A very cheap algebra data sufficinecy word problem, disguised as critical thinking problem.
Answer should not take more than a minute to reveal itself:- BY THE WAY THE CORRECT ANSWER IS C
THINGS YOU SHOULD KNOW BEFORE SOLVING THIS QUESTION:-
LESS LIKELY MEANS PROBABILITY IS 49% OR LESS THAN 49%
EQUALLY LIKELY MEANS PROBABILITY IS 50%-50%
MORE LIKELY MEANS PROBABILITY IS 51% OR MORE THAN 51 %
To start in a fair an unbiased manner :-
Assume there are 1000 parents.
500 parents have Phd. 500 DO NOT have PhD (Do not skew this ratio. Even though any ratio would give you the correct answer, you must solve these kind of question by assuming both sides are equal A=B and then you will not have to test other two cases A<B or A>B. After seeing the solution , try to solve this problem with any ratio you want and you will still get the right answer)
NOW STARTS THE REAL QUESTION (ALGEBRA + PROBABILITY)
WE WILL SOLVE ALGEBRA FIRST AND THEN MOVE TO PROBABILITY.
A) All other factors being equal, children whose parents earned doctorates are
more likely to earn a doctorate than children whose parents did not earn doctorates.
Parents with PHD = 500
More likely = 51 %
Children having PHD = 51 % of 500 = 255 PHD
B) Over 70 percent of
all doctorate holders do not have a parent that also holds a doctorate.
Keep the term all doctorate in mind .
ALL doctorate means = (all kids= all whose parents have phd = 255)AND(kids whose parents have no phd=x)
The percentage of kids whose parents don't have phd is not given to us in the question stem. but we can easily find it
The percentage of phd kids whose parents don't have phd is x % of 500 (remember 500 parents don't have phd)= x% of 500 = (x/100)of 500 = 5x
now you know
Over 70 percent of
all doctorate holders do not have a parent that also holds a doctorate.
70 % (255 +5x)=do not have parent that also holds a doctorate.
or
70 % (255 +5x)=non phd parent (how many non phd parents are there = 500 non phd parents)
70 % (255 +5x)=500
70/100 (255 +5x)=500
7/10 (255 +5x)=500
7 (255 +5x)=
500*10 (we took 10 to the right)
7(255 +5x)=5000
1785+35x=5000
35x=5000-1785
35x=3215
x=3215/35
x=92
There are 92 kids who have phd but whose parents don't have phd.
NOW COMES THE PROBABILITY PART :-
92 KIDS HAVE PHD BUT THIER 500 PARENTS HAVE NO PHD
PROBABILITY OF KID HAVING PHD BUT PARENTS HAVING NO PHD = 92/500 = 18.4 %
255 KIDS HAVE PHD AND THIER 500 PARENTS HAVE PHD (We derived this as the very beginning of the question. remember the more likely to have phd clause.)
PROBABILITY OF KID HAVING PHD AND PARENTS HAVING PHD = 255/500 = 51%
This is what Hart said in her argument but in a different way.
Which of the following is the most accurate evaluation of Hart's reply?
(C) It is consistent with Choi's claim.
Choi: All other factors being equal, children whose parents earned doctorates are more likely to earn a doctorate than children whose parents did not earn doctorates.
Hart: But consider this: Over 70 percent of all doctorate holders do not have a parent that also holds a doctorate.
Which of the following is the most accurate evaluation of Hart's reply?
(A) It establishes that Choi's claim is an exaggeration.
(B) If true, it effectively demonstrates that Choi's claim cannot be accurate.
(C) It is consistent with Choi's claim.
(D) It provides alternative reasons for accepting Choi's claim.
(E) It mistakes what is necessary for an event with what is sufficient to determine that the event will occur.
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FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.