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Must be True, Maybe True, Could be True & Always True

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GyMrAT
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Must be True, Maybe True, Could be True & Always True [#permalink] New post   15 May 2018, 06:35
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I am generally perplexed by the following question types & don't have a concrete strategy to solve them.

I) Must be True
II) Maybe True
III) Could be True
IV) Always True
V) Cannot be True

The question types usually have three expressions or the expressions themselves are the answer choices. Need to understand the difference between them & the number of test cases i should test to satisfy them.

The most difficulty i face is when the questions involve inequations & requires testing numbers. I do follow the (>1, 1 to 0, 0, 0 to -1, -1, <-1) number testing approach, however it is too time consuming sometimes.

Has anyone devised a solid strategy to hit these questions outta the park?

I am sure there are others who find these questions challenging.

Requesting the Quant experts (Bunuel mikemcgarry VeritasPrepKarishma EgmatQuantExpert MathRevolution to kindly chime in & help out.

Thanks
GyMrAT
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KarishmaB
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Must be True, Maybe True, Could be True & Always True [#permalink] New post   Updated on: 26 Nov 2023, 03:09
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GyMrAT wrote:
I am generally perplexed by the following question types & don't have a concrete strategy to solve them.

I) Must be True
II) Maybe True
III) Could be True
IV) Always True
V) Cannot be True

The question types usually have three expressions or the expressions themselves are the answer choices. Need to understand the difference between them & the number of test cases i should test to satisfy them.

The most difficulty i face is when the questions involve inequations & requires testing numbers. I do follow the (>1, 1 to 0, 0, 0 to -1, -1, <-1) number testing approach, however it is too time consuming sometimes.

Has anyone devised a solid strategy to hit these questions outta the park?

I am sure there are others who find these questions challenging.

Requesting the Quant experts (Bunuel mikemcgarry VeritasPrepKarishma EgmatQuantExpert MathRevolution to kindly chime in & help out.

Thanks
GyMrAT


Note a few things:

"Must be True" and "Always True" are the same.
"May be true" and "Could be true" are the same.
"Cannot be true" might actually be a very simple question type since all you have to do is find one instance in which it is true to reject it. Though it is certainly rare to see this.
Must be true is the most common type out of these. I have written a post describing "must be true" question types here: https://anaprep.com/algebra-game-must-b ... questions/

"Must be true" and "Could be true" questions using inequalities are discussed here: https://anaprep.com/algebra-must-be-tru ... questions/

Originally posted by KarishmaB on 15 May 2018, 09:30.
Last edited by KarishmaB on 26 Nov 2023, 03:09, edited 1 time in total.
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Re: Must be True, Maybe True, Could be True & Always True [#permalink] New post   15 May 2018, 14:26
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GyMrAT wrote:
I am generally perplexed by the following question types & don't have a concrete strategy to solve them.

I) Must be True
II) Maybe True
III) Could be True
IV) Always True
V) Cannot be True

The question types usually have three expressions or the expressions themselves are the answer choices. Need to understand the difference between them & the number of test cases i should test to satisfy them.

The most difficulty i face is when the questions involve inequations & requires testing numbers. I do follow the (>1, 1 to 0, 0, 0 to -1, -1, <-1) number testing approach, however it is too time consuming sometimes.

Has anyone devised a solid strategy to hit these questions outta the park?

I am sure there are others who find these questions challenging.

Requesting the Quant experts (Bunuel mikemcgarry VeritasPrepKarishma EgmatQuantExpert MathRevolution to kindly chime in & help out.

Thanks
GyMrAT


Good question.

Here is how I approach it:
I) Must be True - Same as IV below
II) Maybe True - Same as III below
III) Could be True - Same as II above
IV) Always True - Same as I above
V) Cannot be True - Not same as anything above

For Must be true or Always true, you need to find an answer that cannot be made false, or said differently has to satisfy the equation/quantity in question. On the flip side, a could be true or may be true basically says that the answer may or may not be true.
Note that Cannot be true is the same as Must be true, except it is negated.

As far as strategy, I've found that plugging in smart numbers always helps. What do I mean by smart? If the answer choices are all multiples of 3, do not pick 100.

Does this help?
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Re: Must be True, Maybe True, Could be True & Always True [#permalink] New post   22 May 2018, 22:48
VeritasPrepKarishma wrote:
GyMrAT wrote:
I am generally perplexed by the following question types & don't have a concrete strategy to solve them.

