Sudipto's Doubts...

Dear Mentors, Below qs as my weak area as unable to solve in 2 min during exam :

Is m+z > 0?

i) m-3z>0 ii) 4z-m>0

and

Is xy>0 ?

i) x-y>-2 ii) x-2y < -6

Any trick to pace up?


Regards, Sudipto





Solution:


In such questions, the trick is to get a 'yes' as well as 'no' for each statement.
Is m+z > 0?

i) m-3z>0 ii) 4z-m>0

Statement 1: Let's assume such values that the condition m-3z>0 is satisfied and we get a 'yes' as well as 'no' for m+z>0
m=5, z=+/-1 --> m-3z>0 and yes, m+z>0 (when m is positive and much greater than z) .... case (i)
m=+/-1, z=-1 --> m-3z>0 but no, m+z />0 (when m is a small positive/negative integer and z is a negative integer).... case (ii)
Yes and no both are possible and hence, insufficient.

Similarly,

Statement 2: First simplify to get it m,z in same order as that in statement 1. Hence, 4z-m>0 means m-4z<0
Let's assume such values that the condition m-4z<0 is satisfied and we get a 'yes' as well as 'no' for m+z>0
m=2, z=1 --> m-4z<0 and yes, m+z>0 (when m and n are both positive and m is not much greater than z)....case (iii)
m= -5, z=+/-1 --> m-4z<0 but no, m+z />0 (when m is a big negative number and n is a small positive/negative number)....case (iv)
Yes and no both are possible and hence, insufficient.

Statement I as well as II are each alone insufficient. Hence, let's combine.

We need to satisfy both the conditions m-3z>0 as well as m-4z<0 and try to get a 'yes' as well as 'no' for m+z>0
Cases (ii) and (iv) can be eliminated as they won't satisfy m-3z>0. Cases (i) and (iii) remain and in both cases, we get 'yes' and 'no' is not possible. Hence, sufficient.

Alternate way of combining:
Combining,we get, 3z0 , m also needs to be positive.
Hence, both m and z are positive and thus, a 'no' for m+z<0 is not possible.
Hence, 'yes' on combining, and thus, sufficient.

Hence, the answer is (c)

Please try the second questions yourself, using the approach suggested. It looks lengthy in explaining but is quite logical in approach. Try to get a 'yes' as well as 'no' while satisfying the conditions and when you fail to get both yes and no, it's sufficient!

Nandini's Doubt...

Town T has 35,000 residents, 40 percent of whom earn at least
$50,000 per year. What percent of those who earn at least
$50,000 per year work for Company X?
(1) 5,600 of the residents of Town T work for Company X.
(2) Company X has 1,800 employees who earn at least
$50,000 per year.​

My answer came out to be "E" on the reasoning that even if company X has 1800 employees who make more than $50k p.y., it says nowhere that all the employees of company X are from town T. From that logic we cannot conclude that all 1800 are from town T like what is assumed while marking "B" as an answer.


Explanation:

Statement 1: Many of these 5600 may work for other companies. Insufficient.
Statement 2: Many of these 1800 may not be resident of Town T.
Combining: Still, many of the 5600 may work for other countries and many of 1800 may not be resident of Town T. Insufficient.

E.

Hi Sudipto,

Here's the solution..

- One letter that's to go in the right envelope: 4C1 = 4 cases.
- Second letter has three choices but only two incorrect choices; hence --> 2 cases
- Third letter has two choices but only one incorrect choice --> 1 case
- Fourth letter has only one choice and that's an incorrect envelope --> 1 case

Total: 4x2x1x1 = 8 cases.

Hence, the total number of cases is 8.

Probability = 8/4! = 1/3

Hi Sudipto,

Here's the complete question with answer choices...


A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

A. 10,700
B. 10,800
C. 10,900
D. 11,000
E. 11,100

We need to minimize the population for one and therefore, we'll try to maximize the population for the other 10.
Let's assume the population of district with minimum people = x
The population of all the other districts (assuming the maximum possible value for each) = 1.1x
Total population = x + 1.1x*10 = 12x =132000
Hence, x= 11,000

Answer is D

A City with 132,000 is to be divided into 11 voting districts. No district is to have a population more than 10% of any other district. What is the minimum population for any district? - GMAT prep

Can anyone please help me with this PS appeared in GMAT Prep:

X prepared 4 diff letters to be sent to 4 diff addresses. For each letter X prepared an envelope with correct address. If 4 letters are to be put into 4 envelopes at random, what is the probability that only one letter will be put into envelope with correct address?

