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If a≤b≤c≤d is a≥20?  1) a+b+c+d=170 2) 5a≥2d

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If a≤b≤c≤d is a≥20?  1) a+b+c+d=170 2) 5a≥2d [#permalink]

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New post 09 Mar 2017, 22:25
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If \(a≤b≤c≤d\) is \(a≥20\)? 

1) \(a+b+c+d=170\)

2) \(5a≥2d\)
[Reveal] Spoiler: OA

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Re: If a≤b≤c≤d is a≥20?  1) a+b+c+d=170 2) 5a≥2d [#permalink]

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New post 14 Apr 2017, 11:26
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ziyuen wrote:
If \(a≤b≤c≤d\) is \(a≥20\)? 

1) \(a+b+c+d=170\)

2) \(5a≥2d\)


stmt-1:
If nothing is told whether a, b, c and d are integers, +ve or -ve then this stmt-1 is certainly insufficient.

stmt-2:
only given about a and d but nothing about c and d. insuff

stmt-1+2:

d <= 5a/2

now test the extreme value that is 20.
d <= 5*20/2
d <= 50

so if a = 20 then all b, c & d has to be 50 for a+b+c+d to be 170.

now if you take any less value of a the sum of b+c+d will not be sufficient to make a+b+c+d to be 170 because for lower than 20 value of a d will be lesser than 50.

this is why a has to be >= 20. Answer is then C.
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Re: If a≤b≤c≤d is a≥20?  1) a+b+c+d=170 2) 5a≥2d [#permalink]

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New post 11 Jul 2017, 18:53
If a≤b≤c≤da≤b≤c≤d is a≥20a≥20?

1) a+b+c+d=170a+b+c+d=170

2) 5a≥2d

We are asked if a≥20.

From (1), we know that the sum of a+b+c+d=170.
a can be any number since we don't know the magnitude of the numbers, or whether the numbers are positive or negative.
INSUFFICIENT.

From (2) we know that 5a≥2d, so 5a/2≥d. a and d could be any number.
INSUFFICIENT.

With (1) and (2):
Let's assume the minimum possible value of a when a=b=c=d, and 5a/2=d.
a+b+c+d=170
a+a+a+5a/2=170
11a/2=340
a=30.91
Thus a≥20.
SUFFICIENT

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Re: If a≤b≤c≤d is a≥20?  1) a+b+c+d=170 2) 5a≥2d [#permalink]

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New post 13 Jul 2017, 01:55
Minimum Value of a after both statements are combined would be 20
d=2.5a
b=2.5a
c=2.5a
a=a

a+b+c+d=8.5a
8.5a=170
2=20 ( Minimum Values )

And Max will be 42.5( 4a=170)

So Option C is correct .

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Re: If a≤b≤c≤d is a≥20?  1) a+b+c+d=170 2) 5a≥2d   [#permalink] 13 Jul 2017, 01:55
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