which of the following lists the number of point at which a circle can intersect a triangle
A?) 1
B) 1,2
C) 2, 4, 6
D) 1,2,3,4,5 & 6
C) 2, 4, 6
Took me one whole minute to understand the problem 
which of the following lists the number of point at which a circle can intersect a triangle
A?) 1
B) 1,2
C) 2, 4, 6
D) 1,2,3,4,5 & 6
In a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
a. 19
b. 10
c. 9
d. 8
e. 7
A group of 8 friends want to play a trivia game. How many different ways can the friends be divided into 4 teams of 2 people?
OA is 105
Post the approach pls!!
which of the following lists the number of point at which a circle can intersect a triangle
A?) 1
B) 1,2
C) 2, 4, 6
D) 1,2,3,4,5 & 6
My take is D
Is intersecting a triangle same as touching one of its vertices??
I am confused.
rohitforever SaysMy take is D
In a group of 68 students, each student is registered for at least one of three classes History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
a. 19
b. 10
c. 9
d. 8
e. 7
My take is A
Is intersecting a triangle same as touching one of its vertices??
I am confused.
Yes touching counts in intersection
ahh.. I see. then u r right. D should be the ans.
Re-Confirmed your point here:
Circle-Line Intersection -- from Wolfram MathWorld
rohitforever SaysYes touching counts in intersection
b=10 should be the answer.
This one is simple... If anyone needs explanation,please let me know.
This one is simple... If anyone needs explanation,please let me know.
In a group of 68 students, each student is registered for at least one of three classes History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
a. 19
b. 10
c. 9
d. 8
e. 7
I will try to explain:
We have to SELECT 4 groups each having 2 members.
So the first two member can be chosen in 8C2 ways.
The second 2 member team can be chosen in 6C2 ways.
Similarly last two teams : 4C2 and 2C2 ways
Therefore total number of ways in which
4 teams can be chosen= 8C2*6C2*4C2*2C2.
Now we dont care the order in which teams are chosen,therefore we must divide the total number of ways by the number of ways in which teams can be ordered (i.e. 4!=24).
Hence the answer is
8C2*6C2*4C2*2C2/4! = 28*15*6*1/24 = 7*15 = 105
We have to SELECT 4 groups each having 2 members.
So the first two member can be chosen in 8C2 ways.
The second 2 member team can be chosen in 6C2 ways.
Similarly last two teams : 4C2 and 2C2 ways
Therefore total number of ways in which
4 teams can be chosen= 8C2*6C2*4C2*2C2.
Now we dont care the order in which teams are chosen,therefore we must divide the total number of ways by the number of ways in which teams can be ordered (i.e. 4!=24).
Hence the answer is
8C2*6C2*4C2*2C2/4! = 28*15*6*1/24 = 7*15 = 105
A group of 8 friends want to play a trivia game. How many different ways can the friends be divided into 4 teams of 2 people?
OA is 105
Post the approach pls!!
A four-sided die is rolled 4 times. What is the probability of getting a 4 at least twice.
A.17/256
B.67/256
C.4/5
D.12/64
E.17/256
IMO B 67/256
Using combinatorics:
Total possible outcomes are 4*4*4*4= 256
Total possible outcomes of getting one 4 = (1*3*3*3)*4 = 168
Total possible outcomes of getting NO 4 = 3*3*3*3 = 81
Total possible outcomes of getting one 4 OR NO 4 = 168 + 81 = 189
Therefore total possible outcomes of getting atleast two times 4 = 256 - 189=67
Probablity = 67/256
QUOTE=pj02;1632030]A four-sided die is rolled 4 times. What is the probability of getting a 4 at least twice.
A.17/256
B.67/256
C.4/5
D.12/64
E.17/256
Hello ,
I had a question set to which I could not find answers. I am posting here. I am new to the group so pardon me if this creates trouble.
Q1
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the
3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride
the roller coaster 3 times, what is the probability that the passenger will ride in each of
the 3 cars?
A. 0
B. 1/9
C. 2/9
D. 1/3
E. 1
Q2:
Running at their respective constant rates, machine X takes 2 days longer to produce w
widgets than machine Y. At these rates, if the two machines together produce 5/4 w
widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
A. 4
B. 6
C. 8
D. 10
E. 12
Answer:
Q3:
June 25, 1982, fell on a Friday. On which day of the week did June 25, 1987, fall? (Note:
1984 was a leap year.)