Another doubt

Our cat is cuter than that in the shelter --> Should be correct as that refers to new copy of antecedent "cat".
Our cat is cuter than the cats in the shelter. ---> Here we cannot use "those" in place of "cats" as it would not agree with the antecedent "cat" which is singular and so this sentence is correct.
Our cat is cuter than the cat in the shelter. --> This is incorrect as we could have used the pronoun "that" like in first sentence
Please confirm if my understanding is correct here.


Explanation:

Our cat is cuter than that in the shelter --> Should be correct as that refers to new copy of antecedent "cat".
Yes, alright.

Our cat is cuter than the cats in the shelter. ---> Here we cannot use "those" in place of "cats" as it would not agree with the antecedent "cat" which is singular and so this sentence is correct.
Of course, as there is no 'cats' in the sentence and thus, there's nothing that 'those' can refer to.
In case there were 'cats' in the sentence somewhere...let's take an example:
Our cat is cuter than those in the shelter as the cats there dirty
'Those' in this sentence refers to the 'cats' (in the proceeding part of the sentence) and not to the 'cat' (in the preceeding part of the sentence); the problem is not of pronoun agreement. The problem is whether you want to compare one cat with multiple cats. If yes, the sentence is on. Hence, as with most of the high caliber questions on GMAT, it boils down to meaning.

Our cat is cuter than the cat in the shelter. --> This is incorrect as we could have used the pronoun "that" like in first sentence
It would not be correct to say that the sentence is "incorrect"; repeated usage of a noun (rather than pronoun) doesn't lead to an error but does sound 'awkward'. Hence, use of 'that' is more appropriate, use of 'cat' again is not a pure mistake.

Ankit's Doubt


At Shiprock, New Mexico, a perennially powerful girls' high school basketball team has become a path to college for some and a source of pride for a community where the household incomes of 49 percent of them are below the poverty level.
(A) where the household incomes of 49 percent of them are
(B) where they have 49 percent of the household incomes
(C) where 49 percent of the household incomes are
(D) which has 49 percent of the household incomes
(E) in which 49 percent of them have household incomes

The correct answer according to the book is C but C uses incorrect use of "where", according to Manhatten SC book Page no. 87, "where" can only be used to modify a noun place.
Here the noun it modifies is community which is certianly not noun place, please clarify.


One of the bad these SC books do is that they create a stringent rule for every small thing. Practically, there aren't so many rules and such forceful 'rules' are actually norms- followed 95% times but there are exceptions in 5% cases. So "community where" or "society where" or "culture where" are many exceptions I can straightaway think of. Technically, the reason is that though community/society/culture are not place nouns, meaning-wise, they can assume that role.

The right approach is to look for the real 'deal breakers' and let the idiomatic usages be the last virtue to apply. In this question, 'society where' / 'society in which' is not the deal breaker. The use of pronoun 'they/them' is the main problem and that gets us rid of A, B, E. It's between C and D; use of 'has' in D leads to an awkward, 'possessive' relationship and must be eliminated.

C is the best choice.

Some SC Doubts
==================
Stage 2- 650+

Questions:
15- Please explain the meaning of the question.

Camille Claudet worked continuously through the 1880’s and early 1890’s with the sculptor Auguste Rodin; since there are very few signed works of hers, the inescapable conclusion seems to be one of Claudet conceiving and executing part of Rodin’s enormous production of that period.
(A) inescapable conclusion seems to be one of Claudet conceiving and executing part of Rodin’s enormous production of that period
(B) conclusion of Claudet conceiving and executing part of Rodin’s enormous production of that period seems inescapable
(C) conclusion seems inescapable that part of Rodin’s enormous production of that period was conceived and executed by Claudet
(D) conclusion of part of Rodin’s enormous production of that period having been conceived and executed by Claudet seems inescapable
(E) seemingly inescapable conclusion is that Claudet would have conceived and executed part of Rodin’s enormous production of that period

--> Meaning,
During 1880s and 1890s Camille Claudet worked continuously with sculptor Auguste Rodin. There are only few signed worker of her. i.e. Camille's. The conclusion is that she conceived and executed part of Rodin's vast production.. i.e. she is the creator of many works that are considered Rodin's.

