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# Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math

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Intern
Joined: 20 Mar 2018
Posts: 41
Location: Ghana
Concentration: Finance, Real Estate

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12 Dec 2018, 04:17
Staphyk wrote:
used a time consuming way in solving ,help with an efficient way

A does a work in 8hours,B does the same work in 16hours and C does it in 12hours. A starts working and is joined by B after 2hours,after 3hours of working together ,A leaves and C joins. How much more time will it take to complete the work if B and C continue to work until it’s over?
600 level?

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Hey Staphyk,

Rate of work of A = 1/8
Rate of work of B = 1/16
Rate of work of C = 1/12

Before B and C start working,
A works for 5 hours (2 + 3) and hence does (1/8)*5 = 5/8 of the work.
B works for 3 hrs and hence does (1/16)*3 = 3/16 of the work

So before B and C start working, 5/8 + 3/16 = 13/16 of the work is already over and just 3/16 is left.

Combined rate of B and C = 1/16 + 1/12 = 7/48

Time taken = Work/Rate = (3/16) / (7/48) = 9/7 hrs

I would say 650 level.
Thanks you , But what makes it 650 is it the calculation involved (eating up time ) ,Wording or logical deductions it demands or some upper level concept one must have

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India

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13 Dec 2018, 03:02
Staphyk wrote:
Staphyk wrote:
used a time consuming way in solving ,help with an efficient way

A does a work in 8hours,B does the same work in 16hours and C does it in 12hours. A starts working and is joined by B after 2hours,after 3hours of working together ,A leaves and C joins. How much more time will it take to complete the work if B and C continue to work until it’s over?
600 level?

Sent from my iPhone using GMAT Club Forum mobile app

Hey Staphyk,

Rate of work of A = 1/8
Rate of work of B = 1/16
Rate of work of C = 1/12

Before B and C start working,
A works for 5 hours (2 + 3) and hence does (1/8)*5 = 5/8 of the work.
B works for 3 hrs and hence does (1/16)*3 = 3/16 of the work

So before B and C start working, 5/8 + 3/16 = 13/16 of the work is already over and just 3/16 is left.

Combined rate of B and C = 1/16 + 1/12 = 7/48

Time taken = Work/Rate = (3/16) / (7/48) = 9/7 hrs

I would say 650 level.
Thanks you , But what makes it 650 is it the calculation involved (eating up time ) ,Wording or logical deductions it demands or some upper level concept one must have

Sent from my iPhone using GMAT Club Forum mobile app

In an actual GMAT questions, calculations involved are minimal. They will never make it a higher level question. The question is a little convoluted with 3 people working at different rates and for different times and all that needs to be handled separately. That makes this question a little harder.
_________________

Karishma
Veritas Prep GMAT Instructor

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Joined: 20 Mar 2018
Posts: 41
Location: Ghana
Concentration: Finance, Real Estate

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13 Dec 2018, 03:24
Staphyk wrote:
[quote="Staphyk"]used a time consuming way in solving ,help with an efficient way

A does a work in 8hours,B does the same work in 16hours and C does it in 12hours. A starts working and is joined by B after 2hours,after 3hours of working together ,A leaves and C joins. How much more time will it take to complete the work if B and C continue to work until it’s over?
600 level?

Sent from my iPhone using GMAT Club Forum mobile app

Hey Staphyk,

Rate of work of A = 1/8
Rate of work of B = 1/16
Rate of work of C = 1/12

Before B and C start working,
A works for 5 hours (2 + 3) and hence does (1/8)*5 = 5/8 of the work.
B works for 3 hrs and hence does (1/16)*3 = 3/16 of the work

So before B and C start working, 5/8 + 3/16 = 13/16 of the work is already over and just 3/16 is left.

Combined rate of B and C = 1/16 + 1/12 = 7/48

Time taken = Work/Rate = (3/16) / (7/48) = 9/7 hrs

I would say 650 level.
Thanks you , But what makes it 650 is it the calculation involved (eating up time ) ,Wording or logical deductions it demands or some upper level concept one must have

Sent from my iPhone using GMAT Club Forum mobile app

In an actual GMAT questions, calculations involved are minimal. They will never make it a higher level question. The question is a little convoluted with 3 people working at different rates and for different times and all that needs to be handled separately. That makes this question a little harder.[/quote]Thank you

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Intern
Joined: 20 Mar 2018
Posts: 41
Location: Ghana
Concentration: Finance, Real Estate

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17 Dec 2018, 01:54
Hello Karishma ,
Kindly help me with this question ,am confused and don’t know where to start from
In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only two of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A?

