If x is an integer, what is the least possible value of |19 - 3x| ?

Question

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

EgmatQuantExpert · Accepted Answer

Solution

Given:  
• x is an integer

To find:  
• The least possible value of |19 – 3x|

Approach and Working:   
• As it is a modulus expression, the value of it cannot be negative. The least value of any modulus expression can be 0.
• If we equate |19 – 3x| = 0, we get x = 19/3
 o As x is an integer, the nearest possible values for x will be 6 or 7 
• If x = 6, |19 – 3x| = 1 
• If x = 7, |19 – 3x| = 2
• If we take any other values of x, like x = 5 or x = 8, the value of the expression |19 – 3x| increases from 1.
 o Therefore, the least possible value of |19 – 3x| is 1.

Hence, the correct answer is option B.

Answer: B

RohitGoyal1123 · Answer

Least possible value of a mod function is 0

Here 0 can be attained by 19 = 3x or at x = 19/3, but since x is integer, the closest integer to 19/3 is 6

So at x=6, the function |19-3x| is least and the value is |19-18| = 1

Hence  B

stonecold · Answer

Given Data   -> x is an integer
We are now asked for the least possible value of |19 - 3x|

The least value of |p| for any variable p is always zero. But here x is an integer.
Lets use hit and trial and try on some values.
x=5 => 4
x= 6 => 1
x= 7 => 2
x= 8 => 5

Clearly the least value is 1.

Smash that B!

KSBGC · Answer

we are looking for least possible value. It's also given that x is an integer. but no sign is specific. 
Now what could be the value of x. If we take 6 as a value of x we will get 3*6=18. Ultimately, we will get 1.

One may check other values. This question needs a bit common sense. 
The correct answer is B.

prabsahi · Answer

Finally got it..Kudos!!

ScottTargetTestPrep · Answer

We want to find a multiple of 3 that is close to 19, such as 18. So if x = 6, then we have:

|19 - 3x| = |19 - 18| = 1

Alternate Solution:

The smallest value for an absolute value is 0. Thus, we can solve:

19 - 3x = 0

3x = 19

x = 6 ⅓

Since x must be an integer, and since all the answer choices are positive, we see that x = 6 is the greatest possible value for x. Thus, we have:

|19 - 3x| = |19 - 18| = 1

Answer: B

push12345 · Answer

|19-3x| is always positive or zero
This value can be minimum to zero and max is undefined

Since zero is not possible as x need to be 19/3 for this.
But x is an integer so next min value it can take is 1

I.e. when x=6, value would be 1

Posted from my mobile device

stonecold · Answer

The highlighted part is incorrect. Remember -> Zero is Neither Positive Nor Negative!

gmatns2018 · Answer

could you please post a list of such important points to remb before exam ? would be of great help to many

e.g |x| --> always +ve except for '0'
always consider +ve . -ve '0' and fraction value for values

etc etc

gurmukh · Answer

Try and put up the value of x which when multiply by 3 get as much close to 19 as possible.
x = 6
Value of modulus comes out 1.
Option B is the answer

Posted from my mobile device

Kinshook · Answer

Asked: If x is an integer, what is the least possible value of |19 - 3x| ?

|19-3x| is least when x = 6
|19-3*6| = |19-18| = |1| = 1

IMO B

ihasan · Answer

I approached it by putting integer values starting 5 and found that for x=6 it will be |19-18| = 1.

Also, we can't get '0' for of any integer values

Hence, answer is option 'B'.

MathRevolution · Answer

19 - 3x will be least when 3x will be maximum. Also, modulus will turn the negative values in positive.

19 being prime, it will not be divisible by 3.

We are asked least possible value hence 19-3*6 = 1. ( At x = 7 , it will be 19-21=-2 , |- 2| = 2)

Answer B.

Neghineh · Answer

I do not understand why you can't plug in 0, because then you get either positive 19 or negative 19. What am i doing wrong here?

ihasan · Answer

Mod of +-19 will be +19, which is not the least possible value of the expression.

GMATinsight · Answer

Neghineh  19 is NOT the smallest value of |19 - 3x| hence that's incorrect answer

Understand a basic thing of absolute values.
- Absolute values are always non-negative
- Minimum absolute value on number line is ZERO (0)

Therefore, you need to try to make |19 - 3x| equivalent or close to zero 
SInce, x is an integer therefore 19-3x can NOT be zero as 3x will always be even

but the value of 3x closest to 19 is 18 which is obtained for x = 6

i.e.@x = 6, |19 - 3x| = |19 - 3*6| = |19 - 18| = 1

Answer: Option B

I hope this helps!!!

bumpbot · Answer

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If x is an integer, what is the least possible value of |19 - 3x| ?

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If x is an integer, what is the least possible value of |19 - 3x| ?

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