
IMO C



EgmatQuantExpert wrote:
Archit3110 wrote:
given
b is least integer and d is highest no
and sum of a,b,c= 24
mean of b+24+d/5 =8.8
b+d=20
since d is the highest no it can be 20 and b is least can be 0
so 20-0 = 20
IMO E


EgmatQuantExpert wrote:
A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

    A. 16
    B. 17
    C. 18
    D. 19
    E. 20


To read all our articles:Must read articles to reach Q51

Image



Hi Archit3110,

Please note that a, b, c, d and e are positive integers

Regards,

_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

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Joined: 04 Jan 2015
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A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

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New post 09 Jan 2019, 02:53
Archit3110 wrote:
EgmatQuantExpert

there is a confusion regarding usage of 0 ;
what i know is that 0 is neither +ve or -ve integer

if a statement says n is a set of +ve integers then we begin set n from (1,2,3...)

and if statement says n is a set of non negative integer then we begin set from ( 0,1,2,3,..)

will 0 be considered in set of +ve even integers? i.e (0,2,4,6,.) or not?


Yes, 0 is neither a positive integer nor a negative integer.
    It will be included in a set of non-negative and non-positive integers but it must be excluded from the set of positive or negative integers

Though, 0 is an even integer, it cannot be considered as a positive even integer. Since, 0 is not a positive integer

Regards,
_________________








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Re: A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

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New post 09 Jan 2019, 02:57
EgmatQuantExpert

thanks :)

EgmatQuantExpert wrote:
Archit3110 wrote:
EgmatQuantExpert

there is a confusion regarding usage of 0 ;
what i know is that 0 is neither +ve or -ve integer

if a statement says n is a set of +ve integers then we begin set n from (1,2,3...)

and if statement says n is a set of non negative integer then we begin set from ( 0,1,2,3,..)

will 0 be considered in set of +ve even integers? i.e (0,2,4,6,.) or not?


Yes, 0 is neither a positive integer nor a negative integer.
    It will be included in a set of non-negative and non-positive integers but it must be excluded from the set of positive or negative integers

Though, 0 is an even integer, it cannot be considered as a positive even integer. Since, 0 is not a positive integer

Regards,

_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2432
Re: A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

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New post 11 Jan 2019, 06:12

Solution


Given:
    • A set of 5 distinct positive integers, {a, b, c, d, e}
    • b is the least number and d is the highest number of the set
    • a + c + e = 24
    • Mean of the set = 8.8

To find:
    • The maximum value of (d – b)

Approach and Working:
    • a + c + e = 24 ………………………….………………………………… (1)
    • \(\frac{(a + b + c + d + e)}{5} = 8.8\)
      o Implies, a + b + c + d + e = 5 * 8.8 = 44 …………… (2)

(2) – (1), we get,
    • b + d = 44 – 24 = 20
    • For d – b to be maximum, b must be minimum
      o The minimum value b can take is 1, since b is a positive integer

    • If b = 1, then d = 20 – 1 = 19

Therefore, the maximum value of (d – b) = 19 – 1 = 18

Hence, the correct answer is option C.

Answer: C

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Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
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Algebra- Wavy line | Inequalities

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Re: A set consists of 5 distinct positive integers a, b, c, d, e, ........ &nbs [#permalink] 11 Jan 2019, 06:12
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