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

Question

If  a≤b≤c≤d  is  a≥20 ?

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

(2)  5a≥2d

hloonker · Answer

If a≤b≤c≤d

is a≥20?

(1) - insufficient as A could be 1 or 21/

(2) 5a≥2d - insufficient - as this gives us no base relationship.

Together also - a could be 19 or 21.

Answer: E

Valike · Answer

From Statement 1:

Maximum value of A can be 42.5
Because if A=B=C=D, then all of these will have an equal value of 42.5

Thus, not sufficient.

From Statement 2:

5A >=2D

Thus, A>=2/5D

Again, not sufficient as D can be any 45, which means A is >= 19.
Or If D is 20, Then A is >= 8.

Not Sufficient.

Taking 1 & 2 together,

If D has a value below 42.5, then the equation in statement 1 will not hold true without A being greater than 20.
If D as a value of 45 also, the equation in statement 1 will not hold true without A being greater than 20.

If D has a very large value (like 80), the equality mentioned in statement 2 will hold true, thus A will be >= 32.

Thus the answer to the question is C

cyrwr1 · Answer

Stmt 1 tells us four numbers add up to 170, find the smallest one. INSUFFICIENT
Stmt 2 tells us a >(2/5)*d okay... insufficient

combining stmt 1+2: bare minimum, we would have a+a+a+ (>5/2)*a = 170 one variable in an equation and a range is produced when simplified.

rahul_ranjan · Answer

Statement 1 Alone:
We have a relation among all the variables, but there are no specific condition on any variable.
So not much can be said about a>=20. It can be either less or more than 20.
However, from the info present in question, maximum value of 'a' can be found i.e. if all the values are equal then maximum value of 'a' will be attained. Therefore, a can attain a maximum value of 42.5 i.e. a<=42.5.
Thus, statement 1 is insufficent.

Statement 2 Alone:
Again, statement 2 is a general relation and a can take any value either less than or more than 20.
So, statement 2 is insufficient.

Both Statement 1 &2:
From statement 1 we found that a<=42.5.
Now, let us find minimum value for 'a'.
From statement 1 & info from question statement minimum value of 'a' would occur when b=c=d
=> a+3d=170
=> minimum value of a=170-3d --------> Eqn. (1)
From statement 2, we have 5a>=2d
=> d<=2.5a
thus, minimum value of 'a' would occur when d is maximum i.e. d=2.5a
=> min(a)=170-3{2.5*min(a)}
=> min(a)=20
=> a>=20
Thus, Statement 1 & 2, together are sufficient to tell a>=20.
Hence, correct option is 'c'.

samarpan.g28 · Answer

Consider statement 1. If a=b=c=d then 170/4=42.5. We can easily determine that a,b,c,d can take 41,42,43,44 since 41+42+43+44=170 and a is greater than or equal to 20.
But, these are not the only values these variables can take. a can be 10, b=c=53 and d=54 so that 10+53+53+54=170. For the latter, a≤b≤c≤d holds true but a is less than 20.
Therefore, statement 1 is insufficient.

Consider statement 2. When a=41, b=42, c=43 and d=44 then 5a=205 and 2d=88. 205≥88 and a≥20.
But if a=10, b=c=53 and d=54 then 5a=50 and 2d=50. Here, 50≤104 and a≤20.
Therefore, statement 2 is insufficient too.

Combine 1 and 2. If 5a≥2d then the minimum value a can hold is 20 and d can hold 50 so that 100≥100.
Now we can say a=20, b=c=d=50. This is sufficient. Option (C) is correct.

ggs123 · Answer

Hi,

I think I know how to solve this

1. Insufficient because -
 a could be equal to d in which case, a=b=c=d=42.5
 or
 a could be 0 and b + c + d could add up to 170

2. 5a≥2d - insufficient - a could be 1 and d could be 2 ( 5 > 4) or a could be 20 and d could be 30 ( 100 > 60)

3. When you combine 1 and 2, you get a + b + c + d = 170 and 5a ≥ 2d => a ≥ 2/5d ( a could be 2/5d or 3/5d .... 5/5d)

Lets think about that. The min value of a is when a = 2/5d and b = c = d
=> 2/5d + 3d = 170
=> 17/5d = 170
=> d = 20

We get the max value of a when a = b = c = d = 42.5

We can conclude that a is always greater than or equal to 20

siddharth_ · Answer

As explained by most of the posts, 1st and 2nd individually are insufficient. Now combining both - let's try and find out the min value of a.

a<= 2/5d; let a = 2/5d - for min value of a, d should also be minimised, so let b=c=d. Thus, 2/5d + 3d = 170. Solving, d=50 and a = 20.

So min value of a is 20, which means 'yes a >= 20' and C is the answer.

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

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