If –10 ≤ a ≤ 5 and 7 ≤ b ≤ 10, what is the least possible value of |a

Question

If –10 ≤ a ≤ 5 and 7 ≤ b ≤ 10, what is the least possible value of |a − b| ?

(A) −2
(B) 0
(C) 2
(D) 3
(E) 5

GMATinsight · Answer

For |a − b| to be smallest, the values of a and b should be of same sign and absolute values should be as close as possible because |a − b| is always non-negative

|a − b| = |5 − 7| = 2

Ansder: Option C

Kinshook · Answer

Asked: If –10 ≤ a ≤ 5 and 7 ≤ b ≤ 10, what is the least possible value of |a − b| ?

Least possible value of |a-b| = 7 - 5 = 2 since |a-b| is the distance between a & b

IMO C

sujoykrdatta · Answer

|a - b| refers to the distance between a and b on the number line
Obviously then, |a - b| becomes minimum when a and b are closest to one another on the number line

We can see that a takes values of 5 and lower (till -10) while b takes values of 7 and higher (till 10)
Thus, the closes a and b approach each other is when a = 5 and b = 7

=> Minimum |a - b| = |7 - 5| = 2

Answer C

varmashreekanth · Answer

Hi,

I have taken the following approach to solve this question. Please correct me if I am wrong.

We have given that,
\(-10<= a <= 5\) -------(1)
\(7<=b<=10\) -------(2)
on re-arranging equation (2), we get
\(10 >=b>=7\) ---------(3)

Now, we know that we can subtract inequalities if they are of opposite signs and the final inequality sign would be the inequality sign of the equation from which the other equation is subtracted.
So we will perform \((1)-(3)\), and the inequality sign of (1) would be taken for the final result. So on performing \((1)-(3)\), we will get,
\( -20 <= a-b <=-2\)

So the extreme values of the equation \(a-b\) are \(-20 \), \(-2\)

Now we have to find out the least value of \(|a-b|\). So we will apply modulus on \(-20\) and \(-2\).
\(|-20| = 20\)
\(|-2| = 2\)

So the least value of \(|a-b| \) is \(2\).

So IMO option C is correct.

ayoubbk · Answer

C since plotting them in a number line and finding the smallest distance between the two ranges yields 2.

JohnGalt1 · Answer

Why it cannot be a zero?

Bunuel · Answer

For |a - b| to be 0, a must be equal to b which is not possible because we are given that –10 ≤ a ≤ 5 and 7 ≤ b ≤ 10 (notice that there is no overlap between possible values of a and b).

BrushMyQuant · Answer

–10 ≤ a ≤ 5 and 7 ≤ b ≤ 10 and we need to find the the least possible value of | a - b |

Now, we know that Least  Absolute Value of a number = 0, as Absolute value of a number is always non-negative

=> a - b = 0
=> a = b

But a and b cannot be equal based on the range given, but they can be close to each other when a = 5 and b = 7 
=> | 5 - 7 | = | - 2 | = 2

So,  Answer will be C 
Hope it helps!

Watch the following video to MASTER Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

If –10 ≤ a ≤ 5 and 7 ≤ b ≤ 10, what is the least possible value of |a

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If –10 ≤ a ≤ 5 and 7 ≤ b ≤ 10, what is the least possible value of |a

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