Parit's Doubt...

Three boxes of supplies have an average(arithmetic mean) weight of 7 kilograms and a median weight of 9kg. What is the max possible weight, in kg, of the lightest box?

A. 1
B. 2
C. 3
D. 4
E. 5


Solution:

The total of three boxes = 7x3 = 21kg

The middle box =9kg and thus, the other two weight 21-9 = 12 kg together.

The heaviest box has to weight at least 9 kg.

Thus, the max weight of the lightest box = 12-9 = 3 kg

The mistakes you must have committed is to assume the heaviest box to weigh more than 9; ie 10. It can as well weight 9 and the median of the set shall still be 9.

Regards,
Maxximus

The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10, respectively. Due to a dramatic increase in the surrounding temperature, the composition of the compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the changed compound, if the total weight is 58 lbs, how much does substance x weigh?
A) 48
B) 36
C) 24
D) 12
E) 10


Solution:

x:y is halved; hence 4:6 becomes 4:12;
x:z is triple; hence, 4:10 becomes 12:10

Let's find the new common ratio; i.e. equate the 'x' part is x:y and x:z; ie x:y = 12:36 and x:z = 12:10

Hence, the common ratio x:y:z is 12:36:10

12k + 36k + 10k = 58 lbs

Hence, k=1 lbs and thus, x= 12 lbs

Option D.

Good question!

Regards,
Maxximus

Prashant Bhatt's doubt...

After winning 80% of his first 40 matches, Igby won 50 percent of his remaining matches. How many total matches did he win?

(1) If Igby had won 50 percent of the total number of matches he played, he would have lost 12 more total matches.
(2) If Igby had won 80% of the total number of matches he played, he would have won 18 more total matches.

Answer: B

Prashant's comment...
​
Solving for the statement A; if we calculate the difference between the number of matches lost given the condition in 1 and the actual statement in question , we can find the number of games played say x. getting to number of games won.

say he played x games after 40.. assuming statement 1 to be true we can get to the equation for the difference between matches lost as:

(40+x)/2- [(40+x)-(32+x/2)] = 12 {games lost ie. 50 percent as per (1) - total played minus those won gives no. that would have been lost more in total }.

i am sure there must be something i am missing while trying to correct myself. please help me with a better explaination so that i may avoid this conceptual error in questions to come.

Thanks.


Regards,
Prashant Bhatt



Our Explanation...

Hi Prashant,

The mistake you have committed (in concluding that statement A is sufficient) is that you have 'assumed' that it's a linear equation that can be solved; when you simplify, you will realize that the LHS and RHS are the same and x on both sides get cancelled; hence, 'x' cannot be determined. Good question!

Here's a solution...

Total matches he played: x+40
Matches he won: 40*0.8 + 0.5x = 32+.5x
Matches he lost = 8+.5x

Statement A: Let's equate the number of matches he lost: 0.5 (x+40) = 8+.5x+12
Hence, .5x+20 = .5x+20
This equation cannot be solved.

Statement B: Sufficient.

Answer: B

​Atul's Doubt...



Table
0-6Days- 0% Discount
7-13- 10%
14-29- 25%
>30- 40%

The table above shows the discount structure for
advanced purchase of tickets at a particular airline.
A passenger bought a ticket at this airline for
$1,050. The ticket agent informed her that, had
she purchased the ticket one day later she would
have paid $210 more. How many days before her
departure did she purchase her ticket?

=> Isn't there any alternate way of solving other than plugging in answer choices as explained in PR solution?




Our Solution:

Hi Atul,

Here's a smart approach...

The cost would have been 1.2 times a day later

The cost after discount means 90% is 1.2 times 75%;
hence, the person got 100-75=25% discount rather than 10%.
Thus, he booked exactly 14 days before the departure!

Atul's doubt...

In contrast to classical guitars, whose owners prefer the dulcet, rounded tones produced by nylon strings, folk guitar owners prefer the bright and brassy sound that only bronze or steel can produce.

A) folk guitar owners prefer the bright and brassy sound
B) folk guitar owners prefer to get a sound that is bright and brassy
C)with a folk guitar the owner gets the preferably bright and brassy sound
D)folk guitars produce a bright and brassy sound, which their owners prefer,
E)folk guitars produce a preferred bright and brassy sound for their owners
​
The solution of this question clearly mentions about misplaced modifier- but shouldn't the usage of 'THAT' in non underlined portion force us to use 'sound' just before 'that'? as 'that' must refer to 'sound'.