A. Sunday
B. Monday
C. Tuesday
D. Wednesday
E. Thursday
Q4:
What is the median number of employees assigned per project for the projects at
Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to
each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to
each project.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Can someone solve and explain the answers to me ?
Thanks
Pranam
Jeff Smith cannot completely remember his four-digit ATM pin number.He only remembers the first two digits, and he knows that each of the last two digits is less than 3.
The ATM machine will allow him 3 tries before Ace is blocked for further access to his account. If he randomly guesses the last two digits each time, what is the probability that he will get access to his account?
Dont have answer options.
Jeff Smith cannot completely remember his four-digit ATM pin number.He only remembers the first two digits, and he knows that each of the last two digits is less than 3.
The ATM machine will allow him 3 tries before Ace is blocked for further access to his account. If he randomly guesses the last two digits each time, what is the probability that he will get access to his account?
Dont have answer options.
I am skeptical on my answer, but here goes my approach. Please YELL if it is wrong!
Since the last two digits are less than 3 each one of them could be {0,1,2}
So total possibilities are: 00,01,02 10,11,12 20,21,22 - overall 9
Out of these one combination is the correct one.
Jeff's attempts:
Probability of Jeff getting it right the first time: 1/9
Probability of Jeff failing first time followed by success second time: 8/9 * 1/9
Probability of Jeff failing first and second times and successful on 3rd: 8/9 * 8/9 * 1/9
Overall probability: 1/9 + 8/81 + 64/729 = 217/729
C) 2, 4, 6
Took me one whole minute to understand the problem
Yes Answer is indeed D, I also marked 2, 4, 6 as i thought intersection doesn't mean touching
Hello ,
I had a question set to which I could not find answers. I am posting here. I am new to the group so pardon me if this creates trouble.
Q1
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the
3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride
the roller coaster 3 times, what is the probability that the passenger will ride in each of
the 3 cars?
A. 0
B. 1/9
C. 2/9
D. 1/3
E. 1
Q2:
Running at their respective constant rates, machine X takes 2 days longer to produce w
widgets than machine Y. At these rates, if the two machines together produce 5/4 w
widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
A. 4
B. 6
C. 8
D. 10
E. 12
Answer:
Q3:
June 25, 1982, fell on a Friday. On which day of the week did June 25, 1987, fall? (Note:
1984 was a leap year.)
A. Sunday
B. Monday
C. Tuesday
D. Wednesday
E. Thursday
Can someone solve and explain the answers to me ?
Thanks
Pranam
Q1:
probability of getting into first car: could be any, so = 1
probability of getting into second car: 2/3
probability of getting into third car: 1/3
Overall probability 1 * 2/3 * 1/3 = 2/9
Q2:
Rate of X + Rate of Y = Rate of (X+Y)
w/(y+2) + w/y = (5/4w) / 3
solve for y, you get, y = 4
=> x = 6
So for w, x takes 6, for 2w, X takes 12.
Q3:
82 - Friday
83 - Saturday
84 - Monday (Add an extra, due to leap year)
85 - Tuesday
86 - Wed
So, 87 - Thursday
Q4:
What is the median number of employees assigned per project for the projects at
Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to
each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to
each project.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Can someone solve and explain the answers to me ?
Thanks
Pranam
35% - Fewer than 2
25% - Greater than 4
----------------------
So 40% - with 3 employees.
Now imagine the number line in increments of 10:
0---10---20---30---40---50---60---70--|-80---90---100
----------------------|--------------------
You can see that 3 lies @ 50 on the number line which is the median.
So (1) and (2) SUFF
Hello ,
I had a question set to which I could not find answers. I am posting here. I am new to the group so pardon me if this creates trouble.
Q1
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the
3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride
the roller coaster 3 times, what is the probability that the passenger will ride in each of
the 3 cars?
A. 0
B. 1/9
C. 2/9
D. 1/3
E. 1
Q2:
Running at their respective constant rates, machine X takes 2 days longer to produce w
widgets than machine Y. At these rates, if the two machines together produce 5/4 w
widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?
A. 4
B. 6
C. 8
D. 10
E. 12
Answer:
Q3:
June 25, 1982, fell on a Friday. On which day of the week did June 25, 1987, fall? (Note:
1984 was a leap year.)
A. Sunday
B. Monday
C. Tuesday
D. Wednesday
E. Thursday
Q4:
What is the median number of employees assigned per project for the projects at
Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to
each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to
each project.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Can someone solve and explain the answers to me ?
Thanks
Pranam
My ans are same as explained by Vikram.