I) Must be True
II) Maybe True
III) Could be True
IV) Always True
V) Cannot be True

The question types usually have three expressions or the expressions themselves are the answer choices. Need to understand the difference between them & the number of test cases i should test to satisfy them.

The most difficulty i face is when the questions involve inequations & requires testing numbers. I do follow the (>1, 1 to 0, 0, 0 to -1, -1, <-1) number testing approach, however it is too time consuming sometimes.

Has anyone devised a solid strategy to hit these questions outta the park?

I am sure there are others who find these questions challenging.

Requesting the Quant experts (Bunuel mikemcgarry VeritasPrepKarishma EgmatQuantExpert MathRevolution to kindly chime in & help out.

Thanks
GyMrAT


Note a few things:

"Must be True" and "Always True" are the same.
"May be true" and "Could be true" are the same.
"Cannot be true" might actually be a very simple question type since all you have to do is find one instance in which it is true to reject it. Though it is certainly rare to see this.
Must be true is the most common type out of these. I have written a post describing "must be true" question types here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2017/0 ... -question/

"Must be true" and "Could be true" questions using inequalities are discussed here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/1 ... mats-gmat/



Thanks VeritasPrepKarishma the links are very helpful.

I am assuming these question types will generally take more than average time to solve, since they require testing several cases.
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Re: Must be True, Maybe True, Could be True & Always True [#permalink] New post   22 May 2018, 22:59
strivingFor800 wrote:
GyMrAT wrote:
I am generally perplexed by the following question types & don't have a concrete strategy to solve them.

I) Must be True
II) Maybe True
III) Could be True
IV) Always True
V) Cannot be True

The question types usually have three expressions or the expressions themselves are the answer choices. Need to understand the difference between them & the number of test cases i should test to satisfy them.

The most difficulty i face is when the questions involve inequations & requires testing numbers. I do follow the (>1, 1 to 0, 0, 0 to -1, -1, <-1) number testing approach, however it is too time consuming sometimes.

Has anyone devised a solid strategy to hit these questions outta the park?

I am sure there are others who find these questions challenging.

Requesting the Quant experts (Bunuel mikemcgarry VeritasPrepKarishma EgmatQuantExpert MathRevolution to kindly chime in & help out.

Thanks
GyMrAT


Good question.

Here is how I approach it:
I) Must be True - Same as IV below
II) Maybe True - Same as III below
III) Could be True - Same as II above
IV) Always True - Same as I above
V) Cannot be True - Not same as anything above

For Must be true or Always true, you need to find an answer that cannot be made false, or said differently has to satisfy the equation/quantity in question. On the flip side, a could be true or may be true basically says that the answer may or may not be true.
Note that Cannot be true is the same as Must be true, except it is negated.

As far as strategy, I've found that plugging in smart numbers always helps. What do I mean by smart? If the answer choices are all multiples of 3, do not pick 100.

Does this help?


Thanks strivingFor800

Yes plugging in smart numbers definitely helps, however there are a few questions(non official) i encountered on Gmat club, which require multiple cases to be tested. Those took me more than 3 mins to solve, i reckon such questions are not GMAT type. They are good for conceptual practice but not the real thing.

I found the official questions on this question type to be a lot less rigorous & these are the ones that are tricky & thus require smart number plugging in.

Correct me if i am wrong, since I am yet to finish all the Quant OG questions.
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Re: Must be True, Maybe True, Could be True & Always True [#permalink] New post   23 May 2018, 02:43
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GyMrAT wrote:
I am generally perplexed by the following question types & don't have a concrete strategy to solve them.

I) Must be True
II) Maybe True
III) Could be True
IV) Always True
V) Cannot be True

The question types usually have three expressions or the expressions themselves are the answer choices. Need to understand the difference between them & the number of test cases i should test to satisfy them.

The most difficulty i face is when the questions involve inequations & requires testing numbers. I do follow the (>1, 1 to 0, 0, 0 to -1, -1, <-1) number testing approach, however it is too time consuming sometimes.

Has anyone devised a solid strategy to hit these questions outta the park?

I am sure there are others who find these questions challenging.

Requesting the Quant experts (Bunuel mikemcgarry VeritasPrepKarishma EgmatQuantExpert MathRevolution to kindly chime in & help out.

