If x + y < 9 and 3 x – 2 y < 3 then sum of all possible values of x is (Given that x > 0) ?

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01 Jun 2010 Sum of all possible x

If x + y < 9 and 3 x – 2 y < 3
then sum of all possible values of x is (Given that x > 0) ?

OPtion

1) 10
2) 15
3) 21
4) 28
5) 36
6) 9
7) 12
8) 16
9) 7
10) 6

Solution

According to first condition given
x + y < 9
Implies that y < 9 - x
Implies that 2 y < 18 – 2 x
Implies that 2 y + 3 < 18 – 2 x + 3
Implies that 2 y + 3 < 21 – 2 x (i)
Now according to second given condition
3 x -2 y < 3
Implies that 3 x < 2 y + 3 (ii)
Adding (i) and (ii) conditions, we get
3 x < 2 y + 3 < 21 – 2 x
Implies that 3 x < 21 – 2 x
Implies that 5 x < 21
Hence possible integral values of x = 1, 2, 3, 4
sum of 1+2=3+4 = 10

Correct Option: 1 Best Solution (8)

Saswata Chakraborty   14 years AGO

x+y2x+2y

Like? Yes (1) | No   

Deepak Upreti   14 years AGO

the possible values of X can be 1,2,3,4. so that the sum of x values is 10 (option 1)

Like? Yes (1) | No   

SUDESHNA SEN   14 years AGO

Solving the given two inequalities, we have the possible values of x to be 1,2,3,4. So, the sum of all possible values of x is= 1+2+3+4= 10.....Option 1)

Like? Yes (1) | No   

ASHOK ROY   14 years AGO

Solving the given two inequalities, we have the possible values of x to be 1,2,3,4. So, the sum of all possible values of x is= 1+2+3+4= 10.....Option 1)

Like? Yes (1) | No   

Mamon Sengupta   14 years AGO

Solving the given two inequalities, we have the possible values of x to be 1,2,3,4. So, the sum of all possible values of x is= 1+2+3+4= 10.....Option 1)

Like? Yes (1) | No   

Trishita Dasgupta   14 years AGO

Solving the given two inequalities, we have the possible values of x to be 1,2,3,4. So, the sum of all possible values of x is= 1+2+3+4= 10.....Option 1)

Like? Yes (1) | No   

sanjib biswas   14 years AGO

all possible value of x is 1.2.3.4 then ans. is 10 i.e. option 1.

Like? Yes (1) | No   

Pargat Pal Singh   14 years AGO

x=1,2,3,4 are possible values.

sum=10

Like? Yes (1) | No