Showing posts with label important questions for interview. Show all posts
Showing posts with label important questions for interview. Show all posts
Saturday, January 26, 2013
0
Saturday, January 26, 2013
prakash chalumuri
Microsoft Placement Paper Pattern
There were almost 40 technical questions and 10 analytical questions. .total 50 questions..
About analytical questions
1.find perimeter of a trapezium wit 3 sides given and distance b/w parallel sides given...
2.a triangle ABC is given, a line DE is parallel to base side and that cuts the triangle.. the ratio of area of triangle to the area of trapezium .given DE/BC=3/5..
3.four concentric circles r given .the radius of 1st circle is x.next is 2x,then 3x and 4x. given that area b/w 2nd and 1st is A and 4th and 3rd circles being B.find ratio of A to B
4.difference b/w the perimeters of two concentric circles is 66.find the difference b/w radius..
Ans: 10.5
5.3/p=6,3/q=15......find p-q
Quantitative were simple mostly geometrical type.... technical questions...........
1.which of de following is connectionless protocol
Ans: UDP
2. #define clrscr() 100
main()
{
clrscr();
printf("%d",clrscr());
}
3. which of the followin is used for avoidin network congestion
bufferin
cachin
sourcequench
all of de above
4.main()
{
int a;
printf("%d",scanf(%d,&a));
}
what's o/p of this program. what will b printed
Ans :0
5. main()
{
printf("as");
printf("\bhi");
printf("is\n");
}
what will b printed.
6.main()
{
unsigned short a=-1;
unsigned char b=a;
printf("%d %d ",a,b);
}
what is o/p of the program
a. 65535 -1
b. 65535 65535
c. -1 -1
7.arrays base address is 1000....array is a[5][4]..then what is The correct address of a[4][3]...
Ans:1056
8.one packet is 64bytes..no of pkts send is 16000..then total no of bytes send is
Ans: 1024000
9.#define maxval 5
int main (void)
{
int i=1;
if(i-maxval)
{
printf("inside");
}
else
{
printf("out");
}
find o/p???
10. #define a 3+3
#define b 11-3
main()
{
printf("%d",a*b);
}
what is o/p?????
11.a question in which segment address is given ..logical address is 800..base addresses also given ..u hav 2 find physical address..
12.stack is used in a task
Ans: temporary variables values
13.which of de following is not stored in activation record..
Ans: some heap area
9. In June a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?
A. 12 B. 20 C. 24 D. 30
Ans. C
10. M men agree to purchase a gift for Rs. D. If three men drop out how much more will each have to contribute towards the purchase of the gift/
A. D/(M-3) B. MD/3 C. M/(D-3) D. 3D/(M2-3M)
Ans. D
11. A company contracts to paint 3 houses. Mr.Brown can paint a house in 6 days while Mr.Black would take 8 days and Mr.Blue 12 days. After 8 days Mr.Brown goes on vacation and Mr. Black begins to work for a period of 6 days. How many days will it take Mr.Blue to complete the contract?
A. 7 B. 8 C. 11 D. 12
Ans. C
12. 2 hours after a freight train leaves Delhi a passenger train leaves the same station travelling in the same direction at an average speed of 16 km/hr. After traveling 4 hrs the passenger train overtakes the freight train. The average speed of the freight train was?
A. 30 B. 40 C.58 D. 60
Ans. B
13. If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?
A.-5 B. 4 C. 2 D. 8
Ans. D
ANALYTICAL ABILITY
1. The office staff of XYZ corporation presently consists of three bookkeepers--A, B, C and 5 secretaries D, E, F, G, H. The management is planning to open a new office in another city using 2 bookkeepers and 3 secretaries of the present staff . To do so they plan to separate certain individuals who don't function well together. The following guidelines were established to set up the new office
I. Bookeepers A and C are constantly finding fault with one another and should not be sent together to the new office as a team
II. C and E function well alone but not as a team , they should be separated
III. D and G have not been on speaking terms and shouldn't go together
IV Since D and F have been competing for promotion they shouldn't be a team
1.If A is to be moved as one of the bookkeepers, which of the following cannot be a possible working unit.
