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If a, b, c, d are four integers such that a < b < c < d, Is d-c = c-b

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If a, b, c, d are four integers such that a < b < c < d, Is d-c = c-b  [#permalink]

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New post 28 Jun 2018, 10:41
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Question Stats:

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If a, b, c, d are four integers such that a < b < c < d, Is d - c = c - b ?

(1) All four integers a, b, c, d are less than 5.

(2) Arithmetic mean of a, b, c, d is same as the median of a, b, c, d.
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If a, b, c, d are four integers such that a < b < c < d, Is d-c = c-b  [#permalink]

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New post 28 Jun 2018, 12:06
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amanvermagmat wrote:
If a, b, c, d are four integers such that a < b < c < d, Is d - c = c - b ?

(1) All four integers a, b, c, d are less than 5.

(2) Arithmetic mean of a, b, c, d is same as the median of a, b, c, d.


IMO E

Statement 1: All four integers a, b, c, d are less than 5.

a<b<c<d Lets assume a=1, b=2, c=3, d=4

d-c=4-3=1
c-b=3-2=1 Yes, this satisfies the condition.

Now lets assume a=-10, b-4, c=0, d=1

d-c=1-0=1
c-b=0-(-4)=4 No, this doesn't satisfy the condition.

Therefore, Statement 1 is insufficient.

Statement 2: Arithmetic mean of a, b, c, d is same as the median of a, b, c, d.

Let's assume a=-10, b=-5, c=5, d=10
mean(0/4) = 0 = median(0/2)

d-c=10-5=5
c-b=5-(-5)=10 No, this doesn't satisfy the condition.

Now lets assume a=1, b=2, c=3, d=4
mean (10/4) = 2.5 = (5/2) Median

d-c=4-3=1
c-b=3-2=1 Yes, this satisfies the condition.

Therefore, Statement 2 is insuficient.

Together,
Lets assume a=1, b=2, c=3, d=4
mean (10/4) = 2.5 = (5/2) Median

d-c=4-3=1
c-b=3-2=1 Yes, this satisfies the condition.

Lets assume a=-4, b=-2, c=2, d=4
Median = Mean = 0

d-c=4-2=2
c-b=2-(-2)=4 No, this doesn't satisfy th[/u][/i]e condition.

Even taken Together, the Statements are insufficient to arrive at an answer.

Therefore, Answer is E.
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If a, b, c, d are four integers such that a < b < c < d, Is d-c = c-b  [#permalink]

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New post 28 Jun 2018, 17:45
amanvermagmat wrote:
If a, b, c, d are four integers such that a < b < c < d, Is d - c = c - b ?

(1) All four integers a, b, c, d are less than 5.

(2) Arithmetic mean of a, b, c, d is same as the median of a, b, c, d.


My ans is E

Question asks, whether C is the average of b & d

St1: No valid info to prove or disprove the question

St2: Rearranging we get a+d = b+c

option1 : if a,b,c,d are conseq no., then true.

option2 : a=-8, b=-5, c=-4, d=-1, then false

combining st1 & st2, statement 2 has number choices taken based on statement 1. Still no answer
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If a, b, c, d are four integers such that a < b < c < d, Is d-c = c-b &nbs [#permalink] 28 Jun 2018, 17:45
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