Our Explanation:

What you are suggesting is one way of doing so. However, in D- the correct choice, removing stuff between the two commas leads to the intended meaning that "brights and brassy sound that only blah blah can produce"

A phrase preceded and succeeded by a comma is almost always an extra phrase, removing which should yield a complete sentence- that's the case with D.

Hope that clarifies.

Gurinder's Doubt...

As we now enter an era of broadband communication, most analysts agree that no less than a new breakthrough is necessary to meet the need for higher data storage capacity and faster data transfer rate.

A. that no less than a new breakthrough is necessary
B. that nothing other than a new breakthrough is needed
C. that a new breakthrough is necessary
D. the necessity for a new breakthrough
E. the necessity for a new breakthrough occurring

A vs C

Explanation

The term 'necessary' obviates the need for extra emphasis through 'no less than'. A becomes redundant and C, a better option.

The real problem lies in understanding when the meaning is being changed and the use of those extra words is justified. I know it's tricky...you get that sometimes and sometimes, you don't. Life is tough sometimes with the GMAT SC


Doubt 2:

The Watsons, a prominent Staten Island family, has survived a close brush with financial ruin; its assets are now almost three times greater than what they were before their problems commenced.

A. financial ruin; its assets are now almost three times greater than
B. financial ruin; its assets are now almost three times more than
C. financial ruin; their assets are now almost threefold
D. financial ruin; now with threefold the assets
E. financial ruin; now with assets three times greater than

A vs B

Explanation:

For figures, 'greater' is preferred; 'asset' may sound quantity right now...start your MBA and you'll know it's often a number


Doubt 3:

Two out of every four participants in the Earth Day rallies also attend our annual conference on biodiversity and endangered species.

A. Two out of every four participants in the Earth Day rallies also attend our annual conference on biodiversity and endangered species.
B. Two out of every four participants in the Earth Day rallies also they attend our annual conference on biodiversity and endangered species.
C. Our annual conference on biodiversity and endangered species is attended by two out of every four participants in the Earth Day rallies.
D. Our annual conference, it is on biodiversity and endangered species, is attended by two out of every four participants in the Earth Day rallies.
E. Two out of every four participants in the Earth Day rallies our annual conference on biodiversity and endangered species is attended by them.

A vs C

Explanation

That's straightforward; C is passive.

Doubt 4:

Like Foucault, Derrida shows the power of discourse and language and attempts to deconstruct how meaning is made.

A. Like Foucault, Derrida shows
B. Like Foucault, Derrida is showing
C. As Foucault, Derrida shows
D. As did Foucault, Derrida’s showing
E. Derrida shows, as does Foucault,

A vs E

Explanation:
You're taking the rules too grammatically..
Read closely, it's the two nouns and not the actions being compared; E is quite awkward.
Example: Just like India, America believes in democracy; while 'believes' is a verb, you don't say "just as India, so does America..."
As is used when two actions/clauses are compared...
India adopted democracy in mid nineteenth century, just as America did long ago
But
India, like America, adopted democracy

Doubt 5

Like many successful authors, Salman Rushdie’s first novel, Grimus, about a Native American who receives the gift of immortality, was an abject failure.

A. Like many successful authors, Salman Rushdie’s first novel, Grimus, about
B. As have many successful authors, the first of Salman Rushdie’s novels, Grimus, about
C. Just as with many successful authors, the first of Salman Rushdie’s novels, Grimus, about
D. Just like many successful authors, Salman Rushdie’s first novel, Grimus, on
E. As did many successful authors, Salman Rushdie’s first novel, Grimus, on

Novel on or about

Explanation
The deal breaker is not 'on' or 'about'..both are okay; there are other reasons one lands with A as the best choice. Please approach this question again.


Doubt 6:

Of Mark Twain's many fans, none could feel more pleased—or more vindicated—by the renewed interest than the steadfast editors of the Mark Twain Project at the University of California at Berkeley, who have been at work for 36 years on a scholarly undertaking of almost inconceivable proportions: to hunt down, organize and every scrap of writing that issued from Sam Clemens during his 74 years on earth was interpreted.

