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KarishmaB
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math Updated on: 05 Oct 2022, 23:25
Originally posted by KarishmaB on 21 Oct 2020, 04:34.
Last edited by KarishmaB on 05 Oct 2022, 23:25, edited 1 time in total.
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Lionila
Dear Karishma,

Can you please help me figure out if my conclusions about conditional reasoning on GMAT Quant are correct or not. I mentioning some specific concepts here but I am hoping for a holistic answer.

It seems to me that conditional reasoning is everywhere on GMAT. It's basically the fundamental reasoning style that is needed throughout the test.

DS questions are all about conditional reasoning because we are essentially asked to determine whether the statements are "sufficient" to answer the question with certainty/necessarily true.

On PS:

E.g. "must be true" questions are essentially asking us to find the "necessary condition", so to make a logical deduction from the given information. And "could be true" questions ask us to find one or more "sufficient conditions" from which the required statement in the prompt must follow (necessary condition).

Same goes for many other PS questions. Even if we are not explicitly asked to determine what "must or could be true", we still have to determine what must follow from the given (e.g. properties, constraints etc) or what could be true given a requirement (e.g. come up with possibilities in the from of cases/scenarios).

So my overall conclusion is that when we ask "What could be true? What are possible cases that make this statement true? What do I need to consider etc. - we are determining the sufficient condition(s) and when we ask "What does this mean? What must be true?" - we are determining the necessary condition(s).
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Yes, I couldn't have said it better myself.
Must be true - Parallel in Necessary conditions
Could be true - Parallel in Sufficient conditions
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 21 Oct 2020, 05:13
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Dear Karishma,
I am planning to take the exam next month and co-ordinate geometry seems to be my weak link. I tend to forget/mix up formulas and sometimes, can't even understand the questions. Can you tell me what are the formulas I need to memorize and what sort of practice questions should I work on to improve my understanding of this particular branch of mathematics?
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 21 Oct 2020, 07:29
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Lionila
Dear Karishma,

Can you please help me figure out if my conclusions about conditional reasoning on GMAT Quant are correct or not. I mentioning some specific concepts here but I am hoping for a holistic answer.

It seems to me that conditional reasoning is everywhere on GMAT. It's basically the fundamental reasoning style that is needed throughout the test.

DS questions are all about conditional reasoning because we are essentially asked to determine whether the statements are "sufficient" to answer the question with certainty/necessarily true.

On PS:

E.g. "must be true" questions are essentially asking us to find the "necessary condition", so to make a logical deduction from the given information. And "could be true" questions ask us to find one or more "sufficient conditions" from which the required statement in the prompt must follow (necessary condition).

Same goes for many other PS questions. Even if we are not explicitly asked to determine what "must or could be true", we still have to determine what must follow from the given (e.g. properties, constraints etc) or what could be true given a requirement (e.g. come up with possibilities in the from of cases/scenarios).

So my overall conclusion is that when we ask "What could be true? What are possible cases that make this statement true? What do I need to consider etc. - we are determining the sufficient condition(s) and when we ask "What does this mean? What must be true?" - we are determining the necessary condition(s).

Yes, I couldn't have said it better myself.
Must be true - Parallel in Necessary conditions
Could be true - Parallel in Sufficient conditions

Check this post. It discusses must be true and could be true questions:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/1 ... mats-gmat/
Show more


Thank you so very much Karishma!!!
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 21 Oct 2020, 13:07
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Kp0027
Hi karishma I had a question I was wondering if you could help me with it, it’s about difference of two squares.

The Q asks for the result of (4h^2 - 64) / (h+4).

The correct answer is given as 4h-16 and I understand the explanation.

However I don’t understand why instead of factorising by 4 like in the solution, we cannot simply use the current form of the equation and change 4h^2-64 into (2h-8)(2h+8) rather than factorising by 4 first. It doesn’t give me the same answer so must be wrong and I am not sure why.

Thanks

It isn't wrong and it does give you the same answer.

