Lesson: The Table Method

Comment on The Table Method

vishalshrm539's picture

In the x<x^2 question, can we take x=1..?
gmat-admin's picture

You bet!
When we plug in x = 1, the answer to the target question is "No, x is NOT less than x^2"

vishalshrm539's picture

Ok..thank you sir

Hello guys
I think there is a mistake in the exercise done at 3:30 on this video, when is said divided, he is actually doing subtraction.
Sorry to bother
Best
gmat-admin's picture

Thanks for that, but "division" is correct here. 5 divided by 3 equals 1 with remainder 2.

Hi Brent,
I would like to ask based on your experience if I could take CAT each Week or it would not reflect any changes in my progress.
gmat-admin's picture

If you've already reviewed all of the GMAT content, then taking regular practice tests (CAT's) is a great idea. This will help build your test-taking skills AND help identify any remaining area(s) of weakness.

While carefully analyzing your practice tests, there are four main types of weakness to watch out for:
1. specific Quant skills/concepts (e.g., algebra, standard deviation, etc.)
2. specific Verbal skills/concepts (e.g., verb tenses, assumption CR questions, etc.)
3. test-taking skills (time management, endurance, anxiety etc.)
4. silly mistakes

For the first two weaknesses, the fix is pretty straightforward. Learn the concept/skill and find some practice questions to strengthen that weakness.

If your test-taking skills are holding you back, then you need to work on these. Be sure to review out time management video at http://www.gmatprepnow.com/module/general-gmat-strategies/video/1244

Finally, if silly mistakes are hurting your score, then it's important that you identify and categorize these mistakes so that, during tests, you can easily spot situations in which you're prone to making errors. I write about this and other strategies in the following article: http://www.gmatprepnow.com/articles/avoiding-silly-misteaks-gmat

Cheers,
Brent

Hey Brent,

Just getting started on these videos so maybe this will be come more clear in time, but I'm having trouble understanding sufficient/insufficient.

For example, the question at 4:25 and the statement x is positive. Doesn't this statement provide sufficient information to definitively answer "Is x < x^2?". When x = 2 we can definitively answer the question, yes, x < x^2. When x = .5 we can definitively answer the question, no, x < x^2.

If I'm remembering correctly from the previous video, we don't want to fall into the trap of answering the target question. We only want to answer whether the statement is sufficient to answer the target question. In this case, wouldn't the statement be sufficient to answer the question?

I guess I'm having trouble determining what qualifies as sufficient to answer the target question and what's just answering the target question.

Thanks,

Alex
gmat-admin's picture

Good question, Alex.

Data Sufficiency questions can seem very strange at first. The important thing is to keep asking yourself "Does this statement provide enough information to definitively answer the target question?"

Here, the target question asks "Is x < x²?"
This is a YES/NO question, so a statement will be considered sufficient if we can definitively answer in one of the two following ways:

- YES, x IS less than x²
- NO, x is NOT less than x²

When we test two possible values of x (x = 2 and x = 0.5), we get different answers to the target question.

In the first case (x = 2), the answer is "YES, x IS less than x²"
In the second case (x = 0.5), the answer is "NO, x is NOT less than x²"

So, which is it? Is or isn't x less than x²?

We can't say for certain. So, that statement is not sufficient.

Does that help?

Cheers,
Brent

yup, very helpful. Thanks!

Hi Brent!

I know that the statement 1 is not sufficient because if x=1, but before to see it, don’t make sense for me because is not clear in my mind why isn't right 0.5 < 0.25. I see that 0.25 is greater than 0.5.

Best Regards
gmat-admin's picture

Be careful. 0.25 is not greater than 0.5

0.25 = 25/100 = 1/4
0.5 = 5/10 = 1/2

1/2 of a pizza is more than 1/4
In other words, 0.5 > 0.25

Does that help?

Cheers,
Brent

Alex, I do understood by myself... I was thinking in a box HAHA

What is the remainder when positive integer x is divided by 3?

I chose the number 1 and 5 as a test case which is different from what you use. Is there a strategy on choosing smart numbers?
gmat-admin's picture

You're referring to the question at 2:40 in the above video.

Your numbers (x = 1 and x = 5) also work.

The goal with testing values is to (hopefully) find conflicting answers to the target question, which means the statement is not sufficient.

With your numbers (x = 1 and x = 5), we get just that.

If x = 1, then the answer to the target question is "The remainder is 1 when x is divided by 3"
If x = 5, then the answer to the target question is "The remainder is 2 when x is divided by 3"

Since we cannot answer the target question with certainty, the statement is not sufficient.

The next video covers how to choose good numbers to test: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1102

Cheers,
Brent

Hi Brent, I understand on question 2.40 we are testing the table method. But would it have been safe to deduce that since we have no information of x being divided by 3 in statement 1 but it is divided by 4, it is safe to say that it is insufficient as the statement does not have any correlation with the metrics given in the target question. I'm just trying to test a different approach here. Please let me know
gmat-admin's picture

Here's the question:
What is the remainder when positive integer x is divided by 3?
Statement 1: When x is divided by 4 the remainder is 1

The concepts you're referring to are covered later in the course (at https://www.gmatprepnow.com/module/gmat-integer-properties/video/842).
The answer to your question depends on what you mean when you say "the statement does not have any correlation with the metrics given in the target question." can you elaborate?

