Problem Solving

If the ages of students in a class vary between 18 and 22 inclusive, which of the following describes all possible ages x in this class?
(A) |x - 18|≤4
(B) |x + 20|≤2
(C) |x - 21|≤1
(D) |x - 22|≤0
(E) |x - 20|≤2

option A

The possible ages of X are 19,20,21,22.

If v substitute the values,option A alone satisfy the ineqaulity.

sanju09 wrote:If the ages of students in a class vary between 18 and 22 inclusive, which of the following describes all possible ages x in this class?
(A) |x - 18|≤4
(B) |x + 20|≤2
(C) |x - 21|≤1
(D) |x - 22|≤0
(E) |x - 20|≤2

out of the given option
|x - 20|≤2

x-20≤2 so x ≤22

-(x-20) ≤2
-x+20 ≤2
18 ≤x

so option E

selango wrote:The possible ages of X are 19,20,21,22.

If v substitute the values,option A alone satisfy the ineqaulity.

|x| <0
mod (x) <0 means x can either be +ve or -ve
means +x<0
-x<0

Ans is E ......

My silly mistake.option E right

amising6 wrote:

selango wrote:The possible ages of X are 19,20,21,22.

If v substitute the values,option A alone satisfy the ineqaulity.

|x| <0
mod (x) <0 means x can either be +ve or -ve
means +x<0
-x<0

I couldn't understand what you are trying to say here.
I am still having hard time figuring out why A cannot be the right answer.
Could you please explain this again in detail?

|a-b| just means how far apart a and b are on the number line.

The ages are between 18 and 22. Thus, the age of any person, x, can be at most 2 away from 20.

Thus, |x-20|<= 2

Testluv wrote:|a-b| just means how far apart a and b are on the number line.

The ages are between 18 and 22. Thus, the age of any person, x, can be at most 2 away from 20.

Thus, |x-20|<= 2

Isnt the ineqaulity in option A also satisfied by the details given in the question?

As you said, the ages are between 18 and 22 and the age of any person X can be at most 4 away from 18.

hardik.jadeja wrote:

Testluv wrote:|a-b| just means how far apart a and b are on the number line.

The ages are between 18 and 22. Thus, the age of any person, x, can be at most 2 away from 20.

Thus, |x-20|<= 2

Isnt the ineqaulity in option A also satisfied by the details given in the question?

As you said, the ages are between 18 and 22 and the age of any person X can be at most 4 away from 18.

The inequality in option A dose satisfy the constraints given in question but if you try and plot it on a number line option A and option E will give you different results .

The question says the age should be between 18 and 22 inclusive .That means 18<= x <= 22 .

If you plot this on a number line only option E matches as it says 18<= x <= 22 .

Although the number line represented by option (A) 14<= x <= 22 covers the same range required by the question its is not the same graph what is required .

rockeyb wrote: The inequality in option A dose satisfy the constraints given in question but if you try and plot it on a number line option A and option E will give you different results .

The question says the age should be between 18 and 22 inclusive .That means 18<= x <= 22 .

If you plot this on a number line only option E matches as it says 18<= x <= 22 .

I wasn't aware that we have to keep graphs in mind while answering such questions.. The question just asked which of the following describes all possible ages x in this class.

Is this one odd question where we need to consider graphs for picking the right answer or are there many similar questions?

hardik.jadeja wrote:

rockeyb wrote: The inequality in option A dose satisfy the constraints given in question but if you try and plot it on a number line option A and option E will give you different results .

The question says the age should be between 18 and 22 inclusive .That means 18<= x <= 22 .

If you plot this on a number line only option E matches as it says 18<= x <= 22 .

I wasn't aware that we have to keep graphs in mind while answering such questions.. The question just asked which of the following describes all possible ages x in this class.

Is this one odd question where we need to consider graphs for picking the right answer or are there many similar questions?

Just one point to remember whenever faced with an INEQUALITY question + mod operator (||) its better to verify your answer on a number line . Gives you a clear idea .

No this is not one odd question I have seen such questions around so I think these kind of questions are normal. Well I am no expert in this case may be others can shed some light .