Thanks
GyMrAT


11. Must or Could be True Questions



For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: Must be True, Maybe True, Could be True & Always True [#permalink] New post   25 May 2018, 16:58
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You can often quickly eliminate a couple of answer choices on these problems, so that you only need to plug in cases to test the last two or three answer choices. That can save a lot of time.

How you eliminate answer choices will vary depending on the problem, but here's an example:

'If x and y are nonzero integers and x>y, which of the following must be positive?'

(A) x/y

(B) x^2 / y

(C) x^2 / y^2

etc.

Don't immediately start plugging in numbers! Instead, think through what might cause one of these values to be negative. A positive divided by a negative is positive - and both (A) and (B) can fit that scenario, so they can both be eliminated without plugging in exact values.
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Re: Must be True, Maybe True, Could be True & Always True [#permalink] New post   10 Jul 2018, 02:52
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Hello,

The following detailed video (~7 minutes) will explain the concept and help you approach these questions in an effective way.



Hope this helps.

All the best!
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Must be True, Maybe True, Could be True & Always True [#permalink] New post   15 Oct 2019, 05:55
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Thank goodness for this thread. Must be true questions are really confusing for me. Here's an example.

If \(|x| > 3\), which of the following must be true?

I.\(x > 3\)

II. \(x^2 > 9\)

III. \(|x – 1| > 2\)

(A) I only

(B) II only

(C) I and II only

(D) II and III only

(E) I, II, and III

NOTE : This is a question from the link VeritasKarishma shared earlier on the thread. https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2017/0 ... -question/

The final answer is D.
As I solved this, I had no problem with Statement I and II. But when statement III came along, I was stuck. The range of \(x\) for \(|x – 1| > 2\) is \(x<-1\) and \(x>3\).
So \(x\) could be anywhere less than \(-1\) and anywhere beyond \(3\). I want to state specially that It could have values such as \(-1.0001\), \(-1.5\), \(-1.75\), \(-2\), \(-2.5\), \(-2.75\) and etc. (This range has values between \(-1\) and \(-3\)) I'll tell you the reason why in a minute.

Looking at the original inequality, \(|x| > 3\). After solving, you'll realize that x could be anywhere less than \(-3\) and anywhere greater than \(3\). Look at the values less than \(-3\). numbers between \(-1\) and \(-3\) are not a part of this range.

I didn't understand the explanation on the link for this specific part of the question on the link.

\(x<-3 ∪ x<3\) is a subset of \(x<-1 ∪ x>3\) isn't it? So will that make it sufficient to say that \(|x – 1| > 2\) must be true?

PS - A clarification for this will help a lot of other people like myself. Kindly do help! Slight margins between choosing the correct option and a wrong one!
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Re: Must be True, Maybe True, Could be True & Always True [#permalink] New post   09 Dec 2019, 04:22
VeritasKarishma wrote:
GyMrAT wrote:
I am generally perplexed by the following question types & don't have a concrete strategy to solve them.

I) Must be True
II) Maybe True
III) Could be True
IV) Always True
V) Cannot be True

The question types usually have three expressions or the expressions themselves are the answer choices. Need to understand the difference between them & the number of test cases i should test to satisfy them.

The most difficulty i face is when the questions involve inequations & requires testing numbers. I do follow the (>1, 1 to 0, 0, 0 to -1, -1, <-1) number testing approach, however it is too time consuming sometimes.

Has anyone devised a solid strategy to hit these questions outta the park?

I am sure there are others who find these questions challenging.

Requesting the Quant experts (Bunuel mikemcgarry VeritasPrepKarishma EgmatQuantExpert MathRevolution to kindly chime in & help out.

Thanks
GyMrAT


Note a few things:

"Must be True" and "Always True" are the same.
"May be true" and "Could be true" are the same.
"Cannot be true" might actually be a very simple question type since all you have to do is find one instance in which it is true to reject it. Though it is certainly rare to see this.
Must be true is the most common type out of these. I have written a post describing "must be true" question types here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2017/0 ... -question/

"Must be true" and "Could be true" questions using inequalities are discussed here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/1 ... mats-gmat/


Hi VeritasKarishma

I was going through one of your post and found the following solution, which I need help to understand. WOuld you kindly help me understand where I am mistaken to comprehend it.