A. to hunt down, organize and every scrap of writing that issued from Sam Clemens during his 74 years on earth was interpreted.
B. to hunt down, to organize and every scrap of writing that issued from Sam Clemens during his 74 years on earth was interpreted.
C. to hunt down, organize and interpret every scrap of writing that issued from Sam Clemens during his 74 years on earth.
D. to hunt down, organize and interpret every scrap of writing that issued from Sam Clemens while on earth 74 years.
E. to hunt down, organize and every scrap of writing that issued from Sam Clemens while on earth for 74 years.

Explanation
A and B: not parallel because of the awkward positioning of 'interpreted'
D and E are ugly in the use of 'while on earth'
C is parallel in "hunt down, organize, and interpret"
C is the best choice.

Doubt 7:

As he follows Keneely's Weather Channel team through Bonnie's path, writer David Laskin discovers that the Weather Channel's appeal lies in a particular mix of working professionally, live field reporting, and behind-the-scenes technical wizardry.

A. working professionally, live field reporting, and behind-the-scenes technical wizardry.
B. working professionally, dramatically live field reports, and behind-the-scenes technical wizardry.
C. professionalism, dramatically live field reports, and a wizard technically working from behind-the-scenes.
D. professionalism, reporting live from the field, and behind-the-scenes technical wizardry.
E. professionalism, live field reporting, and technical wizardry from behind-the-scenes.

Explanation:

A classic parallelism question.
Only E is parallel; you may have got confused because of 'ing' in 'reporting' but that's alright as 'reporting' is not a verb here; 'live field reporting' is a noun phrase here, conserving parallelism.

Some doubts from a Guidance Program student.
=========================================
The discoverer of the New World <who everybody called a foolhardy navigator was relatively unknown in both> the Old World and in the New World.

A) who everybody called a foolhardy navigator was relatively unknown in both

B) whom everybody called a foolhardy navigator was relatively unknown in both

C) who everybody called him a foolhardy navigator was relatively unknown in both

D) who everybody called a foolhardy navigator was relatively unknown both in

E) whom everybody called a foolhardy navigator was relatively unknown both in
When I ask the question Who? Answer comes out- the discoverer. Then why whom?
==> Who vs Whom... .In this case, you should always try to replace the word with a pronoun...him or he....e.g. “What did the entire world called him? A foolhardy navigator’..... if the answer is ‘him’, we use ‘whom’, if the answer is ‘his’, we use ‘whose’ etc....


=========================================
QuantumCAT- Q-27 Averages.
The average length of any four fingers of my left hand is 600 mm. Then the average length of all the five fingers of my left
hand is :?
Didn't understand the solution.
==> When will the average be the same for ANY four fingers? When all FIVE fingers are of the same length!So, the length of EVERY finger is x (quite weird, I must say!)
And 4x = 600*4. So x = 600. Average of all 5 = 600 mm.
The solution is incorrect.

=========================================
A rancher is constructing a fence by stringing wire between posts 20
feet apart. If the fence is 400 feet long, how many posts must the rancher use?

18
19
20
21
22

=>
A fence encloses an area of ground to mark a boundary i.e it's a circle!
--> This is an assumption on your part. It is not justified anywhere in the Q.

And IF it is a circle then number of posts used=400/20=20!
However, this question assumes a fence to be an straight line and
hence the answer 20+1=21
What is correct?
--> Yes. The straight line logic is correct. The Q only talks about a fence.

=========================================
Authorities in Switzerland are determined to alter the path of the River Rhone, <because the cost of the damage will be more than 500 million Swiss Francs and will take several years to absorb after the devastating floods.>

A) because the cost of the damage will be more than 500 million Swiss Francs and will take several years to absorb after the devastating floods.

B) whose devastating floods have caused more than 500 million Swiss Francs worth of damage, the cost of which will take several years for the Government to absorb.

C) which caused more than 500 million Swiss Francs of damage from the devastating floods which will take many years to absorb.

D) because several years and more than 500 million Swiss Francs will it take before the government can absorb the devastating damage from the floods.

E) which resulted in more than 500 million Swiss Francs in total cost for the devastating damage of the floods, which will take several years to absorb.


'Whose' can refer to River Rhone?

• Yes. Nothing wrong.

​

=========================================
Because the student <did not review the study material from cover to cover the night before, he seemed> unprepared during the class.

A) did not review the study material from cover to cover the night before, he seemed

B) had not reviewed the study material from cover to cover the night before, he seemed

C) had not reviewed the study material completely the night before, he seemed

D) had not reviewed the study material completely the night before, he seems

E) did not review the study material completely the night before, he seemed



Although the ear indicates that the adverb correctly refers verb 'reviewed', Please elucidate the placement of adverb, 'completely' near the noun 'material' in option C.

