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17 Oct 2009, 07:52
Kudos
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Economist
Your answer as well as Asterixmatrix's are correct according to the wording of the question.
I just assumed it would be harder, since Bunuel posts tough questions haha. Let's see what the OA says.
17 Oct 2009, 09:42
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Heres are my answers:
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?
(B) 32 -
Total ways to seat them with one parent driving: 2 options for driver * 4 options for other seats = 2*4*3*2*1 = 48.
Assuming the 2 sisters do sit together, front seat we have 2 options for driver and 2 options for passenger (the other parent + son) = 4 ways.
Back seats: sisters sit together so either they sit in seats 1 and 2 or seats 2 and 3 = 2 ways. Also sisters themselves can sit in 2 ways so total = 2*2 = 4. So total ways sisters can sit together = 4*4 =16.
So ways they wont sit together = 48-16 = 32 ways.
2. What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?
(C) 7/25 - Total #'s between 100 and 999 inclusive = 9*10*10 = 900. # of numbers with no digit 7 = 8*9*9 = 648. So #'s with a 7 = 1 - 648/900 = 252/900 = 7/25.
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?
(D) 5( sqrt3 - 1) - Length of the diagonal of cube = ((10^2+10^2) + 10^2)^(1/2) = 10 sqrt3. Diagonal includes diameter of circle (10) + 2*length from vertex to sphere.
Length of vertex to sphere = (10*sqrt3- 10)/2 = 5( sqrt3 - 1)
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?
(C) 6 - rains for 5 days from day 56-60. So 10 guys worked for 55 days and accomplished half of the work. If 6 more guys are added to the job then the rate is 16/1100. (since one man's rate is 1/1100). Half the job left means 550/1100 is left. Therefore 550/16 = 34.375 days of more work. Since there were 40 days between day 60 and job completion, it must've rained for 40-34.375 = 5.625 or ~6 days. (I'm not sure if this is correct)
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?
(E) 45 - 64.12 = 6412/100 or 1603/25. 1603/25 gives a remainder of 3, 3206/50 gives remainder of 6 and so on ..pattern = factors of 3. so to get remainder of 45, we multiply everything by 15: 1603*15/(25*15) = 24045/375.
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?
(E) 635 - 2 options: 2 men and 4 women -(i), or 3 men and 3 women -(ii).
Starting with women: for (i): 5C4=5 and for (ii): 5C3 = 10.
Men for (i): 2 further options if 2 men - a) neither of the problematic men chosen = 6C2 = 15 or b) one of them is chose - 2C1*6C1 = 12 so 12+15= 27 ways if (i)
(ii): same 2 options - 6C3 + 2C1*6C2 = 20 + 30 = 50.
Combining men and women - (i): 5*27 = 135 and (ii): 10*50 = 500 so total ways = 635.
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
(D) I and II only - if x = 1/3, then I is correct, if x = 4/5, then II is correct. I couldnt find a way to get III to work.
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 ?
(D) -6 - Area of bxh of triangle = 24. Given base is 4, and drawing the line, easy to see that y intercept has to be -6.
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?
(D) 105 - Let x be # who applied to only X and y who applied to only Y. Then 0.2(x+15) = 15 and 0.25(y+15) = 15. So x = 60 and y = 45 so x+y = 105.
10. What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
(A) 420 - 420 is divisible by all #'s from 1 thru 7.
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?
(B) 32 -
Total ways to seat them with one parent driving: 2 options for driver * 4 options for other seats = 2*4*3*2*1 = 48.
Assuming the 2 sisters do sit together, front seat we have 2 options for driver and 2 options for passenger (the other parent + son) = 4 ways.
Back seats: sisters sit together so either they sit in seats 1 and 2 or seats 2 and 3 = 2 ways. Also sisters themselves can sit in 2 ways so total = 2*2 = 4. So total ways sisters can sit together = 4*4 =16.
So ways they wont sit together = 48-16 = 32 ways.
2. What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?
(C) 7/25 - Total #'s between 100 and 999 inclusive = 9*10*10 = 900. # of numbers with no digit 7 = 8*9*9 = 648. So #'s with a 7 = 1 - 648/900 = 252/900 = 7/25.
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?
(D) 5( sqrt3 - 1) - Length of the diagonal of cube = ((10^2+10^2) + 10^2)^(1/2) = 10 sqrt3. Diagonal includes diameter of circle (10) + 2*length from vertex to sphere.
Length of vertex to sphere = (10*sqrt3- 10)/2 = 5( sqrt3 - 1)
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?
(C) 6 - rains for 5 days from day 56-60. So 10 guys worked for 55 days and accomplished half of the work. If 6 more guys are added to the job then the rate is 16/1100. (since one man's rate is 1/1100). Half the job left means 550/1100 is left. Therefore 550/16 = 34.375 days of more work. Since there were 40 days between day 60 and job completion, it must've rained for 40-34.375 = 5.625 or ~6 days. (I'm not sure if this is correct)
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?
(E) 45 - 64.12 = 6412/100 or 1603/25. 1603/25 gives a remainder of 3, 3206/50 gives remainder of 6 and so on ..pattern = factors of 3. so to get remainder of 45, we multiply everything by 15: 1603*15/(25*15) = 24045/375.
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?
(E) 635 - 2 options: 2 men and 4 women -(i), or 3 men and 3 women -(ii).
Starting with women: for (i): 5C4=5 and for (ii): 5C3 = 10.
Men for (i): 2 further options if 2 men - a) neither of the problematic men chosen = 6C2 = 15 or b) one of them is chose - 2C1*6C1 = 12 so 12+15= 27 ways if (i)
(ii): same 2 options - 6C3 + 2C1*6C2 = 20 + 30 = 50.
Combining men and women - (i): 5*27 = 135 and (ii): 10*50 = 500 so total ways = 635.
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
(D) I and II only - if x = 1/3, then I is correct, if x = 4/5, then II is correct. I couldnt find a way to get III to work.
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 ?
(D) -6 - Area of bxh of triangle = 24. Given base is 4, and drawing the line, easy to see that y intercept has to be -6.
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?
(D) 105 - Let x be # who applied to only X and y who applied to only Y. Then 0.2(x+15) = 15 and 0.25(y+15) = 15. So x = 60 and y = 45 so x+y = 105.
10. What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
(A) 420 - 420 is divisible by all #'s from 1 thru 7.
17 Oct 2009, 20:02
Kudos
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Bunuel
In the second case, we have 1 P in the front seat, so the other can be occupied by the Son, no one else...so we have 2 ways to arrange people in front seats, and 2 ways to arrange backseaters ( with 2 daughters on window seats )...so total there are 2*2 ways...hence I think ans should be 28 and not 32.