A.ABDEH B.ABDGH C.ABEFH D.ABEGH
Ans.B
2.If C and F are moved to the new office, how many combinations are possible
A.1 B.2 C.3 D.4
Ans. A
3.If C is sent to the new office, which member of the staff cannot go with C
A. B B. D C. F D. G
Ans. B
4.Under the guidelines developed, which of the following must go to the new office
A. B B. D C .E D. G
Ans. A
5.If D goes to the new office, which of the following is/are true
I. C cannot go II. A cannot go III. H must also go
A. I only B. II only C. I and II only D. I and III only
Ans. D
2.After months of talent searching for an administrative assistant to the president of the college the field of applicants has been narrowed down to 5--A, B, C, D, E .It was announced that the finalist would be chosen after a series of all-day group personal interviews were held.The examining committee agreed upon the following procedure
I. The interviews will be held once a week
II.3 candidates will appear at any all-day interview session
III. Each candidate will appear at least once
IV. If it becomes necessary to call applicants for additional interviews, no more 1 such applicant should be asked to appear the next week
V. Because of a detail in the written applications, it was agreed that whenever candidate B appears, A should also be present.
VI. Because of travel difficulties it was agreed that C will appear for only 1 interview.
1.At the first interview the following candidates appear A,B,D.Which of the follwing combinations can be called for the interview to be held next week.
A. BCD B. CDE C. ABE D. ABC
Ans. B
2.Which of the following is a possible sequence of combinations for interviews in 2 successive weeks
A. ABC;BDE B. ABD;ABE C. ADE;ABC D. BDE;ACD
Ans. C
3.If A ,B and D appear for the interview and D is called for additional interview the following week,which 2 candidates may be asked to appear with D?
I. A II B III. C IV. E
A. I and II B. I and III only C. II and III only D.III and IV only
Ans. D
4.Which of the following correctly state's) the procedure followed by the search committee
I. After the second interview all applicants have appeared at least once
II. The committee sees each applicant a second time b If a third session, it is possible for all applicants to appear at least twice
A. I only B. II only C. III only D. Both I and II
Ans. A
3. A certain city is served by subway lines A,B and C and numbers 1 2 and 3 When it snows , morning service on B is delayed
When it rains or snows , service on A, 2 and 3 are delayed both in the morning and afternoon When temp. falls below 30 degrees farenheit afternoon service is cancelled in either the A line or the 3 line, but not both. When the temperature rises over 90 degrees farenheit, the afternoon service is cancelled in either the line C or the 3 line but not both. When the service on the A line is delayed or cancelled, service on the C line which connects the A line, is delayed. When service on the 3 line is cancelled, service on the B line which connects the 3 line is delayed.
Q1. On Jan 10th, with the temperature at 15 degree farenheit, it snows all day. On how many lines will service be
affected, including both morning and afternoon.
(A) 2 (B) 3 (C) 4 (D) 5
Ans. D
Q2. On Aug 15th with the temperature at 97 degrees farenheit it begins to rain at 1 PM. What is the minimum number
of lines on which service will be affected?
(A) 2 (B) 3 (C) 4 (D) 5
Ans. C
Q3. On which of the following occasions would service be on the greatest number of lines disrupted.
(A) A snowy afternoon with the temperature at 45 degree farenheit
(B) A snowy morning with the temperature at 45 degree farenheit
(C) A rainy afternoon with the temperature at 45 degree farenheit
(D) A rainy afternoon with the temperature at 95 degree farenheit
Ans. B
4. In a certain society, there are two marriage groups, red and brown. No marriage is permitted within a group. On marriage, males become part of their wives groups; women remain in their own group. Children belong to the same group as their parents. Widowers and divorced males revert to the group of their birth. Marriage to more than one person at the same time and marriage to a direct descendant are forbidden
Q1. A brown female could have had
I. A grandfather born Red II. A grandmother born Red III Two grandfathers born Brown
(A) I only (B) III only (C) I, II and III (D) I and II only
Ans. D
Q2. A male born into the brown group may have
(A) An uncle in either group (B) A brown daughter (C) A brown son (D) A son-in-law born into red group
Ans. A
Q3. Which of the following is not permitted under the rules as stated.
(A) A brown male marrying his father's sister (B) A red female marrying her mother's brother
(C) A widower marrying his wife's sister (D) A widow marrying her divorced daughter's ex-husband
Ans. B
Q4. If widowers and divorced males retained their group they had upon marrying which of the following would be permissible ( Assume that no previous marriage occurred)
(A) A woman marrying her dead sister's husband (B) A woman marrying her divorced daughter's ex-husband
(C) A widower marrying his brother's daughter (D) A woman marrying her mother's brother who is a widower.
