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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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09 Jan 2019, 01:24
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Difficulty:

55% (hard)

Question Stats:

58% (01:18) correct 42% (01:32) wrong based on 43 sessions

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

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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

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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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

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.

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

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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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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
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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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.

_________________

Number Properties | Algebra |Quant Workshop

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Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
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Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
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Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

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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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