Firstly, ‘conclusion…that…’ is the correct structure.

A) 'seems to be one of' is awkward.
B) 'conclusion of Claudet conceiving and executing ' is awkward.
C) Clear and concise, with no errors. The best answer.
D) Too awkward! 'conclusion of part of Rodin’s enormous production of that period having been conceived '
E) 'seemingly inescapable conclusion is that' is awkward too.

C is the best choice.


18- Is the correct option parallel?

Charlotte Perkins Gilman, a late nineteenth-century feminist, called for urban apartment houses including childcare facilities and clustered suburban houses including communal eating and social facilities.
(A) including child-care facilities and clustered suburban houses including communal eating and social facilities
(B) that included child-care facilities, and for clustered suburban houses to include communal eating and social facilities
(C) with child-care facilities included and for clustered suburban houses to include communal eating and social facilities
(D) that included child-care facilities and for clustered suburban houses with communal eating and social facilities
(E) to include child-care facilities and for clustered suburban houses with communal eating and social facilities included

​--> Yes, the best option is D and it maintains parallelism.
Charlotte called for

1. urban apartment houses that included….
2. clustered suburban houses with communal eating and social facilities

Other options lack parallelism because ‘for’ needs to be repeated.

20- why is option C not correct? Please explain the use of TO and FOR.

Coronary angiography, a sophisticated method for diagnosing coronary disease involving the introduction of a dye into the arteries of the heart, is now administered selectively, because it uses x-rays to observe cardiac function.
(A) for diagnosing coronary disease involving the introduction of a dye into the arteries of the heart, is now administered selectively, because it uses
(B) for diagnosing coronary disease involving the introduction of a dye into the arteries of heart, is now administered selectively, because of using
(C) for diagnosing coronary disease, involves the introduction of dye into the arteries of the heart and is now administered selectively, because it uses
(D) to diagnose coronary disease that involves the introduction of a dye into the arteries of the heart, is now administered selectively, because it uses
(E) to diagnose coronary disease involving the introduction of a dye into the arteries of the heart, which is now administered selectively, uses

-->
C is the correct answer.
To vs For
To – to be used when the intent of the main verb is explained with the verb following ‘to’.
For – when ‘to’ is inappropriate.

Eg1
My grandfather uses a wooden chair to sit/for sitting.
Main verb: ‘uses’ , action ‘sit’. Is sitting on the intent of using? Yes. That means ‘to sit’ is correct.
My grandfather uses a wooden chair to sit.

Eg 2
My grandfather uses a wooden stick as a tool to walk/for walking.
Main verb: ‘uses’, action ‘walking’. Is walking the intent of using? No. That means ‘for walking’ is correct.
My grandfather uses a wooden stick as a tool to for walking.



Stage 2- 600+
136-Please explain the meaning of the question.

136. The use of chemical pesticides in this country is equally extensive or more so than ten years ago.
(A) equally extensive or more so than ten years ago
(B) equal to or more extensive than ten years ago
(C) as extensive as ten years ago or more
(D) equal to, if not more, than ten years ago
(E) as extensive as it was ten years ago, if not more so


--> Fairly simple.
The use of pesticides is as extensive (vastly spread) or more than it was ten years ago.
E is the best choice.


Also,please explain the meaning of 'Subjunctive Mood'

-->
Subjunctive mood is used when we have an opinion or wish.
Eg
If I were rich, I would go on a world tour.
Now, this is a wish, and hence it is an example of subjunctive mood.
On the GMAT, the following criteria should be used to find correct usage of subjunctive mood.
IF and WOULD.. .IF something happens, something else WOULD happen. Also, since, in most cases, the condition with IF is hypothetical, a ‘were’ is used instead of a ‘was’. The above example explains this.


The usage of 'If Only Because'.
-->
“If only because” sounds weird but it is a phrase with meaning: “If for no other reason than that”.
There is nothing else special in the phrase’s use in the question.