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India

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17 Dec 2018, 20:36
Staphyk wrote:
Hello Karishma ,
Kindly help me with this question ,am confused and don’t know where to start from
In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only two of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A?

Sent from my iPhone using GMAT Club Forum mobile app

LEt's make a 3*3 matrix here:

.................................................. A ......... B ........... C........... Total

Public School...........................................................................25

Parochial School......................................................................16

Private Independent School......................2...............................9

Total.........................................18..........17.............................50

Step 2: C has equal number of the 3 school types

.................................................. A ......... B .............. C......................... Total

Public School..............................................................5...........................25

Parochial School.........................................................5...........................16

Private Independent School......................2.................5...........................9

Total.........................................18..........17.......50-18-17=15.................50

Step 3: No of private independent schools in district A

.................................................. A ......... B .............. C......................... Total

Public School..............................................................5...........................25

Parochial School.........................................................5...........................16

Private Independent School.......9-2-5.......2.................5...........................9

Total.........................................18..........17...............15.................50

Answer: A has 2 private independent schools

Alternatively,

All you need to do is focus on what you need. You need to find the number of private schools in A. Total no. of private schools is 9 and in B, you have 2 of them. So there are 7 private schools distributed between A and C. All you need to find is the number of private schools in C to get the number of private schools in A. What is given to you about C? C has an equal number of each of the three kinds of schools. Total number of schools in C = 50 - (18 + 17) = 15. So no. of private schools in C = 15/3 = 5
Therefore, A must have 7 - 5 = 2 private schools.
_________________

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 20 Mar 2018
Posts: 41
Location: Ghana
Concentration: Finance, Real Estate

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18 Dec 2018, 08:13
Staphyk wrote:
Hello Karishma ,
Kindly help me with this question ,am confused and don’t know where to start from
In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 16 parochial schools, and 9 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only two of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A?

Sent from my iPhone using GMAT Club Forum mobile app

LEt's make a 3*3 matrix here:

.................................................. A ......... B ........... C........... Total

Public School...........................................................................25

Parochial School......................................................................16

Private Independent School......................2...............................9

Total.........................................18..........17.............................50

Step 2: C has equal number of the 3 school types

.................................................. A ......... B .............. C......................... Total

Public School..............................................................5...........................25

Parochial School.........................................................5...........................16

Private Independent School......................2.................5...........................9

Total.........................................18..........17.......50-18-17=15.................50

Step 3: No of private independent schools in district A

.................................................. A ......... B .............. C......................... Total

Public School..............................................................5...........................25

Parochial School.........................................................5...........................16

Private Independent School.......9-2-5.......2.................5...........................9

Total.........................................18..........17...............15.................50

Answer: A has 2 private independent schools

Alternatively,

All you need to do is focus on what you need. You need to find the number of private schools in A. Total no. of private schools is 9 and in B, you have 2 of them. So there are 7 private schools distributed between A and C. All you need to find is the number of private schools in C to get the number of private schools in A. What is given to you about C? C has an equal number of each of the three kinds of schools. Total number of schools in C = 50 - (18 + 17) = 15. So no. of private schools in C = 15/3 = 5
Therefore, A must have 7 - 5 = 2 private schools.
Thank you

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Joined: 04 Jun 2018
Posts: 127

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19 Dec 2018, 19:54

Is there any non algebraic way of doing the following question?
We could do it by number plugging but I was looking for something logical and fast.
Do let me know!

https://gmatclub.com/forum/bill-and-ted ... s#p2193868

Regards
Nitesh
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India

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20 Dec 2018, 05:00
nitesh50 wrote:

Is there any non algebraic way of doing the following question?
We could do it by number plugging but I was looking for something logical and fast.
Do let me know!

https://gmatclub.com/forum/bill-and-ted ... s#p2193868

Regards
Nitesh

Nitesh, I have come across such questions often and used the options to arrive at the answer. Since the relation is quadratic, I haven't been able to find a straight forward logical way to arrive at the answer.
https://gmatclub.com/forum/bill-and-ted ... l#p2194227
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Karishma
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20 Dec 2018, 10:03
https://gmatclub.com/forum/if-m-and-n-a ... 01636.html

in this question the final condition becomes:

IS (1/3+n/3) > Rem (1/3+m/3)?

Now the mistake I made on this question is that
I cancelled remainder of 1 on each side.

SO my statement then became:
n/3 > m/3

In this case when analysing option B, I found the option to be NS.

n/3=2
then m/3=
0 yes
1 yes
2 no

Now why can't we cancel the remainders on either side.
Can you tell me why can't I do cancel the remainders on either side.
Any additional theory on this specific concept will really help me.