Ans. D
5. I. All G's are H's II. All G's are J's or K's III All J's and K's are G's
IV. All L's are K's V. All N's are M's VI. No M's are G's
Q1. If no P's are K's which of the following must be true
(A) No P is a G (B) No P is an H (C) If any P is an H it is a G (D) If any P is a G it is a J
Ans. D
Q2. Which of the following can be logically deduced from the stated conditions
(A) No M's are H's (B) No H's are M's (C) Some M's are H's (D) No N's are G's
Ans. D
Q3. Which of the following is inconsistent with one or more conditions
(A) All H's are G's (B) All H's are M's (C) Some H's are both M's and G's (D) No M's are H's
Ans. C
Q4. The statement "No L's are J's" is
I. Logically deducible from the conditions stated
II Consistent with but not deducible from the conditions stated
III. Deducible from the stated conditions together with the additional statements "No J's are K's"
(A) I only (B) II only (C) III only (D) II and III only
Ans. D
Placement Paper Pattern for Microsoft [All Types of questions]
Microsoft Placement Paper Pattern
There were almost 40 technical questions and 10 analytical questions. .total 50 questions..
About analytical questions
1.find perimeter of a trapezium wit 3 sides given and distance b/w parallel sides given...
2.a triangle ABC is given, a line DE is parallel to base side and that cuts the triangle.. the ratio of area of triangle to the area of trapezium .given DE/BC=3/5..
3.four concentric circles r given .the radius of 1st circle is x.next is 2x,then 3x and 4x. given that area b/w 2nd and 1st is A and 4th and 3rd circles being B.find ratio of A to B
4.difference b/w the perimeters of two concentric circles is 66.find the difference b/w radius..
Ans: 10.5
5.3/p=6,3/q=15......find p-q
Quantitative were simple mostly geometrical type.... technical questions...........
1.which of de following is connectionless protocol
Ans: UDP
2. #define clrscr() 100
main()
{
clrscr();
printf("%d",clrscr());
}
3. which of the followin is used for avoidin network congestion
bufferin
cachin
sourcequench
all of de above
4.main()
{
int a;
printf("%d",scanf(%d,&a));
}
what's o/p of this program. what will b printed
Ans :0
5. main()
{
printf("as");
printf("\bhi");
printf("is\n");
}
what will b printed.
6.main()
{
unsigned short a=-1;
unsigned char b=a;
printf("%d %d ",a,b);
}
what is o/p of the program
a. 65535 -1
b. 65535 65535
c. -1 -1
7.arrays base address is 1000....array is a[5][4]..then what is The correct address of a[4][3]...
Ans:1056
8.one packet is 64bytes..no of pkts send is 16000..then total no of bytes send is
Ans: 1024000
9.#define maxval 5
int main (void)
{
int i=1;
if(i-maxval)
{
printf("inside");
}
else
{
printf("out");
}
find o/p???
10. #define a 3+3
#define b 11-3
main()
{
printf("%d",a*b);
}
what is o/p?????
11.a question in which segment address is given ..logical address is 800..base addresses also given ..u hav 2 find physical address..
12.stack is used in a task
Ans: temporary variables values
13.which of de following is not stored in activation record..
Ans: some heap area
9. In June a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?
A. 12 B. 20 C. 24 D. 30
Ans. C
10. M men agree to purchase a gift for Rs. D. If three men drop out how much more will each have to contribute towards the purchase of the gift/
A. D/(M-3) B. MD/3 C. M/(D-3) D. 3D/(M2-3M)
Ans. D
11. A company contracts to paint 3 houses. Mr.Brown can paint a house in 6 days while Mr.Black would take 8 days and Mr.Blue 12 days. After 8 days Mr.Brown goes on vacation and Mr. Black begins to work for a period of 6 days. How many days will it take Mr.Blue to complete the contract?
A. 7 B. 8 C. 11 D. 12
Ans. C
12. 2 hours after a freight train leaves Delhi a passenger train leaves the same station travelling in the same direction at an average speed of 16 km/hr. After traveling 4 hrs the passenger train overtakes the freight train. The average speed of the freight train was?
