1. Joshua and Jose work at an auto repair center with 4 other workers. For a survey on healthcare insurance, 2 of the 6 workers are randomly chosen to beinterviewed. What is the probability that Joshua and Jose will be chosen? A.1/15 B.1/12 C.1/9 D.1/6 E.1/3
2. The sum of first 50 positive even integers is 2550. What is the sum of even intergers from 102 to 200 inclusive? A.5100 B.7550 C.10100 D.15500 E.20100
3. Is the hundredth digit of decimal d greater than 7? i. The tenths digit of 10d is 7 ii. The thousandths digit of d/10 is 7
Q. At a dinner party 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is total number of possible seating arrangements for the group?
No. of ways of arranging n people in a circular arrangement is given by (n-1)!
In this case, no. of ways of arranging 5 people in a circle = 4! = 24.
Plz correct me if I'm wrong!
Please help with the following problem:
Q. At a dinner party 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is total number of possible seating arrangements for the group?
Q. In an office, 40 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
Q. In an office, 40 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
(A) 48 (B) 64 (C) 50 (D) 144 (E) 160
OA is A. Donno how can that be?
Regards MSD
I think OA is correct
Total workers = x
10% x= 16 so x=160
atleast 5 year exp means >= 5yr exp
so 40% includes that 16 people who have atleast 10 yr exp
so to get no: of workers between 5 & 10 yr exp 40%x - 16= 48
Q. If the perimeter of a square region S and a circular region C is equal then the ratio of the area of S to that of C is closest to
A.3/2 B.4/3 C.3/4 D.2/3 E.1/2
Regards MSD
Let perimtr of circle C=2*pi => radius of this circle=1 unit primetr of sq S=C=2*pi side of sq=2*pi/4=1.57 (appx.) area of sq=1.57^2=2.45 (appx.)----(1) area of circle=pi*1^2=3.14(appx.)----(2) ratio=2.45/3.14 which is option A and B r ruld out....as they r >1 option E is ruled out as 1/2 of 3.14 has to b arnd 1.57 option D can't be bcoz (2+0.45)/(3+0.14) which means numr has increased in greater proportion as compared to denominator...(0.45/2 is more than 0.14/3) and hence the ratio can't remain 2/3
x is a factor of y and y is a factor of z.. Hence we have..
x * n = y -> (I) y * k = z -> (II) => x*nk = z -> (III)
xz is even. Take III above. Multiply both sides by x.
x^2 * nk = xz. For xz to be even, either x^2 has to be even or n*k has to be even. X^2 won't be even if x is odd. Hence, n*k has to be even always. If n*k is even always, using that in III above, z has to be even always.
y is even This is simpler. Using 'y is even' in II above, we immediately know that z has to be even (doesnt matter what k is).
I am not sure if I am missing something here, but this seems relatively straightforward.
A) gives u a formula with two unknowns and asks u to solve. B) too gives u two unknowns and asks u to solve.
If u substitute X(l) as X(5) and X(l-1) as X(4) in the first statement, u would have 2 unknowns and 2 equations to solve them. Once u get X(5) and X(4), X(1) is easy to get.
Hence, C is the answer -> Both statements are needed.
x is a factor of y and y is a factor of z.. Hence we have..
x * n = y -> (I) y * k = z -> (II) => x*nk = z -> (III)
xz is even. Take III above. Multiply both sides by x.
x^2 * nk = xz. For xz to be even, either x^2 has to be even or n*k has to be even. X^2 won't be even if x is odd. Hence, n*k has to be even always. If n*k is even always, using that in III above, z has to be even always.
y is even This is simpler. Using 'y is even' in II above, we immediately know that z has to be even (doesnt matter what k is).
Hence, each statement alone is sufficient.
Could u pls explain hw u conclude that x is odd.......
Could u pls explain hw u conclude that x is odd.......
No, I didnt conclude that x is odd. That mechanism was needed to prove that xz can be 'even' even when x is odd. If x was even, you could have used that directly in (III) to determine that z was even. (III) didnt give us the answer only when x was odd. Hence, in this situation, we needded another way to prove it.
x is a factor of y and y is a factor of z.. Hence we have..
x * n = y -> (I) y * k = z -> (II) => x*nk = z -> (III)
xz is even. Take III above. Multiply both sides by x.
x^2 * nk = xz. For xz to be even, either x^2 has to be even or n*k has to be even. X^2 won't be even if x is odd. Hence, n*k has to be even always. If n*k is even always, using that in III above, z has to be even always.
Hence, each statement alone is sufficient.
ashishjha100 Says
Could u pls explain hw u conclude that x is odd.......
hi ashish...vikram has already explained..extension of vikram's approach:
It is given that xz is even, hence there are 3 possibilities: 1) x is odd and z is even OR 2) x is even and z is odd OR 3) x is even and z is even
with given data, 2nd possibility not possible..
Now, if x is even, z automatically turns to be even and if x is odd then also z has to be even for xz to be even..
Please help with the following DS questions from Gmat Prep:
Q.I In a xy-plane, does the line with equation y=3x+2 contain the point (r,s)? 1. (3r+2-s) (4r+9-s) = 0 2. (4r-6-s) (3r+2-s) = 0
Q.II A manufacturer conducted a survey to determine how many people buy products P & Q. What fraction of people surveyed said that they buy neither product P nor product Q? 1. 1/3 of the people surveyed said that they buy product P but not Product Q 2. 1/2 of the people survey said that they buy product Q
Q.III During a 80 mile trip Marla travelled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x miles per hour for the last 40-y miles of the trip. The time that Marla too to travel the 40 miles was what percent of the time it would have taken her if she had traveled at an average speed of x miles per hour for the entire trip? 1. x = 48 2. y = 20