The solution goes like this:
We are given that x^3 – 4x^5 < 0. This inequality can be solved to:

x^3 ( 1 – 4x^2) < 0

x^3*(2x + 1)*(2x – 1) > 0

x > 1/2 or -1/2 < x < 0

This is our universe of the values of x. It is given that all values of x lie in this range."

I understand we reversed the sign of inequality by taking out - from the first expression, but my solution gives me a value of x>1/2 (same as yours) and x<-1/2 as well (contradicting yours). Can you help me understand where i went wrong. Also how do we go about when there are three expressions (i. x^3 , ii. (2x-1) and iii. (2x+1) ) in the equality. The above inequality is telling me that the product of three expressions is greater than zero. So all three expression could either be -ve or could be +ve or two of them could be negative and one positive. How do we proceed ahead in solving this? Thanks in advance for you support.


Regards,
Deeuce
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Must be True, Maybe True, Could be True & Always True [#permalink] New post   Updated on: 26 Nov 2023, 03:10
Expert Reply
deeeuce wrote:
VeritasKarishma wrote:
GyMrAT wrote:
I am generally perplexed by the following question types & don't have a concrete strategy to solve them.

I) Must be True
II) Maybe True
III) Could be True
IV) Always True
V) Cannot be True

The question types usually have three expressions or the expressions themselves are the answer choices. Need to understand the difference between them & the number of test cases i should test to satisfy them.

The most difficulty i face is when the questions involve inequations & requires testing numbers. I do follow the (>1, 1 to 0, 0, 0 to -1, -1, <-1) number testing approach, however it is too time consuming sometimes.

Has anyone devised a solid strategy to hit these questions outta the park?

I am sure there are others who find these questions challenging.

Requesting the Quant experts (Bunuel mikemcgarry VeritasPrepKarishma EgmatQuantExpert MathRevolution to kindly chime in & help out.

Thanks
GyMrAT


Note a few things:

"Must be True" and "Always True" are the same.
"May be true" and "Could be true" are the same.
"Cannot be true" might actually be a very simple question type since all you have to do is find one instance in which it is true to reject it. Though it is certainly rare to see this.
Must be true is the most common type out of these. I have written a post describing "must be true" question types here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2017/0 ... -question/

"Must be true" and "Could be true" questions using inequalities are discussed here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/1 ... mats-gmat/


Hi VeritasKarishma

I was going through one of your post and found the following solution, which I need help to understand. WOuld you kindly help me understand where I am mistaken to comprehend it.

The solution goes like this:
We are given that x^3 – 4x^5 < 0. This inequality can be solved to:

x^3 ( 1 – 4x^2) < 0

x^3*(2x + 1)*(2x – 1) > 0

x > 1/2 or -1/2 < x < 0

This is our universe of the values of x. It is given that all values of x lie in this range."

I understand we reversed the sign of inequality by taking out - from the first expression, but my solution gives me a value of x>1/2 (same as yours) and x<-1/2 as well (contradicting yours). Can you help me understand where i went wrong. Also how do we go about when there are three expressions (i. x^3 , ii. (2x-1) and iii. (2x+1) ) in the equality. The above inequality is telling me that the product of three expressions is greater than zero. So all three expression could either be -ve or could be +ve or two of them could be negative and one positive. How do we proceed ahead in solving this? Thanks in advance for you support.


Regards,
Deeuce


Here is how you solve questions involving multiple factors in inequalities:

https://youtu.be/PWsUOe77__E

Originally posted by KarishmaB on 09 Dec 2019, 21:37.
Last edited by KarishmaB on 26 Nov 2023, 03:10, edited 1 time in total.
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Must be True, Maybe True, Could be True & Always True [#permalink] New post   12 Dec 2019, 05:50
Here is how you solve questions involving multiple factors in inequalities:

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/0 ... e-factors/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/0 ... ns-part-i/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/0 ... s-part-ii/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/0 ... qualities/

Check out all 4 posts first. You will get the correct answer.[/quote]


Thank you VeritasKarishma for the prompt reply... these links were very helpful to understand the concepts.
I still have some confusion though. Would you kindly help me understand this?

why are we reversing the sign when factoring the inequality above? I tried proceeding ahead without reversing it to see how it rolls out. I got x<-1/2 or x>1/2 as the solution for inequality in the question stem. Here are my steps:


Thanks & regards,
Deeuce
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