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Testing Numbers Strategy

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Testing Numbers Strategy

by NeilWatson » Fri Jul 04, 2014 8:20 am
Hello,

Was wondering if I could get some advice on a problem I'm having. I know a big part of beating data sufficiency is being able to test numbers to arrive at the right answer (especially important for yes/no questions), yet I would say this is one of my weaknesses. It's like having to test numbers combined with the time pressures of the test gets to met and my mind shuts down. I end up not picking "easy" numbers to test or numbers that just dont represent the problem well. My exam is in about 2.5 weeks. Do any experts have any recommendations for how I can tune this skill?

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by GMATinsight » Fri Jul 04, 2014 8:46 am
Hi NeilWatson,

1) When it comes to substituting numbers then start from the smalles numbers that you are allowed to plug in as per the constraints mentioned in questions

2) Always plug in the numbers in a specific pattern i.e. in ascending order without leaving numbers in between

3) Plug in the numbers with different properties e/g if first value is even then second should be odd (if you are allowed to take them)

4) Sometimes you have to take values available at the extremes if there is any range of values in order to bring inconsistency in the answers (in DS questions)

Most Importantly, "Always try to prove that given statement is INSUFFICIENT by bringing inconsistent results and accordingly choose the set of values as guided by the questions asked."

Keep your eyes on Questions asked and keep the question in mind all the time you are choosing values to test the consistency of responses obtained by changing various allowed values.

All the best!!!
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by ceilidh.erickson » Fri Jul 04, 2014 9:12 am
Rather than asking yourself "what kinds of numbers should I pick in what situations," you should ask yourself with each question, "what kinds of number would yield a NO answer to this question?" It's usually easy to come up with answers that would give you a "yes," so thinking about what would yield a "no" is the quickest way to prove insufficiency.

If you're not sure which answers will yield which results, Bhoopendra's list is a good one. I would add: when applicable, always start by testing 0 and 1, as those are often the "dealbreaker" values.
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by ceilidh.erickson » Fri Jul 04, 2014 9:41 am
For more on testing values, see:
https://www.beatthegmat.com/questions-th ... tml#561400
https://www.beatthegmat.com/tricky-1-fro ... tml#717206
https://www.beatthegmat.com/manhattan-ad ... tml#563825
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by Brent@GMATPrepNow » Fri Jul 04, 2014 10:38 am
Plugging numbers typically works best when you suspect that the statement is NOT SUFFICIENT. In these cases, all you need to do is find values that yield different (conflicting) answers to the target question.

If the statement is SUFFICIENT, then plugging in values will only give you a general idea of whether or not the statement is sufficient, but you won't be able to make any definitive conclusions.

For example, let's say we have the following target question: If n is a positive integer, is (2^n) - 1 prime?
Let's say statement 1 says: : n is a prime number:

Now let's plug in some prime values of n:
If n = 2, then (2^n) - 1 = 2² - 1 = 3, and 3 IS prime
If n = 3, then case (2^n) - 1 = 2³ - 1 = 7, and 7 IS prime
If n = 5, then (2^n) - 1 = 2� - 1 = 31, and 31 IS prime
At this point, it certainly APPEARS that statement guarantees that (2^n) - 1 is prime? Let's try one more prime value of n.
If n = 7, then (2^n) - 1 = 2� - 1 = 127, and 127 IS prime

So, can we be 100% certain that statement 1 is sufficient? No. The truth of the matter is that statement 1 is NOT SUFFICIENT. To see why, let's examine the possibility that n = 11
If n = 11, then (2^n) - 1 = (2^11) - 1 = 2047, and 2047 is NOT prime


Here's a different example:
Target question: Is x > 0?
Let's say statement 1 says: 5x > 4x

Now let's plug in some values of x that satisfy the condition that 5x > 4x.
x = 3, in which case x > 0
x = 0.5, in which case x > 0
x = 15, in which case x > 0
x = 1000, in which case x > 0

Once again, it APPEARS that statement 1 provides sufficient information to answer the target question. Can we be 100% certain? No. Perhaps we didn't plug in the right numbers. Perhaps there's a number that we could have plugged in such that x < 0

If we want to be 100% certain that a statement is SUFFICIENT, we'll need to use a technique other than plugging in.
Here, we can take 5x > 4x, and subtract 4x from both sides to get x > 0 VOILA - we can now answer the target question with absolute certainty.
So, statement 1 is SUFFICIENT.