==> You are right...‘completely reviewed’ of ‘reviewed the complete material’ would have been more appropriate. But, nothing wrong with ‘reviewed the material completely’. Also, among the options, C is the best.
You will always find such ‘dubious’ correct answers, so use the elimination method!

=========================================

The letters of the word PROMISE have to be arranged so that no two vowels come together. Find the number of arrangements.
As per my understanding - total arrangement is 7!
and no 2 vowels come together 3C2 = 3 and this also can be done in 2 ways
thus total arrangement when 2 vowels come together are 6! * 2*3

hence 2 vowels are not together is 7! - 6.6! = 720

but it is giving answer 1440

Please correct me where I am wrong. --> Basically there are 6*6! = 4320 ways that have two Vs together. But wait! These also include ALL 3 Vs together, and such cases have been double counted. e.g. OIEPROM would be counted while considering OI and also considering IE. So we need to subtract all-3-Vs cases.

All 3 Vs together = 3 Vs as one unit + 4 other units = 5! * (3!) = 720.

So, the number of ways in which 3Vs are together is 4320-720 = 3600.

Now subtract that from 7! ==> 7! - 3600 = 1440.

Note: It is easier to go with the logic mentioned below.
================ We know that there are 4 Consonants and 3 Vowels. The constraint is that the Vs should not be together. So, lets first make sure that all the 4 Cs are sitting with at least one letter between them. The arrangement is something like the following...

_ C _ C _ C _ C _

Now, the 3 Vs can take any of the place and we will not violate the constraint. There are 5 empty slots and only 3 Vs, so that means there will be two empty slots, which we will ignore. (In that case, there will be 2 Cs adjacent to each other, but that does not matter.)

So, we have,

Alternative 1
4 Cs can sit in 4 spaces allocated for Cs = 4!
AND
3 Vs can sit in 5 possible places = 5C3
AND
among the 3 selected places, they can sit in 3! ways.
= 4! * 5C3 * 3! = 1440

Alternative 2
4 Cs can sit in 4 spaces allocated for Cs = 4!
AND

3 Vs can sit in 5 possible places with importance to order = 5P3
= 4! * 5P3 = 1440


================

Some interesting probability problems from Quantum Cat... Please download the file for images... (https://app.box.com/s/6gchm5otlvb5dyz5l0uil15njwy143re)
============================


42.
Four dice are thrown simultaneously. Find probability that two of them show the same face and remaining two show different faces.

There are four empty slots and we have to fill four numbers (1-6) in them. The Q asks us to find our probability such that two numbers are same, and the remaining two show different numbers.

Lets first fill the first blank. Remember that we can choose to fill any blank first, but for the same of simplicity, we will fill the first blank. We will return to this point later...

For the first blank, we can pick any number from 6 numbers. So the number of ways in which we can fill it up is 6C1.

Now lets pick the second number which is the same as the first number...so number of ways = 1.

The third and four numbers, have to be different than the number in first two slots. So, we have only 5 numbers now and we need two different numbers from 5...so the number of ways will be 5C2.

So far, we have filled all four slots. But we have picked the numbers from slot 1 to slot 4. We could have picked any order... To account for this, we have to rearranges these numbers... So now the problem is, there are four number, and rearrange them. That will be done in 4! Ways. But since two of these numbers are similar, we have to divide this number by 2!. This is the same logic as the MISSISSIPPI example. So, rearrangement can happen in 4!/2! ways.

So, for the needed scenario, total number of ways is 6C1 * 5C2 *4!/2! = 720.

The total sample space has 6*6*6*6 ways.
So required probability = 720/6^4 = 5/9.

43.

Four dice are thrown simultaneously. Find probability that at least two of them show the same face.

We will use similar logic as we did in the previous Q.
P (At least 2) = P(2 similar faces) + P(3 similar faces) + P(all similar faces).
P(2 similar faces) = this is the same problem as above. = 720/6^4.

P(3 similar faces) =>
N(favourable events) =
Pick first number from 6 numbers = 6C1
Pick the second number such that it is the same as the first number = 1
Pick the third number such that it is the same as the first two numbers = 1
Pick the fourth number from remaining 5 numbers = 5C1
Now again, to account for rearrangements, we will have to multiple all the above by 4!/3! ....4! because of rearrangement of 4 numbers and 3! because three numbers are same.
So, N(favourable events) = 6C1 * 5C1 * 4!/3! = 120

Sp, P(3 similar faces) = 120/6^4

P(4 similar faces) = This can happen when all four numbers are the same.. There are 6 such cases = 6/6^4.