(2h-8)(2h+8) / (h + 4)

(2h-8)*2*(h+4) / (h+4)

(cancel off h+4)

(2h - 8)*2

4h - 16
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Thank you for the help :)
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 21 Oct 2020, 23:41
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Hey VeritasKarishma

Thanks a lot. Request your help with this post too on the Venn Diagram Question:

https://gmatclub.com/forum/the-table-ab ... l#p2632733

I have tagged you.

Tia
Kanishka

Done.
Show more

Thanks I see my error. Basically i interpreted not favourable for either as "favourable for both or not favourable for both", whereas it surely makes sense to say that if you don't favour either, you don't favour both, so favour both is incorrect. I went by negation of either that either A or B when negated means both A and B or not A & not B.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 27 Oct 2020, 23:26
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Hi VeritasKarishma,

I was going through your notes on P&C (Ultimate thread) I came across this question towards the end.
There are x people and y chairs in a room where x and y are positive prime numbers. How many ways can the x people be seated in the y chairs (assuming that each chair can seat exactly one person)?

(1) x + y = 12

(2) There are more chairs than people.

I understood that we select 5 out of 7 chairs first to sort 5 children.
But we don't make use of Mr.V here.
In essence 7C5 *5 ! is the same as 7!/2! (Considering 2 identical empty positions (mr. vs) right).
Also, we should use the vacant position logic only if there are constraints ? else simple select and arrange if positions > people.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 27 Oct 2020, 23:55
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kagrawal16
Hi VeritasKarishma,

I was going through your notes on P&C (Ultimate thread) I came across this question towards the end.
There are x people and y chairs in a room where x and y are positive prime numbers. How many ways can the x people be seated in the y chairs (assuming that each chair can seat exactly one person)?

(1) x + y = 12

(2) There are more chairs than people.

I understood that we select 5 out of 7 chairs first to sort 5 children.
But we don't make use of Mr.V here.
In essence 7C5 *5 ! is the same as 7!/2! (Considering 2 identical empty positions (mr. vs) right).
Also, we should use the vacant position logic only if there are constraints ? else simple select and arrange if positions > people.
Show more

Yes, they are just different ways of thinking about the same thing. If a vacant chair makes you uncomfortable, add a figment of your imagination Mr V.
Say if you need to arrange 5 people in 6 chairs, either think you have 6 people (an extra Mr V) so number of arrangements = 6!
or think that you select 5 of the 6 chairs in 6C5 ways and then arrange in 5! ways. You still get 6! as the answer.

Use whichever chain of thought you prefer.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 12 Nov 2020, 10:17
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Points A and B are 120 km apart. A motorcyclist starts from A to B along straight road AB with speed 30 kmph. At the same time a cyclist starts from B along a road perpendicular to road AB, with a speed of 10 kmph. After how many hours will the distance between them be the least?

A. 3 hours
B. 3.4 hours
C. 3.5 hours
D. 3.6 hours
E. None

Hi VeritasKarishma,
I was able to solve the question but had a small doubt.
Why doesn't it work to use the GM method in this question
xy<=(x^2 + y^2) / 2
so (120-30t)^2 = x^2
y^2 = (10t)^2

equate x=y for minimum and we get t=3.


We use the method for the hypotenuse of a triangle. Why not this case. Is it because they are a function of a common variable t.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 17 Nov 2020, 00:04
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kagrawal16
Points A and B are 120 km apart. A motorcyclist starts from A to B along straight road AB with speed 30 kmph. At the same time a cyclist starts from B along a road perpendicular to road AB, with a speed of 10 kmph. After how many hours will the distance between them be the least?

A. 3 hours
B. 3.4 hours
C. 3.5 hours
D. 3.6 hours
E. None

Hi VeritasKarishma,
I was able to solve the question but had a small doubt.
Why doesn't it work to use the GM method in this question
xy<=(x^2 + y^2) / 2
so (120-30t)^2 = x^2
y^2 = (10t)^2

equate x=y for minimum and we get t=3.