A. 30 B. 40 C.58 D. 60
Ans. B
13. If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?
A.-5 B. 4 C. 2 D. 8
Ans. D
ANALYTICAL ABILITY
1. The office staff of XYZ corporation presently consists of three bookkeepers--A, B, C and 5 secretaries D, E, F, G, H. The management is planning to open a new office in another city using 2 bookkeepers and 3 secretaries of the present staff . To do so they plan to separate certain individuals who don't function well together. The following guidelines were established to set up the new office
I. Bookeepers A and C are constantly finding fault with one another and should not be sent together to the new office as a team
II. C and E function well alone but not as a team , they should be separated
III. D and G have not been on speaking terms and shouldn't go together
IV Since D and F have been competing for promotion they shouldn't be a team
1.If A is to be moved as one of the bookkeepers, which of the following cannot be a possible working unit.
A.ABDEH B.ABDGH C.ABEFH D.ABEGH
Ans.B
2.If C and F are moved to the new office, how many combinations are possible
A.1 B.2 C.3 D.4
Ans. A
3.If C is sent to the new office, which member of the staff cannot go with C
A. B B. D C. F D. G
Ans. B
4.Under the guidelines developed, which of the following must go to the new office
A. B B. D C .E D. G
Ans. A
5.If D goes to the new office, which of the following is/are true
I. C cannot go II. A cannot go III. H must also go
A. I only B. II only C. I and II only D. I and III only
Ans. D
2.After months of talent searching for an administrative assistant to the president of the college the field of applicants has been narrowed down to 5--A, B, C, D, E .It was announced that the finalist would be chosen after a series of all-day group personal interviews were held.The examining committee agreed upon the following procedure
I. The interviews will be held once a week
II.3 candidates will appear at any all-day interview session
III. Each candidate will appear at least once
IV. If it becomes necessary to call applicants for additional interviews, no more 1 such applicant should be asked to appear the next week
V. Because of a detail in the written applications, it was agreed that whenever candidate B appears, A should also be present.
VI. Because of travel difficulties it was agreed that C will appear for only 1 interview.
1.At the first interview the following candidates appear A,B,D.Which of the follwing combinations can be called for the interview to be held next week.
A. BCD B. CDE C. ABE D. ABC
Ans. B
2.Which of the following is a possible sequence of combinations for interviews in 2 successive weeks
A. ABC;BDE B. ABD;ABE C. ADE;ABC D. BDE;ACD
Ans. C
3.If A ,B and D appear for the interview and D is called for additional interview the following week,which 2 candidates may be asked to appear with D?
I. A II B III. C IV. E
A. I and II B. I and III only C. II and III only D.III and IV only
Ans. D
4.Which of the following correctly state's) the procedure followed by the search committee
I. After the second interview all applicants have appeared at least once
II. The committee sees each applicant a second time b If a third session, it is possible for all applicants to appear at least twice
A. I only B. II only C. III only D. Both I and II
Ans. A
3. A certain city is served by subway lines A,B and C and numbers 1 2 and 3 When it snows , morning service on B is delayed
When it rains or snows , service on A, 2 and 3 are delayed both in the morning and afternoon When temp. falls below 30 degrees farenheit afternoon service is cancelled in either the A line or the 3 line, but not both. When the temperature rises over 90 degrees farenheit, the afternoon service is cancelled in either the line C or the 3 line but not both. When the service on the A line is delayed or cancelled, service on the C line which connects the A line, is delayed. When service on the 3 line is cancelled, service on the B line which connects the 3 line is delayed.
Q1. On Jan 10th, with the temperature at 15 degree farenheit, it snows all day. On how many lines will service be
affected, including both morning and afternoon.
(A) 2 (B) 3 (C) 4 (D) 5
Ans. D
Q2. On Aug 15th with the temperature at 97 degrees farenheit it begins to rain at 1 PM. What is the minimum number
of lines on which service will be affected?
(A) 2 (B) 3 (C) 4 (D) 5
Ans. C
Q3. On which of the following occasions would service be on the greatest number of lines disrupted.
