Absolute values

Hi sarthakaggarwal,

The concept of Absolute Values is relatively rare on the GMAT; you'll likely see it just 1-2 times on Test Day. By extension, focusing too much on that one subject might not be the best use of your time right now (especially if you are missing out on lots of potential points in other areas). That having been said, most GMAT questions are written so that they can be approached in more than one way - and if you're trying to take an Algebra-heavy, 'math' approach to these types of questions, then that might be making solving these prompts more difficult.

Do you have any examples of the types of Absolutely value questions that you find challenging?

GMAT assassins aren't born, they're made,
Rich
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Hi sarthakaggarwal,

Do you have any examples that you can share here?
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Thank you for the reply
The absolute value questions troubling me the most are the could be true and must be true questions.
Most of the times i miss a certain case and get my answer wrong and even in questions i answer correctly i spend like 3-4 mins

Thank you for the reply i am having most trouble in could be true and must be true questions which involve the concepts of absolute values and inequalties
Most of the times I somehow took the longer and more difficult approach and i don't know when to use which approach
One of the gmat club exam question i did wrong was-

If x and y are positive integers, is x a prime number?


(1) |x−2|<2−y

(2) x+y−3=|1−y|

Hi sarthakaggarwal,

Many DS questions can be solved by TESTing VALUES - and this prompt gives us a great opportunity to do so. As with any question, you have to pay attention to the 'restrictions' that the prompt places on us, including the fact that the result of an Absolute Value calculation will NEVER be a negative number (that result will either be a positive number or a 0).

If X and Y are POSITIVE INTEGERS, is X a PRIME number?

1) |X−2| < 2−Y

2) X+Y−3 = |1−Y|

Here, we're restricted to positive integers ONLY and we're asked if X is a PRIME number. This is a YES/NO question.

1) |X−2| < 2−Y

Notice that the 'left side' of this inequality includes an Absolute Value, so that part of the calculation cannot be any smaller than 0. This is interesting, since the 'right side' must be GREATER than the 'left side', but we are SUBTRACTING a positive number from 2. This severely limits the value of Y.

Y CANNOT be 3.... since 2-3 = -1... and that won't be greater than the 'left side'
Y CANNOT be 2.... since 2-2 = 0... and that won't be greater than the 'left side'

Remember that Y MUST be a positive integer, so there's only one option left. Y MUST be 1. We can 'lock' that value in place.

Y = 1

Now we have...
|X-2| < 1

Again, we're restricted to positive integers only for X - and there's only one possible value for X that will fit this inequality: it's when X = 2. This would give us...

|2-2| < 1
0 < 1

Since X = 2, the answer to the question is YES... and since there's only one possible answer, the answer is really ALWAYS YES.
Fact 1 is SUFFICIENT.

Notice how no special calculations were needed here; just a bit of Arithmetic and TESTing VALUES to determine what options are possible. Fact 2 will require a little more work, but the type of work will be the same.

2) X+Y−3 = |1−Y|

Here, the 'right side' of the equation can never be any smaller than 0, but the 'left side' includes a "-3", so we have to be sure that the result of that part of the calculation never drops below 0. Let's try TESTing some values and see what happens...Remember that both X and Y must be POSITIVE INTEGERS.

IF.... Y = 1
X+1-3 = |1-1|
X - 2 = 0
X = 2... Here, the answer to the question is YES.

IF.... Y = 2
X+2-3 = |2-1|
X - 1 = 1
X = 2... Here, the answer to the question is YES.

IF.... Y = 3
X+3-3 = |3-1|
X = 2
X = 2... Here, the answer to the question is YES.

Notice the pattern? If you're not sure yet, then feel free to try a few more TESTs (since you're just doing basic Arithmetic, that additional work shouldn't take too long. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Thank you!
I was solving it using traditional approach and end up wasting a lot of time
Next time onwards I will try to use tricks like these.

Hi Sarthak,

A couple of weeks ago, I was struggling with questions involving Inequalities and Absolute Values.

Let me share with you the resources I used to study this module.

If you are already familiar with the basic concepts then you can directly jump to Aditya's Webinars on this topic. Both of them are a must watch!
Afterwards, check out Avi's Webinars. He advocates a reasoning based approach that is less quant-heavy.
Finally, do practice all the questions from Bunuel's practice sets. Add all the questions you get wrong to your error log for future review.
It goes without saying that the more you practice, the more comfortable you will be solving these questions.

Introduction & Concept Building
1. The Tested Tutor | Absolute Values | Inequalities
2. Target Test Prep Webinar on Absolute Values

Advanced Concepts
1. Aditya Kumar's Webinars (CrackVerbal) | Inequalities | Absolute Values
2. Avi Gutman's Webinars (Quant Reasoning) | Video 1 | Video 2

Practice Problems
1. Absolute Value - GMAT Patterns
2. Inequality & Absolute Value - Bunuel's Collection

All the best with your prep!
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