The above mentioned doubt can also be explained with reference to Question 7 SC from the Stage 3 book.

Building large new hospitals in the bistate area would constitute a wasteful use of resources, on the basis of avoidance of duplicated facilities alone.
(A) on the basis of avoidance of duplicated facilities alone
(B) on the grounds of avoiding duplicated facilities alone
(C) solely in that duplicated facilities should be avoided
(D) while the duplication of facilities should be avoided
(E) if only because the duplication of facilities should be avoided

-->
It is clear that whatever comes after the comma, should explain why building hospitals WOULD be waste of resources. So, trying to fit the IF…WOULD logic here, we need something like the following..
IF something happens…it WOULD be waste of resources….
The underlined part should explain the ‘IF something happens’ piece. A, B, C, D don’t have anything of the sort. So, E is the best answer. The only confusing part is ‘if only because’ which is explained above.

Q1.
A certain class consists of 8 students, including Kim. Each day,
three tasks must be completed and are assigned as follows:
one of the 8 students is selected at random to complete Task A,
one of the remaining 7 students is selected at random to
complete Task B, and one of the remaining six students is
selected at random to complete Task C. What is the
probability that Kim will be selected to complete one of the
three tasks?
(A) 1/3
(B) 3/8
(C) 1/24
(D) 1/336
(E) 1/512

Student query:
Why the answer is not 1/8 +1/7 +1/6 ?If Kim is not selected for the first task then probability of her getting selected in second task is 1/7 and not 1/8 and so forth.

--> Hmmm.
Lets consider the case in which Kim is assigned task B. In what case does it happen? When Kim IS NOT CHOSEN FOR task A. We need to consider this.
P(task B) = P(One student apart from Kim is selected for task A) * P(Kim selected for task B). In your approach, you are ignoring the first part.
So, using the above logic,
P(task A) = 1/8
P(task B) = 7/8 * 1/7 = 1/8
P(task C) = 7/8 * 6/7 * 1/6 = 1/8

So required probability = 1/8 + 1/8 + 1/8 = 3/8.

There is another, simpler way to solve this. Why are we bothered about which task Kim does? All we need is that she is picked up for one task. That means the scenario is: I am selecting three students from 8 students and I want Kim in that three. That means,
P(I want Kim in the first three) = 1 - P(Kim is not in the first three)
P(Kim is not in the first three) = P(all three students chosen are from 7 other students) = 7C3/8C3 = 5/8.
P(I want Kim in the first three) = 1 - 5/8 = 3/8.

Q2.
A certain board game has a row of squares numbered 1 to 100.
If a game piece is placed on a random square and then moved
7 consecutive spaces in a random direction, what is the
probability the piece ends no more than 7 spaces from the
square numbered 49?
(A) 7%
(B) 8%
(C) 14%
(D) 15%
(E) 28%

Can you please explain the meaning of the question?Also are non perfect squares considered in the question?

--> Lets understand the scenario. So there is a board game, that has 100 squares numbered from 1 to 100. This is one-dimentional, not a chess-board like 10*10 board. This is clear from "a row of squares".
So we pick a number at random. Then we have two options, either to move left or right. We pick one direction, and move 7 spaces in that direction. We need to find the probability that the destination cell is "no more than 7 spaces from 49". That is destination cell is between 42 and 56, inclusive.
In how many ways can this happen?

42 - This is possible when we pick 35 and move right or pick 49 and move left = P(picking 35) * P(picking right) + P(picking 42) * P(picking left)
P(42) = 1/100 * 1/2 + 1/100 * 1/2 = 1/100.
Similarly, P(43) = 1/100...P(56)=1/100.

We need to add all these probabilities.
So, P(42-56) = 1/100 + 1/100...15 times = 15/100 = 15%.

Who Vs Whom

Student Query:
I was reading SC Grail and came across following sentence "Among all the applicants, I haven't yet decided who to meet with." on page 128, this sentence seems incorrect to me, instead of "who" it should have been "whom" i.e. "Among all the applicants, I haven't yet decided who whom to meet with."

--> You are right. If we try to answer the question "who/whom did I meet with?", the answer would be "I met with HIM/HER". Since HIM/HER are in objective form, the correct question would have "WHOM" in it.