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Videoorchard
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FDP Smart Numbers!

by Videoorchard Thu Jan 22, 2015 12:54 pm

Hello,


My question is regarding making use of the smart numbers (i.e 100) especially in the questions like the below .

Question Detail:
From the previous chapter in Manhattan, the author asserts to make use of smart numbers only when the question doesn't explicitly specify real numbers/quantity's such as 200,300 etc. Okay, sounds great? Lets look at the problem below.


Question:
According to a survey, 3/5 of students at university X eat lunch at dining hall, while only 1/6 of the university's faculty members eat lunch at the dinning hall.

Qty A:
No of students and faculty members who eat lunch at the uni dinning hall.

Qty B:
No of students and faculty members who donot eat lunch at the uni dinning hall.


My Approach:
I made of the smart number i.e 100 for this question and i ended up with the answer i.e qty B.

Why can't we make use of smart numbers for the problem such as above?

Question Source:
FDP Strategy guide pg.146

Thanx! :)
n00bpron00bpron00b
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Re: FDP Smart Numbers!

by n00bpron00bpron00b Thu Jan 22, 2015 9:32 pm

The question says -

a) 3/5 of students at university X eat lunch @ dining hall

b) 1/6 of university faculty eat lunch @ dining hall

Unknown : the number of students and number of faculty (we are more concerned about the individual split rather than the total)

may be you could work backwards - select any value for total no. of students such that 3/5 * (value selected for total students) = integer (since we are dealing with people ; non integer results are not acceptable) and any value for total no. of faculty such that 1/6 * (value selected for total faculty) = integer.

Case 1:

Lets assume - students = 150 and faculty = 150 (total 300)
3/5 of students eat lunch at dining hall = 3/5 x 150 = 90
1/6 of faculty eat lunch at dining hall = 1/6 x 150 = 25

Col A : Faculty + students who eat at dining hall = 90+25 = 115
Col B : Faculty + students who do not eat @ dining hall = 300- 115 = 185

Col B greater

Since it is a QC problem and we are assuming values ; check for case where the answer might differ (to prove "D")

Case 2 :

Assume, Students = 780 ; faculty = 120 (total : 900)
students who dine at hall = 3/5*780 = 468
faculty who dine at hall = 1/6 * 120 = 20

Col A : 488
Col B : 900 - 488 = 412

Col A is greater

Hence "D"
Videoorchard
Prospective Students
 
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Re: FDP Smart Numbers!

by Videoorchard Sat Jan 24, 2015 5:14 am

Hi Noob,

Great explanation as always! Thanx! :)

So, just to summarize on what i construed, the best way to tackle QC problems is to actually try out different scenario's such as:

case 1: No of students: 200, No of Faculty: 120 (Student > Faculty)

Case 2: No of students: 50, No of Faculty: 180 (Student < Faculty)

For general (Non-QC) questions, just solely picking smart numbers such as 100, should work fine. You probably wouldn't need to do anything "case test" as above!

Feel free to correct me if you think otherwise! :)

Thanx again!
n00bpron00bpron00b
Students
 
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Re: FDP Smart Numbers!

by n00bpron00bpron00b Sat Jan 24, 2015 5:06 pm

#) It is not just simply making one quantity greater than other and the other way around, make sure you do that while keeping these in mind. a) the values that you select should satisfy the given condition in the problem. b) when you plug those values in the given condition they should generate different set of outputs. (this applies to all types of problems)

#) To prove "D" is just one of the several strategies to solve QC problems. It really depends on the nature of a problem ; since you can use multiple approaches to derive the result. In several cases picking smart values might not be the ideal way to go.

#) I would not recommend hard wiring "method to pick smart numbers", yes you could definitely start with very easy values such as 0,100,1,10,0.5 (and narrow down your answer choices by the process of elimination). The only way to develop the intuition is to use those strategies and solve lots of problems and try to recognize patterns.

For general (Non-QC) questions, just solely picking smart numbers such as 100, should work fine. You probably wouldn't need to do anything "case test" as above!


For basic problems picking 100 is kind off safe. Further down the road you will come across a type called Variable in Choice where the above method of picking safe values such as "100" sometimes fails ; the case-test thing comes into play here ; but there are slightly modified strategies to deal with it.

case 1: No of students: 200, No of Faculty: 120 (Student > Faculty)


For Col A :
-> students who dine = 3/5 x 200 = 120
-> professors who dine = 1/6 x 120 = 20
Total : 140

Col B : total students + professors who do not dine = 80 + 100 = 180

Col B greater

Case 2: No of students: 50, No of Faculty: 180 (Student < Faculty)


-> students who dine = 3/5 x 50 = 30
-> professors who dine = 1/6 x 180 = 30

Col A : total students + professors who dine = 60
Col B : total students + professors who do not dine = 20 + 150 = 170

Again Col B greater

See the whole purpose of proving contradicting answer gets invalidated. And somethings this is the major flaw of picking values for QC ; given the time constraint it becomes difficult to capture the right set of values to prove "D".
tommywallach
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Re: FDP Smart Numbers!

by tommywallach Sat Jan 24, 2015 7:13 pm

Amazing responses from Noob as always. Just to wrap it up.

1) On QC, you pick numbers with the goal of proving D. I often use the acronym FONZE to help choose what kind of numbers to pick (Fractions, One, Negatives, Zero, Extremes).

2) On FDP questions with no values given, pick Smart numbers. Often that number will be 100 (particularly on percents based question), but just as often it's not 100. For example, in a question that mentions sixths and fifths, you might pick 30.

3) On VIC questions (Variables in Answer choices), you always pick a number that makes life easy but not too easy. You never pick 0 or 1, and even 100 is often problematic (for fairly complex reasons).

So those are the three times you use plugging in on the GRE. What fun!

-t