Adding all these, required probability = (720+120+6)/6^4 = 47/72.


Q12 and 13.
.
This is really simple if you draw a table. The table represents the genders of the children...

Q12.

P(both boys, given that one is a boy).

In this case, we will only consider the sample space where ONE BOY is already known. There are THREE such cases. Out of those three, how many have BOTH BOYS? Only one.
So, required probability = 1/3

Q13.
P(both boys, given that older child is a boy).
So lets first truncate the sample space. In how many ways we know that the first child is a boy? TWO cases. Out of those two, in how many cases are both boys? Only one.

So, required probability = 1/2




Q18.
P(At least one red ball) = 1- P(No red ball)

P(No red ball) = P(Both balls are selected from 2 White and 4 Black balls) = (2+4)C2 / 9C2 = 6C2/9C2 = 5/12

P(At least one red ball) = 1- P(No red ball) = 1 – 5/12 = 7/12


Q21.
In the {1...9} set, there are 5 odd numbers and 4 even numbers.

This is conditional probability because we know that the sum is even. Under this circumstance, we have to find the P(both numbers are odd).

Lets first get P(even sum). This can happen when both numbers are even or both numbers are odd.
So, N(even sum) = 5C2 + 4C2 and N(sample space for even sum) = 9C2
So, P(even sum) = (5C2 + 4C2)/9C2 = 4/9

P(both numbers are odd, without any restriction on sum) = N(2 odd numbers from 5 odd numbers)/N(2 odd numbers from 9 numbers) = 5C2/9C2 = 5/18.

So,
P(both numbers are odd, when sum is even) = P(both numbers are odd, without any restriction on sum)/P(even sum)
P(both numbers are odd, when sum is even) = (5/18) / (4/9) = 5/8.





Q36.

The explanation on page 784 is good. Lets see a little more in detail.
So, when will the testing procedure end on the 12^th bulb...when the 12^th bulb is the last defective bulb? We know that there are two possibilities of defective bulbs. It could be either 2 defective bulbs or 3 defective bulbs. The individual probabilities are 0.4 and 0.6 as given.


So, P(the testing ends of 12^th bulb) = P(the testing ends of 12^th bulb, when there are 2 defective bulbs) + P(the testing ends of 12^th bulb, when there are 3 defective bulbs).

Lets look at the P(the testing ends of 12^th bulb, when there are 2 defective bulbs) case.

P(the testing ends of 12^th bulb, when there are 2 defective bulbs) =>
In this case, there are 18 good bulbs, and 2 defective bulbs.
Out of the first 11 bulbs, we got ten good bulbs and one defective bulb. The 12^th bulb was the second defective bulb.

Lets split the event into first 11 bulbs and the last bulb.

Part 1: Until the 11^th bulb
N (the testing ends of 12^th bulb, when there are 2 defective bulbs, until the 11^th bulb) = 18C10 (good bulbs) * 2C1 (first defective bulb)
N (Sample space the testing ends of 12^th bulb, when there are 2 defective bulbs, until the 11^th bulb) = 20C11.

Part 2: The 12^th bulb
N (the testing ends of 12^th bulb, when there are 2 defective bulbs, the 12^th bulb) = 1 (there is only defective bulb left)
N (Sample space the testing ends of 12^th bulb, when there are 2 defective bulbs, the 12^th bulb) = 9 (there are 9 more bulbs left).

So
P (the testing ends of 12^th bulb, when there are 2 defective bulbs) = P(Part 1) * P(Part 2)
N (the testing ends of 12^th bulb, when there are 2 defective bulbs = (18C10 * 2C1 / 20C11) * (1/9)



Now lets look at the P(the testing ends of 12^th bulb, when there are 3 defective bulbs) case.

P(the testing ends of 12^th bulb, when there are 3 defective bulbs) =>
In this case, there are 17 good bulbs, and 3 defective bulbs.
Out of the first 11 bulbs, we got 9 good bulbs and 2 defective bulbs. The 12^th bulb was the third defective bulb.

Lets split the event into first 11 bulbs and the last bulb.

