GMAT Problem Solving Discussions

hi ajay
in the following prob.
1)If x and y are positive, is x^3 > y
(1)square root of x >y
(2)x > y
Q.1
using st.1 alone,
let x=4, y=1....sqrt(x)>y....and x^3>y in all cases for x,y>0
hence, st.1 alone is sufficient
i differ from ur ans
coz, x is only a positive number so sq rt of x can be 0.2
and clearly x^3 is even smaller
in tht case we wud be unable to gt an answer
i feel this ques cannot be ans evn by using both the statements
do comment
regards
rock

oh yeah!!! sorry dude!!! i overlooked the decimal scenario!!! u r right!! the answer is E...
CAN ANY BODY PROVIDE ME THE SOLUTION OF MY PROBLEM
Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Eugene finishes two places ahead of Chris in the first race, all of the following will be true EXCEPT:

a) Bob finishes ahead of Don.
b) Chris finishes two places ahead of Alan.
c) Don finishes fourth.
d) Bob finishes immediately behind Eugene.
e) Chris finishes ahead of Bob.
2) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Don finishes third in the third race, which of the following must be true of that race?

a) Alan finishes first.
b) Eugene finishes first.
c) Bob finishes second.
d) Chris finishes second.
e) Alan finishes fifth.
3) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Eugene's total for the six races is 36 points, which of the following must be true?

a) Bob's total is more than 36 points.
b) Chris's total is more than 36 points.
c) Alan's total is 36 points.
d) Don's total is less than 36 points.
e) Don's total is 36 points.
4) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Alan finishes first only once, and Don finishes second exactly twice, the lowest total number of points that Bob can earn in the race is:

a) 32 points.
b) 38 points.
c) 40 points.
d) 44 points.
e) 48 points.
5) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Alan finishes first in four races, which of the following could earn a total of fewer than 26 points in the six races?

a) Bob only.
b) Chris only.
c) Don only.
d) Eugene of Chris.
e) Don or Chris.
6) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Frank enters the third race and finishes behind Chris and Don, which of the following must be true of that race?


a) Eugene finishes first.
b) Alan finishes sixth.
c) Don finishes second.
d) Frank finishes fifth.
e) Chris finishes third.
7) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

If Jane wears black shoes she will not wear:

a) red stockings.
b) a blue skirt.
c) a white blouse.
d) blue stockings.
e) a sky blue blouse.
Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

If Jane is color blind and is unable to determine what outfits went well together, how many possible clothing combinations could she have?

a) 24
b) 32
c) 36
d) 44
e) 48
9) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

If Jane wears a brown skirt and a white blouse, she could:

a) not wear blue stockings.
b) not wear brown shoes.
c) not wear black shoes.
d) wear blue stockings.
e) wear red stockings.
10) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

Jane buys a gray scarf. If she wears the new scarf, then she could:

a) not wear blue stockings.
b) not wear brown stockings.
c) not wear black shoes.
d) wear a white blouse.
e) wear black stockings.
11) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

Jane will never wear:

a) blue and red together.
b) white and red together.
c) gray and blue together.
d) white and black together.
e) white and red together.
12) Two men, Barry and David, and two women Ann and Cathy are doctors. One is a surgeon, one a dentist, one an optometrist, and one is a general practitioner. They are seated around a square table, with one person on each side.

1) Barry is across from the dentist.
2) David is not across from the surgeon.
3) The optometrist is on Ann's immediate left.
4) Cathy is the general practitioner.
5) The surgeon and general practitioner are married to each other.
6) The general practitioner is not on Cathy's immediate left.
7) The general practitioner is across from the optometrist.

Which of the following must be true?

a) Barry is the dentist.
b) The surgeon and general practitioner are women.
c) The dentist is across from the surgeon.
d) David is the surgeon.
e) Cathy is across from Ann.
13) Two men, Barry and David, and two women Ann and Cathy are doctors. One is a surgeon, one a dentist, one an optometrist, and one is a general practitioner. They are seated around a square table, with one person on each side.

