What is least possible value of |23 - 7y| is (A)0 (B)1 (C)2 (D)5 (E)9

Question

What is least possible value of |23 - 7y| is

(A)0
(B)1
(C)2
(D)5
(E)9

BrentGMATPrepNow · Accepted Answer

The mistake that some people will make is assuming that y is an integer. These people will incorrectly choose answer choice C.

Since y can be ANY number, we can minimize the value of |23 - 7y| by setting 23 - y equal to zero
If 23 - 7y = 0, then 23 = 7y, which means y = 23/7
In other words, when y = 23/7, we find that |23 - 7y| = 0

Answer:  A

Bunuel · Answer

The absolute value cannot be negative but it can be 0, so the least value of |something| is 0.

Answer: A.

stonecold · Answer

Hi Brent.!! Can you share you inputs on this one => if-x-is-divisible-by-2-14-and-11-which-of-the-following-must-be-the-228248.html

BrentGMATPrepNow · Answer

I just added my response to that thread, but you're not going to like my answer

Cheers, Brent - now with 25% more letters!!

Ashiquzzaman · Answer

Hi Experts,

What does it mean by "least possible value of |23 - 7y|"?
As I understood, the question is asking which can produce closest distance from 0.
If we pick 0 then the distance from 0 will be +-23.
However, picking 2 produce +-9. Isn't it closer than +-23.
Please help me correct my mistake.
Thanks in advance.

ScottTargetTestPrep · Answer

The smallest possible value of the absolute value of any linear expression is 0. So the answer is 0. As Brent said, be sure to not fall for the trap of thinking that y must be an integer.

Answer: A

law258 · Answer

Question doesn't say anything about y strictly being an integer. Therefore, if y=23/7, we'll get 23-23=0

A

alados14 · Answer

So then if the question is rephrased, such that y is an integer, does C becomes that ans?

Bunuel · Answer

Yes. The least value of |23 - 7y| when y is an integer is 2, for y = 3. Here is a question with that constraint: https://gmatclub.com/forum/if-y-is-an-i ... 39867.html Hope it helps.

WiziusCareers1 · Answer

To find the least possible value of ∣23−7y∣, we need to understand the properties of absolute values and the constraints placed on the variable y.

1. General Property of Absolute Values 
The absolute value of any real number, denoted by ∣x∣, is defined as the non-negative distance of that number from zero on the number line. Mathematically: ∣x∣ ≥ 0
This means that the smallest possible value any absolute value expression can ever take is 0, provided that there is a value for the variable that makes the internal expression equal to zero.

2. Can the Expression Equal Zero? 
We check if there is a value for y such that:
23 − 7y = 0
7y = 23
y = 23/7
​ 
If y can be any real number (including fractions and decimals), then setting y = 23/7 ≈3.2857 results in 0

3. The "Integer" Trap 
Many students make an error assuming that y must be an integer.
If y were an integer, we would look for the multiple of 7 closest to 23.
If y = 3, then 7y = 21. Hence, ∣23 − 21∣ = 2.

If y = 4, then 7y = 28. Then ∣23 − 28∣ = ∣−5∣ = 5. In this scenario, the least value would be 2 (Option C).

However, since the problem statement does not specify that y is an integer, we must treat y as a real number. In the absence of an "integer" constraint, the absolute value can always reach its theoretical minimum of 0.

Since 0 is achievable for a real number y, and no restriction to integers is provided in the prompt:
The least possible value is 0.
The answer is A.

Approach 2: Direct Answer 
The least possible value for any absolute value equation, when there are no constraints, is zero.
Hence, the answer is A.

What is least possible value of |23 - 7y| is (A)0 (B)1 (C)2 (D)5 (E)9

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is least possible value of |23 - 7y| is (A)0 (B)1 (C)2 (D)5 (E)9

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards