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13 May 2020, 06:41
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B
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Difficulty:
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Question Stats:
44% (02:45) correct
56%
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If a, b, c and d are positive consecutive multiples, not necessarily in that order, of a positive integer x greater than 1, is a + b + c + d ≥ 50?
(1) c = 15
(2) The difference between d and b is divisible by only four positive integers, one of which is 10.
Are You Up For the Challenge: 700 Level Questions
(1) c = 15
(2) The difference between d and b is divisible by only four positive integers, one of which is 10.
Are You Up For the Challenge: 700 Level Questions
13 May 2020, 09:54
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Statement 1-
Case 1- a=6; b=9; d=12; c=15
a+b+c+d = 42 (No)
Case 1- a=5; b=10; c=15; d=20
a+b+c+d = 50 (Yes)
Insufficient
Statement 2-
Number of Factors of 10(2*5) = (1+1)*(1+1) = 4.
Difference of d-b =10
Hence each of them must be multiple of 5.
Minimum possible sum of a,b,c and d = 5+10+15+20=50 (since all are positive integers)
Hence, a+b+c+d is always greater than or equal to 50
Sufficient
Case 1- a=6; b=9; d=12; c=15
a+b+c+d = 42 (No)
Case 1- a=5; b=10; c=15; d=20
a+b+c+d = 50 (Yes)
Insufficient
Statement 2-
Number of Factors of 10(2*5) = (1+1)*(1+1) = 4.
Difference of d-b =10
Hence each of them must be multiple of 5.
Minimum possible sum of a,b,c and d = 5+10+15+20=50 (since all are positive integers)
Hence, a+b+c+d is always greater than or equal to 50
Sufficient
Bunuel
14 May 2020, 14:28
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Bunuel
Statement 1: if c=15 then we have consecutive multiples of 3,5 or 15.
6+9+12+15<50 and 15+30+45+60>50.Clearly insufficient
Statement 2: if the difference is divisible by 10,then its divisible by 1,2 and 5 since if something is divisible by 10 it must be divisible by 2 and 5 and of course 1. The difference can't be
more than 10 because then we'd have 4 and 20 as possible dividing integers.The difference is thus 10. d and b can not be the first and the last numbers since 10 can not be spread out into 3 equal integer spaces.This means d and b are consecutive multiples or have one multiple between them. IF they are consecutive multiples then they are multiples of 10.The sum of any 4 consecutive positive multiples of 10 is greater than 50.
If d and b have one multiple between them,then they are multiples of 5.The sum of any 4 consecutive positive multiples of 5 is greater than 50.
Statement 2 is sufficient
Answer is B
