sum of three positive integers is 21. If greatest integer is 2 more than the least, then how many so

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24 Oct 2012 integers

sum of three positive integers is 21. If greatest integer is 2 more than the least, then how many solutions are possible.

OPtion

1) 9
2) 7
3) 4
4) 5
5) 1
6) 2
7) 8
8) 6
9) 3
10) none of these

Solution

according to the given conditions
L+M+G = 21 and G-L = 2
so G = L+2 and L+M+L+2 = 21 so 2L+M = 19 so M = 19-2L
so these three integers are L, 19-2L, L+2
possible solution is 6, 7, 8

Correct Option: 5 Best Solution (8)

Rijo   12 years AGO

numbers are 8 7 6

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SHITANSHU SONI   12 years AGO

let no.s be n-1,n,n+1 as they are 3 consecutive no.s
thus n-1 + n + n+1 = 21
3n = 21
n = 7
only one combination is possible...

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Muhammad Ahmed   12 years AGO

6+7+8=21

Like? Yes (2) | No (2)  

Rakesh Kumar Kohli   12 years AGO

The three positive numbers are 6,7,8
The difference between least 6 and greatst 8 is 2.
So there is only one solution.

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anju   12 years AGO

second sentance shows that these are consecutive numbers that's why only 1 ans will be possible....
let x is d smallest one so equ will be-
x+(x+1)+(x+2)=21;
3x+3=21;x=6.
so smallest no. is 6 then second no. is 7 & 8 is the greatest no....

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Ashita Kaushik   12 years AGO

Here as satisfied by the question let three positive integers be x,x+1,x+2
so as given: x+x+1+x+2=21
so x comes out to be 6
hence the numbers come out to be 6,7,8
and as given the second condition which is the greatest number is 2 more than the least number which is also satisfied as 8 is 2 more than 6..
Hence ther is only one solution which satisfies the condition so the correct option is option number 5 which is 1

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Tijo Jose   12 years AGO

Let the numbers in non-decreasing order be a, b, c.
Given:
* c = a + 2
* a + b + c = 21
* a

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Vedsar Kushwaha   12 years AGO

Since, the greatest number is two more than the least number. Therefore, the three numbers must be in consecutive form. i.e, x,x+1 and x+2.
Hence there will be only one solution to this problem.

Like? Yes (1) | No (4)