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# Good set of PS 2

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Math Expert
Joined: 02 Sep 2009
Posts: 58309
Re: Good set of PS 2  [#permalink]

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17 Mar 2013, 06:35
SravnaTestPrep wrote:
Dear Bunuel,

Consider this:

In how ways 3 scholars be selected from a pool of 10 scholars so that 2 are selected on merit.

Let us say one possible set of scholars is: A B C with A and B being selected on merit and C on other considerations. We have the same set which is : C B A but Now C and B being selected on merit and A on other considerations.

Don't you think the two groups are unique even though constituted by the same people?

"How many 3 member committees be formed from 6 people so that each has at least one man and one woman?"

Here "one man and one woman" is analogous to "merit" in the above example. The point is you are not going to select "one man and one woman" randomly. This is not an abstract problem and so the solution should be based on the practical facts. Since whether ordering is important or not for a particular problem is crucial to using the right formula we need to be right in making that decision.

The way one would think, the selection of a committee is done in the above case would be not by the roll of dice but by some practical considerations. So to first satisfy the essential requirement that I select a man and a woman I go by some practical considerations. The fact that I first select "A" over "B" says that I prefer "A" in some way over "B" or "A" is in some way more important than "B". So to me the selection AaB is different from the selection BaA since order, though not physical, is implied. It is like in the first case "A" is selected on merit and "B" on merit in the second case.

As I pointed out your solution of question #6 is not correct: according to the questions groups {AaB} and {BaA} are the same. The correct answer is 635 (E), not 2160.
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Math Expert
Joined: 02 Sep 2009
Posts: 58309
Re: Good set of PS 2  [#permalink]

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17 Mar 2013, 06:51
1
SravnaTestPrep wrote:
Dear Bunuel,

Consider this:

In how ways 3 scholars be selected from a pool of 10 scholars so that 2 are selected on merit.

Let us say one possible set of scholars is: A B C with A and B being selected on merit and C on other considerations. We have the same set which is : C B A but Now C and B being selected on merit and A on other considerations.

Don't you think the two groups are unique even though constituted by the same people?

"How many 3 member committees be formed from 6 people so that each has at least one man and one woman?"

Here "one man and one woman" is analogous to "merit" in the above example. The point is you are not going to select "one man and one woman" randomly. This is not an abstract problem and so the solution should be based on the practical facts. Since whether ordering is important or not for a particular problem is crucial to using the right formula we need to be right in making that decision.

The way one would think, the selection of a committee is done in the above case would be not by the roll of dice but by some practical considerations. So to first satisfy the essential requirement that I select a man and a woman I go by some practical considerations. The fact that I first select "A" over "B" says that I prefer "A" in some way over "B" or "A" is in some way more important than "B". So to me the selection AaB is different from the selection BaA since order, though not physical, is implied. It is like in the first case "A" is selected on merit and "B" on merit in the second case.

Another discussion of this question is here: a-committee-of-6-is-chosen-from-8-men-and-5-women-so-as-to-104859.html
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Math Expert
Joined: 02 Sep 2009
Posts: 58309
Re: Good set of PS 2  [#permalink]

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07 Apr 2018, 14:29
1. A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?
(A) 28
(B) 32
(C) 48
(D) 60
(E) 120

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-family-con ... 31430.html

2. What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?
(A) 271/900
(B) 27/100
(C) 7/25
(D) 1/9
(E) 1/10

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 88572.html

3. A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?
(A 10( sqrt3- 1)
(B) 5
(C) 10( sqrt2 - 1)
(D) 5( sqrt3 - 1)
(E) 5( sqrt2 - 1)

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-sphere-is- ... 27461.html

4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the project early. If the job was done in 100 days, how many days after day 60 had rain?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-contractor ... 26158.html

5. If s and t are positive integer such that s/t=64.12, which of the following could be the remainder when s is divided by t?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-s-and-t-a ... 35190.html

6. A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed if two of the men refuse to serve together?
(A) 3510
(B) 2620
(C) 1404
(D) 700
(E) 635

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-committee- ... 98238.html

7. If x is positive, which of the following could be the correct ordering of 1/x,2x and x^2 ?
I. x^2<2x<1/x
II. x^2<1/x<2x
III. 2x<x^2<1/x

(A) None
(B) I only
(C) III only
(D) I and II only
(E) I II and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-x-is-posi ... 71070.html

8. In the xy plane, Line k has a positive slope and x-intercept 4. If the area of the triangle formed by line k and the two axes is 12, What is the y-intercept of line K ?
(A) 3
(B) 6
(C) -3
(D) -6
(E) -4

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-xy-pl ... 00739.html

9. Of the applicants passes a certain test, 15 applied to both college X and Y. If 20 % of the applicants who applied college X and 25% of the applicants who applied college Y applied both college X and Y, how many applicants applied only college X or college Y?
(A) 135
(B) 120
(C) 115
(D) 105
(E) 90

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/of-the-appli ... 62891.html

10. What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
(A) 420
(B) 840
(C) 1260
(D) 2520
(E) 5040

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 38733.html
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Re: Good set of PS 2   [#permalink] 07 Apr 2018, 14:29

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