Given that x+y>z, x,y,z are positive integers then 1) x>z 2) y>z 3) x-y>z 4) xy>=z 5) x/y> H

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08 Sep 2011 inequities

Given that x+y>z, x,y,z are positive integers
then
1) x>z
2) y>z
3) x-y>z
4) xy>=z
5) x/y>
How many of these 5 conditions are definitely true for all values of x,y and z

OPtion

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

Solution

only xy>=z is true always on the basis of given conditions

Correct Option: 1 Best Solution (10)

Shourya Goyal   12 years AGO

only condition 4 is true.....
let x = 3, y = 4 & z = 5, x,y,z E Z+
x+y>z (3+4>5)
here....
3 >/ 5 FALSE
4 >/ 5 FALSE
3 - 4 >/ 5 FALSE
3.4 = 12 >= 5 TRUE
3/4 >/5

Like? Yes (7) | No (3)  

@SI-IW@NI 12U13EY   12 years AGO

x+y>z does signifies only 1 of the above conditions n it does not signifies any-other condition........
to speak more specifically over the answer let us take the three positive integers be 2,2,3 (since no condition is given regarding the value of x,y,z except that they r positive integers)
2+2>3
also,
2>3 (condition1 and 2 are false)
2*2>3 (condition 4 holds true)
2-2>3 (condition 3 false)
2/2>3 (condition5 false)
so,except 4 every-other condition proves to be false
now to check for condition 4 furthermore,
let,x=1
y=1
z=1
x+y>z
1*1>=z (condition 4 true)


hence answer is 1

Like? Yes (2) | No   

Dr.Dipin Singh   12 years AGO

x+y>z, x,y,z are positive integers
then
xy>=z is definitely true.

xy=Z is possible if x or y =1
otherwise
xy>z

Like? Yes (3) | No (2)  

Mullaji Zubair Dawood   12 years AGO

as x+y>z,
one condition is obviously True.i.e xy>=z

Like? Yes (1) | No   

maddali sarika   12 years AGO

x*y >=z,because multlipicationsign have value than +

Like? Yes (1) | No   

Arjun S Sanakan   12 years AGO

only option 4 in the qn shows the correct answer.bsoz x,y,z be any +ve integer, the equation is correct..

Like? Yes (1) | No   

SOURAV ROY   12 years AGO

as x+y>z
den it must be x*y>z
becoz x,y,z are possitive integer

Like? Yes (1) | No (1)  

soumya goyal   12 years AGO

lets take x=1 y=3 and z=2
x>z ==> 1>2 no
y>z ==> if let y=1 x=3 and z=2
then this will also not true
x-y>z 1-3>2 no
xy>=z 1*3>=2 yes
x/y>z 1/3>2 no
hence only 1 condition would be true for any value of x,y,z

Like? Yes (4) | No (4)  

krishna kumar gupta   12 years AGO

by hit and trial method...
only xy>=z will true..

Like? Yes (1) | No (1)  

Harsh rajpal   12 years AGO

1, 2, 3 condition are definitely not true, because there may be some cases that contradict the.

4th one is true as x and y are positive.

5th is incomplete condition

Like? Yes (1) | No (1)