Regards
nitesh
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India

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21 Dec 2018, 01:37
nitesh50 wrote:
https://gmatclub.com/forum/if-m-and-n-are-positive-integers-is-the-remainder-of-101636.html

in this question the final condition becomes:

IS (1/3+n/3) > Rem (1/3+m/3)?

Now the mistake I made on this question is that
I cancelled remainder of 1 on each side.

SO my statement then became:
n/3 > m/3

In this case when analysing option B, I found the option to be NS.

n/3=2
then m/3=
0 yes
1 yes
2 no

Now why can't we cancel the remainders on either side.
Can you tell me why can't I do cancel the remainders on either side.
Any additional theory on this specific concept will really help me.

Regards
nitesh

Is remainder of (n + 1)/3 greater than the remainder of (m + 1)/3?
Is this same as saying "Is remainder of n/3 greater than remainder of m/3?"
- No, it is not.

Say, n = 5, m = 4

n/3 remainder = 2 (Greater)
m/3 remainder = 1

(n + 1)/3 remainder = 0
(m + 1)/3 remainder = 2 (Greater)

So the two questions are not equivalent. Adding 1 to number doesn't necessarily add 1 to the remainder. It could make the remainder go 0.
_________________

Karishma
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Posts: 41
Location: Ghana
Concentration: Finance, Real Estate

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21 Dec 2018, 22:09
Dear Karishma ,
Please what does it mean if I can’t solve a question like the below ?
A room contains 160 people,15% of whom a women.A group of people,30% of whom are women leaves the room. Of the people remaining the room,10% are women ,How many people left the room?

Regards,
Staphyk

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India

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24 Dec 2018, 03:07
Staphyk wrote:
Dear Karishma ,
Please what does it mean if I can’t solve a question like the below ?
A room contains 160 people,15% of whom a women.A group of people,30% of whom are women leaves the room. Of the people remaining the room,10% are women ,How many people left the room?

Regards,
Staphyk

Sent from my iPhone using GMAT Club Forum mobile app

Hey Staphyk,

You cannot judge yourself based on a single question. The best of us sometimes make the silliest of mistakes or experience brain freeze on a question. That said, it seems many people get stuck in this question so though it may seem easy after looking at the solution, it certainly may not seem that way the first time you see it.

Tip: Think of weighted average whenever you mix two groups together or whenever you separate a group into two different groups.
In this question, a group fo 160 people split into two groups - one group that leaves (L) and one group that is remaining (R).

wL/wR = (10 - 15)/(15 - 30) = 1/3

So 1/4th of the total people left i.e. (1/4)*160 = 40 people left.
_________________

Karishma
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Intern
Joined: 20 Mar 2018
Posts: 41
Location: Ghana
Concentration: Finance, Real Estate

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24 Dec 2018, 04:32
Staphyk wrote:
Dear Karishma ,
Please what does it mean if I can’t solve a question like the below ?
A room contains 160 people,15% of whom a women.A group of people,30% of whom are women leaves the room. Of the people remaining the room,10% are women ,How many people left the room?

Regards,
Staphyk

Sent from my iPhone using GMAT Club Forum mobile app

Hey Staphyk,

You cannot judge yourself based on a single question. The best of us sometimes make the silliest of mistakes or experience brain freeze on a question. That said, it seems many people get stuck in this question so though it may seem easy after looking at the solution, it certainly may not seem that way the first time you see it.

Tip: Think of weighted average whenever you mix two groups together or whenever you separate a group into two different groups.
In this question, a group fo 160 people split into two groups - one group that leaves (L) and one group that is remaining (R).

wL/wR = (10 - 15)/(15 - 30) = 1/3

So 1/4th of the total people left i.e. (1/4)*160 = 40 people left.
Simple solution,Thanks Karishma

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Posts: 127

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12 Jan 2019, 03:09

Please have a look at this question.

https://gmatclub.com/forum/is-a-positiv ... l#p2206226

Regards
Nitesh
Intern
Joined: 07 Jul 2018
Posts: 29

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14 Jan 2019, 02:16
Hi,

I am facing this silly doubt which is bothering me in DS questions.

Is $$\sqrt{n}$$ = n
or +n or -n?

To think of it $$\sqrt{81}$$ , we can square 9 and -9 to get it.
But after reading many sources and watching youtube videos, they say it can only be positive.

Secondly, if it is only positive then following is contradictory

$$\sqrt{X^2}$$ = |X|
Then X can take both positive and negative values, so this is contradictory.

I was solving a question and I struggled with this equation
$$p^2$$= $$(q+1)^2$$
What would this give?

