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28 Jun 2018, 11:41
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
42% (02:20) correct
58%
(01:53)
wrong
based on 98
sessions
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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.
(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.
28 Jun 2018, 13:06
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amanvermagmat
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.
28 Jun 2018, 18:45
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amanvermagmat
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