(A) A snowy afternoon with the temperature at 45 degree farenheit
(B) A snowy morning with the temperature at 45 degree farenheit
(C) A rainy afternoon with the temperature at 45 degree farenheit
(D) A rainy afternoon with the temperature at 95 degree farenheit
Ans. B
4. In a certain society, there are two marriage groups, red and brown. No marriage is permitted within a group. On marriage, males become part of their wives groups; women remain in their own group. Children belong to the same group as their parents. Widowers and divorced males revert to the group of their birth. Marriage to more than one person at the same time and marriage to a direct descendant are forbidden
Q1. A brown female could have had
I. A grandfather born Red II. A grandmother born Red III Two grandfathers born Brown
(A) I only (B) III only (C) I, II and III (D) I and II only
Ans. D
Q2. A male born into the brown group may have
(A) An uncle in either group (B) A brown daughter (C) A brown son (D) A son-in-law born into red group
Ans. A
Q3. Which of the following is not permitted under the rules as stated.
(A) A brown male marrying his father's sister (B) A red female marrying her mother's brother
(C) A widower marrying his wife's sister (D) A widow marrying her divorced daughter's ex-husband
Ans. B
Q4. If widowers and divorced males retained their group they had upon marrying which of the following would be permissible ( Assume that no previous marriage occurred)
(A) A woman marrying her dead sister's husband (B) A woman marrying her divorced daughter's ex-husband
(C) A widower marrying his brother's daughter (D) A woman marrying her mother's brother who is a widower.
Ans. D
5. I. All G's are H's II. All G's are J's or K's III All J's and K's are G's
IV. All L's are K's V. All N's are M's VI. No M's are G's
Q1. If no P's are K's which of the following must be true
(A) No P is a G (B) No P is an H (C) If any P is an H it is a G (D) If any P is a G it is a J
Ans. D
Q2. Which of the following can be logically deduced from the stated conditions
(A) No M's are H's (B) No H's are M's (C) Some M's are H's (D) No N's are G's
Ans. D
Q3. Which of the following is inconsistent with one or more conditions
(A) All H's are G's (B) All H's are M's (C) Some H's are both M's and G's (D) No M's are H's
Ans. C
Q4. The statement "No L's are J's" is
I. Logically deducible from the conditions stated
II Consistent with but not deducible from the conditions stated
III. Deducible from the stated conditions together with the additional statements "No J's are K's"
(A) I only (B) II only (C) III only (D) II and III only
Ans. D
0
prakash chalumuri
Microsoft Interview Questions Paper:
The following are actual questions from actual interviews conducted by Microsoft employees on the main campus.
Microsoft Consultants are sometimes allowed to have a life, so questions asked of them during interviews don't really count and aren't listed. The questions tend to follow some basic themes: Riddles.
Algorithms
Applications
Thinkers
Riddles
Why is a manhole cover round?
How many cars are there in the USA? (A popular variant is "How many gas stations are there in the USA?")
How many manhole covers are there in the USA?
You've got someone working for you for seven days and a gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?
One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
Imagine a disk spinning like a record player turn table. Half of the disk is black and the other is white. Assume you have an unlimited number of color sensors. How many sensors would you have to place around the disk to determine the direction the disk is spinning? Where would they be placed?
Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?
You have two jars, 50 red marbles and 50 blue marbles. A jar will be picked at random, and then a marble will be picked from the jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?
Pairs of primes separated by a single number are called prime pairs.
Examples are 17 and 19.
Prove that the number between a prime pair is always divisible by 6 (assuming both numbers in the pair are greater than 6). Now prove that there are no 'prime triples.'
There is a room with a door (closed) and three light bulbs. Outside the room there are three switches, connected to the bulbs. You may manipulate the switches as you wish, but once you open the door you can't change them. Identify each switch with its bulb.
Suppose you had 8 billiard balls, and one of them was slightly heavier, but the only way to tell was by putting it on a scale against another. What's the fewest number of times you'd have to use the scale to find the heavier ball?
Imagine you are standing in front of a mirror, facing it. Raise your left hand. Raise your right hand. Look at your reflection. When you raise your left hand your reflection raises what appears to be his right hand. But when you tilt your head up, your reflection does too, and does not appear to tilt his/her head down. Why is it that the mirror appears to reverse left and right, but not up and down?
You have 4 jars of pills. Each pill is a certain weight, except for contaminated pills contained in one jar, where each pill is weight + 1. How could you tell which jar had the contaminated pills in just one measurement?