We use the method for the hypotenuse of a triangle. Why not this case. Is it because they are a function of a common variable t.
Show more

The AM-GM concept will not work. Note here that when t increases, 10t goes up and 120 - 30t decreases at a faster rate.
If t = 1, 10t = 10 and 120 - 30t = 90
If t = 2, 10t = 20 and 120 - 30t = 60
...

The product of two numbers is maximum when the sum is constant.
Here, (10t)^2 + (120 - 30t)^2 is not constant.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 07 Jan 2021, 11:33
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Dear Karishma,

Your articles and thought process are definitely making my brain evolve gradually. However, I got stuck in questions which involve weighted average calculations for 3 sets. Could you please share some explanations for both (easy & difficult questions) as to how can these be dealt logically?

Perhaps like for this one?


https://gmatclub.com/forum/the-average-salary-of-15-people-in-the-shipping-department-144676.html

Thank you already :-)
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 07 Jan 2021, 21:37
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aashigarg
Dear Karishma,

Your articles and thought process are definitely making my brain evolve gradually. However, I got stuck in questions which involve weighted average calculations for 3 sets. Could you please share some explanations for both (easy & difficult questions) as to how can these be dealt logically?

Perhaps like for this one?


https://gmatclub.com/forum/the-average-salary-of-15-people-in-the-shipping-department-144676.html

Thank you already :-)
Show more

Hey aashigarg,
Here you go:
https://gmatclub.com/forum/the-average- ... l#p2699237

I solve these questions using the concept of deviations since it makes the numbers easy to handle.
Alternatively, you can use the weighted formula for 3 like this:

Cavg = ( C1*w1 + C2*w2 + C3*w3)/(w1 + w2 + w3)

20 = (25*5 + 16*4 + C3*6)/15

You get C3 = 18.5
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 21 Mar 2021, 08:14
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nitesh50
Hi VeritasKarishma

https://gmatclub.com/forum/a-coin-made- ... 98446.html

You have posted a reply for this question.
In your solution you have asked:
(Think what would happen if it was given that volume of aluminium was twice the volume of silver)

IMO the ratio for the weight will still remain the same.
Aluminium=10 Silver=20
ON the other hand 2/3 of volume of the coin will be aluminium.

Then we can use proportions :
If 2/3 Volume of C1 = 10gm
Then volume of C2= 10*1.5*volume of c2/volume of c1

This have me an answer of 30gm.

Am I correct here?

Regards
Nitesh

That solution can be modified if we modify the question like this:

A coin made of alloy of aluminum and silver measures 2 x 15 mm. If the weight of the coin is 30 grams and the volume of aluminum in the alloy is twice that of silver, what will be the weight of a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum?

Let's consider the first coin:
2*Volume of Silver = Volume of Aluminium
Weight of Silver = 2* Weight of Aluminum for equal volume.

Since the volume of silver is half but its weight is twice for equal volume so for half the volume, the weight of the two will become equal.

Total weight is 30 gms. So silver must be 15 gms and aluminum must be 15 gms.

Volume of first coin \(=\pi∗(15/2)^2∗2=(225/2)∗\pi\)

Volume of second coin \(=\pi∗(15)^2∗1=(225)∗\pi\)

Volume of second coin is twice the volume of the first coin. If volume of aluminium in the first coin is V, the volume of the first coin is (3/2)V. The volume of the second coin is 3V. Since it is all Aluminium, volume of Aluminium in the second coin is 3V. Since weight of Aluminum of weight V was 10 gms, weight of Aluminum of volume 3V will be 30 gms.
Show more


Hi Karishma VeritasKarishma,

Can you please clarify the below points regarding this modified question?
1) The net effect of the two things (I am calling them 'a' and 'b', below):
a) The volume of aluminum in the alloy is twice that of silver
b) The silver is twice as heavy as aluminum (meaning the weight of silver in the alloy is twice that of aluminium)
is that the weight of aluminium in the alloy has become equal to that of silver, each is 15 g now? (I have also highlighted this in Magenta in your reply).

