QR questions

[sfoksn]

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I had few questions on how to solve some QR questions, it would be much appreciated if anybody can lighten the way for me!

The expression [1/5 - 1/x]/[5/x - 1] is equivalent to:

a. -5
b. 5
c. -1/5
d. 1/5
e. x/5

For this question, I just fiddled around with the numbers and found out that i would get negative number, and just guessed out of the negative ones... Is there a tactic to simplify a fraction like this?

A recent survey determined that 2/5 of practicing dentists use a water-pik on their own teeth. If 10 dentists are chosen at random, which expression represents the probability that exactly three of them use a water-pik on their own teeth?

a. C(5,2)(2/5)^7(3/5)^3
b. C(10,2)(2/5)^7(3/5)^3
c. C(10,3)(2/5)^3(3/5)^7
d. C(10,3)(2/5)^7(3/5)^3
e. C(7,2)(2/5)^7(3/5)^3

For this question, I was not sure what the function of C's were..


Thanks in advance!

 

[joonkimdds]

I used to know easy ways to solve these problems but it's been almost 7 months since I took DAT. All i can do for you here is solve the 1st question the way that I can do currently.


(1/5 - 1/x) / (5/x -1)
(x-5 / 5x) / (5-x / x)
(x-5)x / 5x (5-x)
x(x-5) / -5x(x-5)
answer = - 1/5

 

[UCB05]

I had few questions on how to solve some QR questions, it would be much appreciated if anybody can lighten the way for me!

The expression [1/5 - 1/x]/[5/x - 1] is equivalent to:

a. -5
b. 5
c. -1/5
d. 1/5
e. x/5

For this question, I just fiddled around with the numbers and found out that i would get negative number, and just guessed out of the negative ones... Is there a tactic to simplify a fraction like this?

A recent survey determined that 2/5 of practicing dentists use a water-pik on their own teeth. If 10 dentists are chosen at random, which expression represents the probability that exactly three of them use a water-pik on their own teeth?

a. C(5,2)(2/5)^7(3/5)^3
b. C(10,2)(2/5)^7(3/5)^3
c. C(10,3)(2/5)^3(3/5)^7
d. C(10,3)(2/5)^7(3/5)^3
e. C(7,2)(2/5)^7(3/5)^3

For this question, I was not sure what the function of C's were..


Thanks in advance!

c. C(10,3)(2/5)^3(3/5)^7
A question of x out of y times is represented by factors representing:

C(y,x): the number of ways you can get the desired outcome, in this case, 3 out of 10 dentists. It could be the 1st, 2nd, 3rd interviewed, 2nd, 6th, 8th interviewed, 1st, 7th, 10th interviewed, etc. C(10,3) takes all those combinations into account

(P)^x: the number of times you want the favorable outcome to occur, factored into the likelihood of it happening, in this case a 2/5 chance occuring 3 times represented as (2/5)^3

(Q)^y: the number of times you want the unfavorable outcome to occur, factored into the likelihood of it happening, in this case a 3/5 chance occuring 7 times as (3/5)^7

The answer is easy to spot in this case as c) is the only one that has the (2/5)^3 term.


This is the same type of question as a coin flip landing heads exactly 3/10 times, except that people reduce the true equation:
C(10,3)(1/2)^3(1/2)^7 to C(10,3)(1/2)^10 because the probability of heads and tails are the same.

 

[sfoksn]

thank you UCB and joonkimdds! that makes a lot of sense!
\

 

[jay47]

I had few questions on how to solve some QR questions, it would be much appreciated if anybody can lighten the way for me!

The expression [1/5 - 1/x]/[5/x - 1] is equivalent to:

a. -5
b. 5
c. -1/5
d. 1/5
e. x/5

For this question, I just fiddled around with the numbers and found out that i would get negative number, and just guessed out of the negative ones... Is there a tactic to simplify a fraction like this?

I found the easiest way to do the first question is to pick a number and do it. For example:

Just pick 1 and plug it in and see what you get-

[1/5 - 1/x]/[5/x - 1]

[1/5 - 1/1]/[5/1 - 1]

[-4/5]/[4]

[-4/5] * [1/4]

-4/20

-1/5

You can probably do it in your head (with practice) in a matter of about 30 seconds. Much easier than doing any algebra....I couldn't even follow what the Joon did, although it was obviously correct.

 

[Streetwolf]

I found the easiest way to do the first question is to pick a number and do it. For example:

Just pick 1 and plug it in and see what you get-

[1/5 - 1/x]/[5/x - 1]

[1/5 - 1/1]/[5/1 - 1]

[-4/5]/[4]

[-4/5] * [1/4]

-4/20

-1/5

You can probably do it in your head (with practice) in a matter of about 30 seconds. Much easier than doing any algebra....I couldn't even follow what the Joon did, although it was obviously correct.

Bad idea. If the answer was -(1/5)x and you plugged in 1, you'd choose the answer (-1/5). If you chose 2, you'd choose the answer (-2/5), etc.

Joon's way was 100% spot on. He just left out the step where you find the LCD and add the fractions.