TAKEAWAY: Plugging in numbers is best suited for situations in which you suspect that the statement is not sufficient. In these situations, plugging in values can yield results that are 100% conclusive. Conversely, in situations in which the statement is sufficient, plugging in values can hint at sufficiency, but the results are not 100% conclusive.

For more on this, you can watch our free video titled "Choosing Good Numbers: https://www.gmatprepnow.com/module/gmat- ... cy?id=1102

Cheers,
Brent
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by NeilWatson » Fri Jul 04, 2014 12:32 pm
Great reply experts. I will apply what you guys have said. Just what I needed. Thanks
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by NeilWatson » Fri Jul 04, 2014 8:31 pm
Brent@GMATPrepNow wrote:Plugging numbers typically works best when you suspect that the statement is NOT SUFFICIENT. In these cases, all you need to do is find values that yield different (conflicting) answers to the target question.

If the statement is SUFFICIENT, then plugging in values will only give you a general idea of whether or not the statement is sufficient, but you won't be able to make any definitive conclusions.

For example, let's say we have the following target question: If n is a positive integer, is (2^n) - 1 prime?
Let's say statement 1 says: : n is a prime number:

Now let's plug in some prime values of n:
If n = 2, then (2^n) - 1 = 2² - 1 = 3, and 3 IS prime
If n = 3, then case (2^n) - 1 = 2³ - 1 = 7, and 7 IS prime
If n = 5, then (2^n) - 1 = 2� - 1 = 31, and 31 IS prime
At this point, it certainly APPEARS that statement guarantees that (2^n) - 1 is prime? Let's try one more prime value of n.
If n = 7, then (2^n) - 1 = 2� - 1 = 127, and 127 IS prime

So, can we be 100% certain that statement 1 is sufficient? No. The truth of the matter is that statement 1 is NOT SUFFICIENT. To see why, let's examine the possibility that n = 11
If n = 11, then (2^n) - 1 = (2^11) - 1 = 2047, and 2047 is NOT prime


Here's a different example:
Target question: Is x > 0?
Let's say statement 1 says: 5x > 4x

Now let's plug in some values of x that satisfy the condition that 5x > 4x.
x = 3, in which case x > 0
x = 0.5, in which case x > 0
x = 15, in which case x > 0
x = 1000, in which case x > 0

Once again, it APPEARS that statement 1 provides sufficient information to answer the target question. Can we be 100% certain? No. Perhaps we didn't plug in the right numbers. Perhaps there's a number that we could have plugged in such that x < 0

If we want to be 100% certain that a statement is SUFFICIENT, we'll need to use a technique other than plugging in.
Here, we can take 5x > 4x, and subtract 4x from both sides to get x > 0 VOILA - we can now answer the target question with absolute certainty.
So, statement 1 is SUFFICIENT.

TAKEAWAY: Plugging in numbers is best suited for situations in which you suspect that the statement is not sufficient. In these situations, plugging in values can yield results that are 100% conclusive. Conversely, in situations in which the statement is sufficient, plugging in values can hint at sufficiency, but the results are not 100% conclusive.

For more on this, you can watch our free video titled "Choosing Good Numbers: https://www.gmatprepnow.com/module/gmat- ... cy?id=1102

Cheers,
Brent

So regarding your first example, how would you solve that? In a test setting I would probably test 2..maybe 3 cases.
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by Brent@GMATPrepNow » Sat Jul 05, 2014 5:57 am
NeilWatson wrote: So regarding your first example, how would you solve that? In a test setting I would probably test 2..maybe 3 cases.
This would never be a true GMAT question, since there's no convenient way to test whether a number is prime (other than testing lots of possible values).
The example is just meant to show the limitations of plugging in values (if you're unable to find conflicting answers to the target question).

Cheers,
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