Then what does the statement "The silver is twice as heavy as aluminum" signifies?? Haven't we contradicted the given statement?

2) If the weight of Aluminium in the alloy is 15 g (as you have shown in above reply), then the final answer in this question would be 15 * 3 = 45 g, as per my understanding. (I have also highlighted this in Red in your reply).

I'm very much clear about the original question as you have explained in the link:
https://gmatclub.com/forum/a-coin-made- ... ml#p974280

But, I'm confused on this modified question. Please clarify if possible.
TIA.

Regards,
Ravish.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 21 Mar 2021, 22:27
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nitesh50
Hi VeritasKarishma

https://gmatclub.com/forum/a-coin-made- ... 98446.html

You have posted a reply for this question.
In your solution you have asked:
(Think what would happen if it was given that volume of aluminium was twice the volume of silver)

IMO the ratio for the weight will still remain the same.
Aluminium=10 Silver=20
ON the other hand 2/3 of volume of the coin will be aluminium.

Then we can use proportions :
If 2/3 Volume of C1 = 10gm
Then volume of C2= 10*1.5*volume of c2/volume of c1

This have me an answer of 30gm.

Am I correct here?

Regards
Nitesh

That solution can be modified if we modify the question like this:

A coin made of alloy of aluminum and silver measures 2 x 15 mm. If the weight of the coin is 30 grams and the volume of aluminum in the alloy is twice that of silver, what will be the weight of a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum?

Let's consider the first coin:
2*Volume of Silver = Volume of Aluminium
Weight of Silver = 2* Weight of Aluminum for equal volume.

Since the volume of silver is half but its weight is twice for equal volume so for half the volume, the weight of the two will become equal.

Total weight is 30 gms. So silver must be 15 gms and aluminum must be 15 gms.

Volume of first coin \(=\pi∗(15/2)^2∗2=(225/2)∗\pi\)

Volume of second coin \(=\pi∗(15)^2∗1=(225)∗\pi\)

Volume of second coin is twice the volume of the first coin. If volume of aluminium in the first coin is V, the volume of the first coin is (3/2)V. The volume of the second coin is 3V. Since it is all Aluminium, volume of Aluminium in the second coin is 3V. Since weight of Aluminum of weight V was 10 gms, weight of Aluminum of volume 3V will be 30 gms.


Hi Karishma VeritasKarishma,

Can you please clarify the below points regarding this modified question?
1) The net effect of the two things (I am calling them 'a' and 'b', below):
a) The volume of aluminum in the alloy is twice that of silver
b) The silver is twice as heavy as aluminum (meaning the weight of silver in the alloy is twice that of aluminium)
is that the weight of aluminium in the alloy has become equal to that of silver, each is 15 g now? (I have also highlighted this in Magenta in your reply).

Then what does the statement "The silver is twice as heavy as aluminum" signifies?? Haven't we contradicted the given statement?

2) If the weight of Aluminium in the alloy is 15 g (as you have shown in above reply), then the final answer in this question would be 15 * 3 = 45 g, as per my understanding. (I have also highlighted this in Red in your reply).

I'm very much clear about the original question as you have explained in the link:
https://gmatclub.com/forum/a-coin-made- ... ml#p974280

But, I'm confused on this modified question. Please clarify if possible.
TIA.

Regards,
Ravish.
Show more

ravish844:

When we are given "if silver is twice as heavy as aluminium" it means that for the same volume, silver is twice as heavy as aluminium.
So if we take V volume of aluminium and V volume of silver, if weight of this much aluminium is W, weight of the same volume of silver will be 2W.

This means that if we have V volume of aluminium, and we have V/2 volume of silver, weight of both will be W.

This is what the question tells us about the first coin: "the volume of aluminium in the alloy is twice that of silver"
So we realise that weight of both in the coin is the same. Since weight of coin is 30 gm, weight of both is 15 gm each.