Part 1: Until the 11^th bulb
N (the testing ends of 12^th bulb, when there are 3 defective bulbs, until the 11^th bulb) = 17C9 (good bulbs) * 3C2 (first two defective bulbs)
N (Sample space the testing ends of 12^th bulb, when there are 3 defective bulbs, until the 11^th bulb) = 20C11.

Part 2: The 12^th bulb
N (the testing ends of 12^th bulb, when there are 3 defective bulbs, the 12^th bulb) = 1 (there is only defective bulb left)
N (Sample space the testing ends of 12^th bulb, when there are 3 defective bulbs, the 12^th bulb) = 9 (there are 9 more bulbs left).

So
P (the testing ends of 12^th bulb, when there are 3 defective bulbs) = P(Part 1) * P(Part 2)
N (the testing ends of 12^th bulb, when there are 3 defective bulbs = (17C9 * 3C2 / 20C11) * (1/9)


Considering the individual probability of 0.4 and 0.6,
P (the testing ends of 12^th bulb) = 0.4 * P (the testing ends of 12^th bulb, when there are 2 defective bulbs) *
0.6 * P (the testing ends of 12^th bulb, when there are 3 defective bulbs).




Q7
Since the girls are sitting in a round circle, the absolute position of the seat does not matter. However, for the sake of simplicity, lets assign them numbers 1-19. Now, lets say that the first girl sits in a chair…lets say chair #7. In how many ways can the second girl sit such that there are 4 girls in between the two girls? The second girl can sit in chair #2 or chair # 12. So, out of the 19 empty chairs, she has 2 choices. The same scenario occurs no matter where the first girl sits.
So, we can say that, anywhere the first girl sits, the second girl can sit in 2 places of the 19 places, so satisfy the condition. So the required probability is 2/19.

============================

A CR - Conclusion question....

=============================
Fewer elected officials are supporting environment legislation this year than at any time in the last decade.In a study of thirty elected officials, only five were actively campaigning for new environment legislation.This comes at a time when the public's concern for the environment is growing by leaps and bounds.

Which of the following conclusions are supported by the passage above?

--> The passage really says that
- Fewer officials are concerns about environmental legislation when people are increasingly worried about the environment.

So, a conclusion would be something that tries to reconcile the two pieces of the argument.


a)More elected officials are needed to support environment legislation
--> This is a good option. However, 'more' is subjective...i.e. if seven officers out of thirty campaign for the environment, would it change the game? No. But lets keep this option until we get a better option.
b)elected officials have lost touch with the concerns of the public
--> This is out of the scope. Also, it does not connect the two pieces of the argument. It is too generic too.
c)the five elected officials who actively campaigned for new environment legislation, should be congratulated
--> This is out of the scope, again. The argument does not lead to this conclusion, which basically is an opinion unsupported in the argument.
d)If the environment is to be saved,elected officials must support environment legislation
--> This is out of the scope, again. The argument does not lead to this conclusion, which basically is an opinion unsupported in the argument.
e)If elected officials are truly to represent their constituents, many of them must increase their support of environment legislation

--> This is right on spot. This option connects to two pieces of the argument and tries to reconcile them. In fact, it is very similar to Option A but since Option A has a subjective 'more' in it, Option E comes out as a more direct option.

So the winner is Option E.
=============================

A doubt on comparison of countables vs uncountables....
================== Q) Even though the costs of paying baseball players amounts to a sum greater than one half of overall cost of operating a Major League Baseball team last year, Major League Baseball franchise owners were still willing to pay increasingly higher salaries to top players.

A. amounts to a sum greater
B. amounts to more
C. amounted to more
D. amounted to a greater sum
E. amounted to greater

--> Firstly, since the 'franchise owners were still willing to pay' is in past tense, we need past tense in the underline too. This rules out A and B. A and B also have 'costs ...amounts' which is subject verb agreement error.
C - 'more' is correct. So nothing wrong here.
D- 'greater sum than' is both incorrect and awkward.
E - 'greater' is incorrect.

So the correct answer would be E.
==================

An interesting debate on Adjectives vs Adverbs!
================================================== ============================
This refers to the chapter 6 page 82 of Manhattan regarding "Modifiers" . It has given examples of adjective and adverb .

1. Amy writes well
2. Amy is feeling well

According to the book both " well" are modifying the noun Amy and thus are Adjectives


but according to me the first sentence "well" modifies writing and in the second sentence well is modifying feeling . Since both are verbs ( writes and felling ) thus" well" in both the sentences are Adverbs and NOT Adjectives as mentioned in the book .
--> Interesting thought. Lets verify it.
Adverb = something that gives more information about the verb.