1) Barry is across from the dentist.
2) David is not across from the surgeon.
3) The optometrist is on Ann's immediate left.
4) Cathy is the general practitioner.
5) The surgeon and general practitioner are married to each other.
6) The general practitioner is not on Cathy's immediate left.
7) The general practitioner is across from the optometrist.

If both women leave the table, the

a) optometrist and dentist remain.
b) surgeon and optometrist remain.
c) surgeon and general practitioner remain.
d) general practitioner and dentist remain.
e) general practitioner and optometrist remain.

Plaese provide me with a link from wherein I can download question bank for GMAT..

Last Friday a certain shop sold 3/4 of the sweaters in its inventory. Each sweater sold or $20. What was the total revenue last Friday from the sale of these sweaters?


(1) When the shop opened last Friday, there were 160 sweaters in its inventory.
(2) All but 40 sweaters in the shops inventory were sold last Friday.

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.


ans: D EACH Statement ALONE is sufficeint.

Statement 1) total sweaters= 160, so 3/4th of total=3/4*160=120.
1 sweater cost =$20, so total revenue= 20 *120=$2400

Statement 2) inventory left over=(1-3/4)th of total=1/4th of total=40 sweaters. so total=160. 3/4th of total=3/4*160=120
total revenue=$20*120=$2400
CAN ANY BODY PROVIDE ME THE SOLUTION OF MY PROBLEM
Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Eugene finishes two places ahead of Chris in the first race, all of the following will be true EXCEPT:

a) Bob finishes ahead of Don.
b) Chris finishes two places ahead of Alan.
c) Don finishes fourth.
d) Bob finishes immediately behind Eugene.
e) Chris finishes ahead of Bob.
2) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Don finishes third in the third race, which of the following must be true of that race?

a) Alan finishes first.
b) Eugene finishes first.
c) Bob finishes second.
d) Chris finishes second.
e) Alan finishes fifth.
3) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Eugene's total for the six races is 36 points, which of the following must be true?

a) Bob's total is more than 36 points.
b) Chris's total is more than 36 points.
c) Alan's total is 36 points.
d) Don's total is less than 36 points.
e) Don's total is 36 points.
4) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Alan finishes first only once, and Don finishes second exactly twice, the lowest total number of points that Bob can earn in the race is:

a) 32 points.
b) 38 points.
c) 40 points.
d) 44 points.
e) 48 points.
5) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Alan finishes first in four races, which of the following could earn a total of fewer than 26 points in the six races?

a) Bob only.
b) Chris only.
c) Don only.
d) Eugene of Chris.
e) Don or Chris.
6) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Frank enters the third race and finishes behind Chris and Don, which of the following must be true of that race?

a) Eugene finishes first.
b) Alan finishes sixth.
c) Don finishes second.
d) Frank finishes fifth.
e) Chris finishes third.
7) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

If Jane wears black shoes she will not wear:

a) red stockings.
b) a blue skirt.
c) a white blouse.
d) blue stockings.
e) a sky blue blouse.
Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

If Jane is color blind and is unable to determine what outfits went well together, how many possible clothing combinations could she have?

a) 24
b) 32
c) 36
d) 44
e) 48
9) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

If Jane wears a brown skirt and a white blouse, she could:

a) not wear blue stockings.
b) not wear brown shoes.
c) not wear black shoes.
d) wear blue stockings.
e) wear red stockings.
10) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

Jane buys a gray scarf. If she wears the new scarf, then she could:

a) not wear blue stockings.
b) not wear brown stockings.
c) not wear black shoes.
d) wear a white blouse.
e) wear black stockings.
11) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

Jane will never wear:

a) blue and red together.
b) white and red together.
c) gray and blue together.
d) white and black together.
e) white and red together.
12) Two men, Barry and David, and two women Ann and Cathy are doctors. One is a surgeon, one a dentist, one an optometrist, and one is a general practitioner. They are seated around a square table, with one person on each side.