Yes, if the volume of Aluminium in coin 1 is V and it weighs 15 gm, volume 3V of aluminium in coin 2 will weight 45 gm.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 10 Sep 2021, 20:35
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Hi VeritasKarishma,
I got Q49 in my two recent CATs (Veritas and Kaplan). But I some time get Q44 or 45 because I miss some easy level questions. And in GMAT Club Tests, I sometimes even get Q32 34. Further I am always left clueless by probability and combinatorics questions and always fear absolute value questions and inequalities questions, making error in 600 level questions as well. (Was same case in Mixture, but thank you for your thread on Mixture in Quant Mega thread).

Can you please help me on how should I make my strategy and the resource to follow, given I have less than 4 weeks to prepare. I want to get Q49 or Q50 in my real exam. I have got to improve my verbal score also during this time, from V35 to V39/40 (I have tagged you in my another post in Verbal forum.)

Thank you.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 12 Sep 2021, 22:18
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Mck2023
Hi VeritasKarishma,
I got Q49 in my two recent CATs (Veritas and Kaplan). But I some time get Q44 or 45 because I miss some easy level questions. And in GMAT Club Tests, I sometimes even get Q32 34. Further I am always left clueless by probability and combinatorics questions and always fear absolute value questions and inequalities questions, making error in 600 level questions as well. (Was same case in Mixture, but thank you for your thread on Mixture in Quant Mega thread).

Can you please help me on how should I make my strategy and the resource to follow, given I have less than 4 weeks to prepare. I want to get Q49 or Q50 in my real exam. I have got to improve my verbal score also during this time, from V35 to V39/40 (I have tagged you in my another post in Verbal forum.)

Thank you.
Show more

Hey Mck2023,

To get a high overall score of say Q50, you should not make errors in questions below 700 level. If there are any topics in which you are struggling for easier questions, please review those topics thoroughly. Often GMAT questions involve multiple concepts tested in each question hence too much discomfort in any topic becomes problematic. The fundamentals of each should be clear else the score could fluctuate a lot depending on the topics that were tested more/less during the test. If you struggle on some advanced application during the test, it may not be that damaging.

I am glad the mixture concept is sorted. I have many posts on Combinatorics and Inequalities & Absolute Values too on my blog. Check here: https://anaprep.com/blogs/
See if this helps.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 01 Nov 2023, 03:49
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KarishmaB can you please help me with this question??

If a taxi driver charges x cents for the first quarter-mile of a trip and (x/5) cents for each additional quarter-mile, what is the charge, in cents, for a trip whose distance in miles is the whole number y?

A. (x+xy)/125

B. (4x + 4xy)/5

C. (4x+xy)/500

D. (4x+xy)/5

E. xy/25


Solution -


Since 1 mile has 4 quarter-miles, a trip of y miles has 4y quarter-miles, and after the first quarter-mile that charges x cents, there are 4y - 1 additional quarter-miles that charge x/5 cents each. Thus, the total cost is:

x + (x/5)(4y - 1)

5x/5 + (4xy - x)/5

(4x + 4xy)/5

Now,
My approach to this question is very different.

Total miles = y
Charges for 1st mile, which is "y/4" = x cents.
Additional miles left = "3y/4". So, charges for them = 3y/4*x/5

Total charges = x + 3xy/20

Where am I going wrong on this? Kindly help me on this. Please help
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 01 Jan 2024, 21:47
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A container contains a mixture of milk and water in the ratio of 4:1. 20 liters of the mixture is removed and replaced with water. This process is repeated one more time. If the final mixture has milk and water in the ratio of 16:9, what was the original quantity of the mixture?

Can you please give me a solution of this problem?

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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 02 Jan 2024, 04:41
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KarishmaB
Request to all forum users:

I am one of the forum experts on the PS forum. If you would like me to take a look at any question on this forum, please mention it on this thread.

Since I receive 100s of mails everyday in my mailbox, unfortunately, it becomes very difficult to follow up on every query even if I am tagged on it. I do take a look at this thread on a daily basis and hence will certainly get to your query if you mention here.