In the meantime, I'll note that, IF statement 1 were "When x is divided by 6 the remainder is 1," then the statement would be SUFFICIENT.

What i mean't by correlation is simply the fact that since we have the target question asking for the remainder when the integer x is divided by "3" but in statement 1 it talks about x being divided by "4", can we assume it is not sufficient as 4 is different from 3.
gmat-admin's picture

Thanks for the clarification.
In that case, we can't conclude that statement 1 is not sufficient just because 4 is different from 3.

For example,
Target question: What is the remainder when x is divided by 3?
Statement 1: When x is divided by 6, the remainder is 1.
This statement is sufficient because it tells us that x must be one of the following values: 1, 7, 13, 19, 25, 31, 37,....etc
Every one of those possible values leaves a remainder of 1 when divided by 3, which means we can answer the target question with certainty.
So, statement 1 is sufficient.

Does rephrasing the target question to read "Is 1<x?" work in this situation?
gmat-admin's picture

I'm assuming you're referring to the question that starts at 4:15 in the above video.

TARGET QUESTION: Is x < x²
You are dividing both sides of the inequality by x, which is a bad idea, since we don't know whether x is POSITIVE or NEGATIVE.

If x is POSITIVE, then we divide both sides by x to get: Is 1 < x?
If x is NEGATIVE, then we divide both sides by x to get: Is 1 > x?

Since we don't know the sign of x, we can't divide both sides by x.

Cheers,
Brent

Any guidelines on when to suspect a statement might be 'insufficient?' Thanks!
gmat-admin's picture

That skill will develop as you learn more and more concepts.

For example, later in the Algebra module, you'll learn that, in most cases, you cannot solve a linear equation for one variable.
Here's what I mean:

TARGET QUESTION: What is the value of x?
(1) x + y = 7
The equation x + y = 7 is a linear equation, which means there are infinitely many solutions to this equation (e.g., x=0 & y=7 AND x=1 & y=6 AND x=2.6 & y=4.4, etc)
So, statement 1 is not sufficient

Cheers,
Brent

Hey Brent!
I want to ask one thing, how are the values being plugged in the Data Sufficiency Questions? For instance, in the very first question, the first value being put is X=1 and than X=4, i find this very difficult like how you deduce to check x at 4 immediately after you check x at 1?
i need to understand how are the values chosen for any DS Question?
Regards
Eka
gmat-admin's picture

Great question!

In the next lesson (https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1102), we discuss "good" numbers to test when using the Table Method. These are numbers that have a wide variety of properties: -10, -1, -1/2, 0, 1/2, 1 and 10

When using the Table Method, we want to test values so that we get different answers to the target question. We also want to test "easy" values that work well with the given information.

For the first question that appears in the above video, statement 1 tells us that, x is positive.
This means we can rule out testing -10, -1, -1/2 and 0.

Testing x = 1 is very easy for us, and when we do this, we find that the answer to the target question is YES.
At this point, our goal is to find an x-value that yields an answer of NO to our target question.

From here, I COULD test x = 10, but that would make our calculations very difficult (e.g., 4^10 = 1,048,576), especially since we don't have a calculator at our disposal.
So rather than test x = 10, I chose a value of x that's less than 10, but still allows me to readily calculate 4^x and 3^(x+1).
So, I chose x = 4.

Does that help?

Hi Brent,

This module is great btw. Just what I was looking for.

I had the same question when it came to selecting test cases/strategic numbers/whatever you want to call them. It's something that still hasn't clicked for me. When I saw you choose 4 immediately after 1 and get opposite results, it just seems like black magic to me.

I went back and tested 2 and 3, and still got yes answers. It's not until 4 when the relationship flips. I can't for the life of me understand why that's the case and how you knew that's where it would happen.
gmat-admin's picture

This is a pretty esoteric point (and extremely unlikely to ever be tested on the GMAT), but one way to understand why the relationship "flips" is to examine the DIFFERENCE between 4^x and 3^(x+1) relative to the value of either 4^x or 3^(x+1).

For example, when x = 1, 4^x = 4, and 3^(x+1) = 9.
Difference = 9 - 4 = 5
When we calculate the ratio of the difference to the value of 4^x, we get: 5/4

When x = 2, 4^x = 16, and 3^(x+1) = 27.
Difference = 27 - 16 = 11
Ratio of the difference to the value of 4^x = 11/16
Notice that the ratio has decreased (from 5/4 to 11/16)

When x = 3, 4^x = 64, and 3^(x+1) = 81.
Difference = 81 - 64 = 17
Ratio of the difference to the value of 4^x = 17/64
Notice that the ratio is still decreasing (from 5/4 to 11/16 to 17/64)

All of this SUGGESTS the ratio MAY decrease so much that it eventually becomes negative (meaning the value of 4^x is greater than 3^(x+1)

Fortunately, it turns out this occurs when x = 4

well explained!

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