Our sentence is "Amy is feeling well."

Verb = "is feeling"

What role does 'well' play? Does it tell us anything about 'the manner in which the verb does the action' ? Now what do we mean by 'the manner in which the verb does the action' ... Lets look at the following..

She thinks quickly. (OR She thinks quick).

How does she 'think'? In what manner does she think? In what manner does the action of thinking takes place? In what manner does the action of this verb take place? ==> 'quickly' ==> then 'quickly' is the adverb. This is the logic that goes with "Amy write well."

But, in our sentence, " Amy is feeling well" , does 'well' relate to 'is feeling'? Can we say that 'the action of feeling takes place well'? No...well talks more of " feeling(Amy) = well" rather than 'feeling takes place in a manner called 'well''.

So 'well' is not an adverb here. It is just an object in the sentence and happens to be an adjective because it tells more about Amy.

=============
Also read the following from page 81.

Be sure not to use an adjective where an adverb is grammatically required, and vice versa. Note that
adjectives, not adverbs, follow linking verbs such as feel. These adjectives do not modify the verb but
rather identify a quality with the noun subject. All of the following examples are correct, although they
differ in meaning:

================================================== ============================

A query on Critical Reasoning - Strengthening the argument.
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A newly discovered disease is thought to be caused by a certain bacterium. However, recently released data notes that the bacterium thrives in the presence of a certain virus, implying that it is actually the virus that causes the new disease.

Which of the following pieces of evidence would most support the data’s implication?
(A) In the absence of the virus, the disease has been observed to follow infection by the bacterium.
(B) The virus has been shown to aid the growth of bacterium, a process which often leads to the onset of the disease.
(C) The virus alone has been observed in many cases of the disease.
(D) In cases where the disease does not develop, infection by the bacterium is usually preceded by infection by the virus.
(E) Onset of the disease usually follows infection by both the virus and the bacterium.

Student's Query: Could you please tell why the answer is (C) and not (D) or (B)? It's because (C) is not relating between virus and bacterium causing disease.
Solution:
Argument: It is believed that bacteria cases disease --> bacteria thrives in presence of virus --> virus, and not bacteria, is the root cause of the disease.
Missing link: What is the link between virus and disease? What about when there is virus and no bacteria? What about when there is bacteria and no virus?
Our expectation from the correct answer choice: To support the argument, we have to show that the virus causes the disease even when there is no bacteria.

A: In this case, the argument won't hold. Does not support.
B: Of little use because bacteria can still cause the disease. We are looking for a scenario where there is no bacteria.
C: Bang on. There is virus, but no bacteria, which confirms the above argument.
D: This only talks about relation between virus and bacteria. Does not tell that 'virus cases disease'.
E: Reverse of the argument. It says that the disease causes virus and bacteria.

Clearly, the answer is C.

In the student's logic, he anticipates a relation between virus and bacteria. That will not support the argument. To support the argument, we have to show the relation between 'virus alone' and 'disease'.

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A Sentence Correction Question
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Josiah saw <where the cost of doing business was escalating at an exceedingly alarming rate.>

A) where the cost of doing business was escalating at an exceedingly alarming rate

B) that the cost of doing business was increasing at a very rapid rate

C) where the cost of doing business was escalating at a very alarming rate

D) where the cost of doing business was increasing at a very rapid rate that

E) the cost of doing business was escalating at an exceedingly alarming rate

(B) 'Escalating at an exceedingly alarming rate' is a wordy cliché and should be abandoned. Similarly, 'where' should not be used for 'that.'

Question:
In the above question ‘Josiah saw where the cost .......' and 'Josiah saw that the cost ........' are two different meanings all together so how is it possible to change the meaning through options..???

--> The correct answer is B because it does not have any errors. It is clear that there should be a 'that' and not 'where' following 'Josiah saw'. This eliminates A,C,D. Between B and E, 'escalating' and 'exceedingly' are either repetitive or are saying that 'the increase was increasing'. So we remove E. B has no errors and hence is the best answer.

Regarding changing of meaning, yes, that is a good observation! Since there is no 'baseline' meaning because the original sentence may not be correct, we do not know which meaning to take! Then how do we proceed? We will go with an option that has 'no errors', simply. Generally, such a multiple-meaning situation will not arise and hence I regard this question as an outlier.
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