Thank you!
A container contains a mixture of milk and water in the ratio of 4:1. 20 liters of the mixture is removed and replaced with water. This process is repeated one more time. If the final mixture has milk and water in the ratio of 16:9, what was the original quantity of the mixture?

Can you please give me a solution of this problem?

KarishmaB

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What is the source of the question? It is not GMAT relevant because the numbers given do not work here. We cannot do the replacement process twice and get the given concentration of milk. If we want to do it twice, we must start with only milk in the initial solution. Here is why:

Here we will employ the concepts of replacement:

\(Cf = Ci * (\frac{Vi}{Vf})^n\)

Since we are adding water back, we should work with the concentration of milk. The initial concentration of milk in the mix is 4/5 and the final concentration is 16/25

\(\frac{16}{25} = \frac{4}{5} * (\frac{Vi}{Vf})^2\)

\((\frac{Vi}{Vf})^2 = \frac{4}{5}\)

This is a problem. 4/5 is not a perfect square. Now we need a calculator but GMAT doesn't have that.
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 08 Jan 2024, 10:38
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Hello and welcome to my PS Forum Expert Topic. Let me know if you have any Problem Solving questions I can help with - strategy, specific ones, etc.

You may know me from forum discussion - I am one of the resident Veritas Prep Experts on GMAT Club. I have over 8,000 posts and 22,000 Kudos. I hope you find my replies and explanations helpful. My most helpful reply to this OG Question received over 100 Kudos.

If you have any specific questions about PS or Math in general such as strategy, approach, etc, please feel free to post them here and I will be happy to address them. I intend to have this thread be as a "Everything You Need to Know about PS" type of thread and will include some FAQ's over time.

Thank you all - good luck on the GMAT and look forward to seeing you in the PS forum!
Karishma.
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Thank you very much for taking the time to answer questions! Really appreciated!!!
In QQ https://gmatclub.com/forum/a-certain-id ... l#p3329994
Is there another approach to do this in a faster way? Perhaps by answer elimination? For example, we directly eliminate option B because we know the answer is not 6! And we eliminate option E because we know it is not 9^4. What about A and D? Any red flags?

My second question is, if we are talking about codes (order is important) and that the same letter appears more than once (there can be identicals), it should be a Permutation right? I do not understand why it is a Combination...
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Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math 09 Jan 2024, 03:11
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KarishmaB
Ask me Anything about GMAT Quant and Math in General


Hello and welcome to my PS Forum Expert Topic. Let me know if you have any Problem Solving questions I can help with - strategy, specific ones, etc.

You may know me from forum discussion - I am one of the resident Veritas Prep Experts on GMAT Club. I have over 8,000 posts and 22,000 Kudos. I hope you find my replies and explanations helpful. My most helpful reply to this OG Question received over 100 Kudos.

If you have any specific questions about PS or Math in general such as strategy, approach, etc, please feel free to post them here and I will be happy to address them. I intend to have this thread be as a "Everything You Need to Know about PS" type of thread and will include some FAQ's over time.

Thank you all - good luck on the GMAT and look forward to seeing you in the PS forum!
Karishma.

Thank you very much for taking the time to answer questions! Really appreciated!!!
In QQ https://gmatclub.com/forum/a-certain-id ... l#p3329994
Is there another approach to do this in a faster way? Perhaps by answer elimination? For example, we directly eliminate option B because we know the answer is not 6! And we eliminate option E because we know it is not 9^4. What about A and D? Any red flags?

My second question is, if we are talking about codes (order is important) and that the same letter appears more than once (there can be identicals), it should be a Permutation right? I do not understand why it is a Combination...
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I replied to the first question in the relevant thread.
It is a permutation. When we say this digit could go in the 1st position, this in the 2nd etc, we are already arranging. Combinations would have been just selecting a group of 6 digits - no arrangement of the digits involved. When we select 6 of our friends to go out for a picnic, it is combinations. When we give them seats in a movie theatre - seat no 1 to be occupied by my fav, seat no 2 to be occupied by my second fav etc, then that is permutations.
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