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# If a, b, c, d and e are different positive integers

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Manager
Joined: 02 Mar 2018
Posts: 59
Location: India
GMAT 1: 640 Q51 V26
GPA: 3.1
If a, b, c, d and e are different positive integers  [#permalink]

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Updated on: 05 Aug 2018, 10:52
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Difficulty:

35% (medium)

Question Stats:

71% (02:06) correct 29% (01:44) wrong based on 58 sessions

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If a, b, c, d and e are different positive integers, which of the five integers is the median?

(1) a = 3b = 2c = 4d = 5e

(2) a > b + c, and c > d + e, and e > d

Originally posted by gsingh0711 on 05 Aug 2018, 09:43.
Last edited by generis on 05 Aug 2018, 10:52, edited 2 times in total.
Edited and formatted the question, renamed the topic
Manager
Joined: 02 Mar 2018
Posts: 59
Location: India
GMAT 1: 640 Q51 V26
GPA: 3.1
Re: If a, b, c, d and e are different positive integers  [#permalink]

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05 Aug 2018, 09:44
1
Explanation:

Given a, b, c, d and e are different positive integers. First arrange the terms is ascending order, and then the middle term (if the terms are odd in number) and the average of two middle terms (if terms are even in number) is the median.

Considering statement 1:
a = 3b = 2c = 4d = 5e
When written in terms of a single variable, five positive integers a, b, c, d and e are a, a/3, a/2, a/4 and a/5, respectively.
⇒ a > c > b > d > e

Hence, when arranged in ascending order, middle term = median = b.

Since we are getting a definite answer from above statement, statement 1 itself is sufficient to provide the answer.

Considering statement 2:
a > b + c , c > d + e and e > d

Since integers are positive, statement 2 implies that a is greater than b and c both; c is greater than d and e both; and e is greater than d.
⇒ a > b & c, c > d & e, and e > d
⇒ d < e < c < a and b can be anything less than a (i.e. on the left side of a on the number line).
(b can be placed between c and a making c as the median; or it can be placed between e and c making b as the median.)

Hence, the middle term, i.e. the median cannot be determined.

Since we are not getting a definite answer from above statement, statement 2 itself is not sufficient to provide the answer.

I think, I deserve a kudus LOL
Manager
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GMAT 1: 650 Q42 V38
GRE 1: Q161 V164
Re: If a, b, c, d and e are different positive integers  [#permalink]

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05 Aug 2018, 09:58
As soon as I got to the second statement, I saw something was amiss, because it said e > d, which was directly contradictory to the result we got in the first statement
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Re: If a, b, c, d and e are different positive integers  [#permalink]

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28 Nov 2019, 20:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: If a, b, c, d and e are different positive integers   [#permalink] 28 Nov 2019, 20:30
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