The SF Chronicle has a word game where all the letters are scrambled up and you have to figure out what the word is. Imagine that a scrambled word is 5 characters long: How many possible solutions are there? What if we know which 5 letters are being used?
Develop an algorithm to solve the word.
There are 4 women who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each woman walks at a different speed. A pair must walk together at the rate of the slower woman's pace.
Woman 1: 1 minute to cross
Woman 2: 2 minutes to cross
Woman 3: 5 minutes to cross
Woman 4: 10 minutes to cross
For example if Woman 1 and Woman 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Woman 4 then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission. What is the order required to get all women across in 17 minutes? Now, what's the other way?
If you had an infinite supply of water and a 5 quart and 3 quart pail, how would you measure exactly 4 quarts?
You have a bucket of jelly beans. Some are red, some are blue, and some green. With your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you have 2 of the same?
If you have two buckets, one with red paint and the other with blue paint, and you take one cup from the blue bucket and poor it into the red bucket. Then you take one cup from the red bucket and poor it into the blue bucket. Which bucket has the highest ratio between red and blue? Prove it mathematically.
Microsoft Interview Questions Papers
Microsoft Interview Questions Paper:
The following are actual questions from actual interviews conducted by Microsoft employees on the main campus.
Microsoft Consultants are sometimes allowed to have a life, so questions asked of them during interviews don't really count and aren't listed. The questions tend to follow some basic themes: Riddles.
Algorithms
Applications
Thinkers
Riddles
Why is a manhole cover round?
How many cars are there in the USA? (A popular variant is "How many gas stations are there in the USA?")
How many manhole covers are there in the USA?
You've got someone working for you for seven days and a gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?
One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?
Imagine a disk spinning like a record player turn table. Half of the disk is black and the other is white. Assume you have an unlimited number of color sensors. How many sensors would you have to place around the disk to determine the direction the disk is spinning? Where would they be placed?
Imagine an analog clock set to 12 o'clock. Note that the hour and minute hands overlap. How many times each day do both the hour and minute hands overlap? How would you determine the exact times of the day that this occurs?
You have two jars, 50 red marbles and 50 blue marbles. A jar will be picked at random, and then a marble will be picked from the jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?
Pairs of primes separated by a single number are called prime pairs.
Examples are 17 and 19.
Prove that the number between a prime pair is always divisible by 6 (assuming both numbers in the pair are greater than 6). Now prove that there are no 'prime triples.'
There is a room with a door (closed) and three light bulbs. Outside the room there are three switches, connected to the bulbs. You may manipulate the switches as you wish, but once you open the door you can't change them. Identify each switch with its bulb.
Suppose you had 8 billiard balls, and one of them was slightly heavier, but the only way to tell was by putting it on a scale against another. What's the fewest number of times you'd have to use the scale to find the heavier ball?
Imagine you are standing in front of a mirror, facing it. Raise your left hand. Raise your right hand. Look at your reflection. When you raise your left hand your reflection raises what appears to be his right hand. But when you tilt your head up, your reflection does too, and does not appear to tilt his/her head down. Why is it that the mirror appears to reverse left and right, but not up and down?
You have 4 jars of pills. Each pill is a certain weight, except for contaminated pills contained in one jar, where each pill is weight + 1. How could you tell which jar had the contaminated pills in just one measurement?
The SF Chronicle has a word game where all the letters are scrambled up and you have to figure out what the word is. Imagine that a scrambled word is 5 characters long: How many possible solutions are there? What if we know which 5 letters are being used?
Develop an algorithm to solve the word.
There are 4 women who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each woman walks at a different speed. A pair must walk together at the rate of the slower woman's pace.
Woman 1: 1 minute to cross
Woman 2: 2 minutes to cross
Woman 3: 5 minutes to cross
Woman 4: 10 minutes to cross
For example if Woman 1 and Woman 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Woman 4 then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission. What is the order required to get all women across in 17 minutes? Now, what's the other way?
If you had an infinite supply of water and a 5 quart and 3 quart pail, how would you measure exactly 4 quarts?
You have a bucket of jelly beans. Some are red, some are blue, and some green. With your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you have 2 of the same?
If you have two buckets, one with red paint and the other with blue paint, and you take one cup from the blue bucket and poor it into the red bucket. Then you take one cup from the red bucket and poor it into the blue bucket. Which bucket has the highest ratio between red and blue? Prove it mathematically.
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