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A, B, C, D and E are five consecutive integers and the average of these five numbers is less than 1/4th of A. Then A is
- a)Negative
- b)Positive
- c)Even
- d)Data Sufficient
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A, B, C, D and E are five consecutive integers and the average of thes...
As a is less than a negative number, so 'a' is also a negative number. Hence option C is correct.
Most Upvoted Answer
A, B, C, D and E are five consecutive integers and the average of thes...
1stly, it is given that a, b, c, d and e are 5 consecutive integers. So,
b=a+1, c= a+2, d=a+3, e=a+4
2ndly, it is given that
(a+b+c+d+e)/5<a/4
=>{a+a+1+a+2+a+3+a+4)/5<a/4
=>4(5a+10)<5a
=>20a+40<5a
=>20a-5a<-40
=>15a<-40
=>a<-40/15
As a is less than a negative number, so 'a' is also a negative number.
b=a+1, c= a+2, d=a+3, e=a+4
2ndly, it is given that
(a+b+c+d+e)/5<a/4
=>{a+a+1+a+2+a+3+a+4)/5<a/4
=>4(5a+10)<5a
=>20a+40<5a
=>20a-5a<-40
=>15a<-40
=>a<-40/15
As a is less than a negative number, so 'a' is also a negative number.
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Community Answer
A, B, C, D and E are five consecutive integers and the average of thes...
Given: A, B, C, D and E are five consecutive integers.
To find: The sign of A, i.e., whether it is negative or positive.
Solution:
Let's assume that the five consecutive integers are x, x+1, x+2, x+3 and x+4.
The average of these five numbers is:
= (x + (x+1) + (x+2) + (x+3) + (x+4)) / 5
= (5x + 10) / 5
= x + 2
Given that the average of these five numbers is less than 1/4th of A.
So, we have:
x + 2 < />
4(x+2) < a="" [multiplying="" both="" sides="" by="" />
4x + 8 < />
Now, we need to find the sign of A.
Since we don't know the value of x, we can't find the exact value of A.
However, we can find the range of values of A.
Let's assume that x is a negative integer.
Then, the lowest value of x can be -4 (because we are given that the five integers are consecutive).
In that case, we have:
4(-4) + 8 < />
-8 < />
This means that A can be any negative integer greater than -8.
Hence, option (a) is correct - A can be negative.
To find: The sign of A, i.e., whether it is negative or positive.
Solution:
Let's assume that the five consecutive integers are x, x+1, x+2, x+3 and x+4.
The average of these five numbers is:
= (x + (x+1) + (x+2) + (x+3) + (x+4)) / 5
= (5x + 10) / 5
= x + 2
Given that the average of these five numbers is less than 1/4th of A.
So, we have:
x + 2 < />
4(x+2) < a="" [multiplying="" both="" sides="" by="" />
4x + 8 < />
Now, we need to find the sign of A.
Since we don't know the value of x, we can't find the exact value of A.
However, we can find the range of values of A.
Let's assume that x is a negative integer.
Then, the lowest value of x can be -4 (because we are given that the five integers are consecutive).
In that case, we have:
4(-4) + 8 < />
-8 < />
This means that A can be any negative integer greater than -8.
Hence, option (a) is correct - A can be negative.
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