Thanks.
Intern
Joined: 27 Nov 2018
Posts: 1

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14 Jan 2019, 02:28
Hello Karishma,

I have a very general question on how to simplify arithmetic computations.
I have to compute 0.17*(26.4/1.65). To simplify it I did rewrite it as: 17*264/1650

Now the solution I found to simplify this calculation further more is the following: (17)*(3*8*11)/(3*5*11*10)

Do you have any tips on how to quickly find these factors of the products I want to simplify? I tried it using prime factorization but it takes too long....

Thanks

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India

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15 Jan 2019, 05:22
2
paulunso wrote:
Hello Karishma,

I have a very general question on how to simplify arithmetic computations.
I have to compute 0.17*(26.4/1.65). To simplify it I did rewrite it as: 17*264/1650

Now the solution I found to simplify this calculation further more is the following: (17)*(3*8*11)/(3*5*11*10)

Do you have any tips on how to quickly find these factors of the products I want to simplify? I tried it using prime factorization but it takes too long....

Thanks

Posted from my mobile device

Usually, in actual application based GMAT questions, you will not be required to do such calculations. Sometimes, the lower level questions might have a direct calculation such as this one in which approximation would work just fine. It will be a rare question in which you actually need an exact value of this.

To approximate: $$0.17 * \frac{26.4}{1.65} = 1.7 * \frac{2.64}{1.65}$$

Double of 1.65 is a bit more than 3 so 2.64 is about 1.5 times of 1.65.

So we get 1.7 * 1.5

1.7 is a bit less than 2 so our answer will be a bit less than double of 1.5 i.e. a bit less than 3.

If you do the actual calculation you get 2.72 so you are close.

I prefer to stick to smaller numbers rather than make them larger. That is why instead of changing 26.4 to 264, I changed 26.4 to 2.64.

That said, if you do need exact values, remove the decimals to get 17*264/1650.
Looking at even numbers, my first instinct is to divide them by the highest power of 2 i.e. is it divisible by 2 or 4 or 8...
The next obvious common factors are 5/3 then 11 etc...
_________________

Karishma
Veritas Prep GMAT Instructor

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India

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15 Jan 2019, 05:31
nitesh50 wrote:

Please have a look at this question.

https://gmatclub.com/forum/is-a-positiv ... l#p2206226

Regards
Nitesh

Guess Gladiator59 has already sorted it out for you. Let me know if something is still unclear.
_________________

Karishma
Veritas Prep GMAT Instructor

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8803
Location: Pune, India

### Show Tags

15 Jan 2019, 05:47
1
Akshit03 wrote:
Hi,

I am facing this silly doubt which is bothering me in DS questions.

Is $$\sqrt{n}$$ = n
or +n or -n?

To think of it $$\sqrt{81}$$ , we can square 9 and -9 to get it.
But after reading many sources and watching youtube videos, they say it can only be positive.

Secondly, if it is only positive then following is contradictory

$$\sqrt{X^2}$$ = |X|
Then X can take both positive and negative values, so this is contradictory.

I was solving a question and I struggled with this equation
$$p^2$$= $$(q+1)^2$$
What would this give?

Thanks.

Yes, this can be a source of confusion. That is why we have a post on it on our blog here: https://www.veritasprep.com/blog/2016/0 ... oots-gmat/

It discusses the cases you have brought up and the 'why' behind each. Let me know if you still have doubts.
Now that you are familiar with principal square root concept.

$$\sqrt{X^2} = |X|$$

$$\sqrt{X^2}$$ is the principal square root of X^2. So whatever you get after finding square root, it will be positive. But what if X is negative? To ensure that you still get a positive value, you take |X|. Let's look at an example.

$$\sqrt{5^2} = \sqrt{25} = |5| = 5$$
This is fine. What we get is a positive number. Since we are talking about principal square root, this is what is expected.

$$\sqrt{(-5)^2} = \sqrt{25}$$
Now what is the answer? It is still 5, right? Still the principal square root. But if I say that $$\sqrt{X^2} = X$$, that gives me -5 as answer because X = -5.
But the principal square root cannot be negative.
So I say $$\sqrt{X^2} = |X|$$

$$p^2 = (q+1)^2$$
All you can say in this case is that their absolute values are the same.
|p| = |q + 1|

Why?
Taking square root both sides, you get
$$\sqrt{p^2} = \sqrt{(q+1)^2}$$
$$|p| = |q + 1|$$
_________________

Karishma
Veritas Prep GMAT Instructor

Re: Veritas Prep PS Forum Expert - Karishma - Ask Me Anything about Math &nbs [#permalink] 15 Jan 2019, 05:47

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