1) Barry is across from the dentist.
2) David is not across from the surgeon.
3) The optometrist is on Ann's immediate left.
4) Cathy is the general practitioner.
5) The surgeon and general practitioner are married to each other.
6) The general practitioner is not on Cathy's immediate left.
7) The general practitioner is across from the optometrist.

Which of the following must be true?

a) Barry is the dentist.
b) The surgeon and general practitioner are women.
c) The dentist is across from the surgeon.
d) David is the surgeon.
e) Cathy is across from Ann.
13) Two men, Barry and David, and two women Ann and Cathy are doctors. One is a surgeon, one a dentist, one an optometrist, and one is a general practitioner. They are seated around a square table, with one person on each side.

1) Barry is across from the dentist.
2) David is not across from the surgeon.
3) The optometrist is on Ann's immediate left.
4) Cathy is the general practitioner.
5) The surgeon and general practitioner are married to each other.
6) The general practitioner is not on Cathy's immediate left.
7) The general practitioner is across from the optometrist.

If both women leave the table, the

a) optometrist and dentist remain.
b) surgeon and optometrist remain.
c) surgeon and general practitioner remain.
d) general practitioner and dentist remain.
e) general practitioner and optometrist remain.

Here are the answers to first set - Car Race

1. e
2. c
3. e
4. d
5. e
6. d

-Vivek

Answers to second set : Jane at fashion design company

7. a
8. e
9. c
10. b
11. a

CAN ANY BODY PROVIDE ME THE SOLUTION OF MY PROBLEM
Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Eugene finishes two places ahead of Chris in the first race, all of the following will be true EXCEPT:

a) Bob finishes ahead of Don.
b) Chris finishes two places ahead of Alan.
c) Don finishes fourth.
d) Bob finishes immediately behind Eugene.
e) Chris finishes ahead of Bob.
2) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Don finishes third in the third race, which of the following must be true of that race?

a) Alan finishes first.
b) Eugene finishes first.
c) Bob finishes second.
d) Chris finishes second.
e) Alan finishes fifth.
3) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Eugene's total for the six races is 36 points, which of the following must be true?

a) Bob's total is more than 36 points.
b) Chris's total is more than 36 points.
c) Alan's total is 36 points.
d) Don's total is less than 36 points.
e) Don's total is 36 points.
4) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Alan finishes first only once, and Don finishes second exactly twice, the lowest total number of points that Bob can earn in the race is:

a) 32 points.
b) 38 points.
c) 40 points.
d) 44 points.
e) 48 points.
5) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Alan finishes first in four races, which of the following could earn a total of fewer than 26 points in the six races?

a) Bob only.
b) Chris only.
c) Don only.
d) Eugene of Chris.
e) Don or Chris.
6) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:

Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.

In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.

If Frank enters the third race and finishes behind Chris and Don, which of the following must be true of that race?

a) Eugene finishes first.
b) Alan finishes sixth.
c) Don finishes second.
d) Frank finishes fifth.
e) Chris finishes third.
7) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

If Jane wears black shoes she will not wear:

a) red stockings.
b) a blue skirt.
c) a white blouse.
d) blue stockings.
e) a sky blue blouse.
Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

If Jane is color blind and is unable to determine what outfits went well together, how many possible clothing combinations could she have?

a) 24
b) 32
c) 36
d) 44
e) 48
9) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

If Jane wears a brown skirt and a white blouse, she could:

a) not wear blue stockings.
b) not wear brown shoes.
c) not wear black shoes.
d) wear blue stockings.
e) wear red stockings.
10) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

Jane buys a gray scarf. If she wears the new scarf, then she could:

a) not wear blue stockings.
b) not wear brown stockings.
c) not wear black shoes.
d) wear a white blouse.
e) wear black stockings.
11) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.

She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.

The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.

Jane will never wear:

a) blue and red together.
b) white and red together.
c) gray and blue together.
d) white and black together.
e) white and red together.
12) Two men, Barry and David, and two women Ann and Cathy are doctors. One is a surgeon, one a dentist, one an optometrist, and one is a general practitioner. They are seated around a square table, with one person on each side.

1) Barry is across from the dentist.
2) David is not across from the surgeon.
3) The optometrist is on Ann's immediate left.
4) Cathy is the general practitioner.
5) The surgeon and general practitioner are married to each other.
6) The general practitioner is not on Cathy's immediate left.
7) The general practitioner is across from the optometrist.

Which of the following must be true?

a) Barry is the dentist.
b) The surgeon and general practitioner are women.
c) The dentist is across from the surgeon.
d) David is the surgeon.
e) Cathy is across from Ann.
13) Two men, Barry and David, and two women Ann and Cathy are doctors. One is a surgeon, one a dentist, one an optometrist, and one is a general practitioner. They are seated around a square table, with one person on each side.

1) Barry is across from the dentist.
2) David is not across from the surgeon.
3) The optometrist is on Ann's immediate left.
4) Cathy is the general practitioner.
5) The surgeon and general practitioner are married to each other.
6) The general practitioner is not on Cathy's immediate left.
7) The general practitioner is across from the optometrist.

If both women leave the table, the

a) optometrist and dentist remain.
b) surgeon and optometrist remain.
c) surgeon and general practitioner remain.
d) general practitioner and dentist remain.
e) general practitioner and optometrist remain.

1. E
2. C
3. C
4. D
5. E
6. D
7. A
8. E
9. C
10.B
11.A
12.C
13.B

hope they are right!!! 😉
Is y an integer?

A.y3 is an integer
B.3y is an integer

need help in solving this...
CAN ANY BODY PROVIDE ME THE SOLUTION OF MY PROBLEM
Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.
If Eugene finishes two places ahead of Chris in the first race, all of the following will be true EXCEPT:
a) Bob finishes ahead of Don.
b) Chris finishes two places ahead of Alan.
c) Don finishes fourth.
d) Bob finishes immediately behind Eugene.
e) Chris finishes ahead of Bob.
2) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.
If Don finishes third in the third race, which of the following must be true of that race?
a) Alan finishes first.
b) Eugene finishes first.
c) Bob finishes second.
d) Chris finishes second.
e) Alan finishes fifth.
3) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.
If Eugene's total for the six races is 36 points, which of the following must be true?
a) Bob's total is more than 36 points.
b) Chris's total is more than 36 points.
c) Alan's total is 36 points.
d) Don's total is less than 36 points.
e) Don's total is 36 points.
4) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.
If Alan finishes first only once, and Don finishes second exactly twice, the lowest total number of points that Bob can earn in the race is:
a) 32 points.
b) 38 points.
c) 40 points.
d) 44 points.
e) 48 points.
5) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.
If Alan finishes first in four races, which of the following could earn a total of fewer than 26 points in the six races?
a) Bob only.
b) Chris only.
c) Don only.
d) Eugene of Chris.
e) Don or Chris.
6) Five racing drivers, Alan, Bob, Chris, Don, and Eugene, enter into a contest that consists of 6 races. The results of all six races are listed below:
Bob always finishes ahead of Chris.
Alan finishes either first or last.
Eugene finishes either first or last.
There are no ties in any race.
Every driver finishes each race.
In each race, two points are awarded for a fifth place finish, four points for fourth, six points for third, eight points for second, and ten points for first.
If Frank enters the third race and finishes behind Chris and Don, which of the following must be true of that race?
a) Eugene finishes first.
b) Alan finishes sixth.
c) Don finishes second.
d) Frank finishes fifth.
e) Chris finishes third.
7) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.
She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.
The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.
If Jane wears black shoes she will not wear:
a) red stockings.
b) a blue skirt.
c) a white blouse.
d) blue stockings.
e) a sky blue blouse.
Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.
She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.
The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.
If Jane is color blind and is unable to determine what outfits went well together, how many possible clothing combinations could she have?
a) 24
b) 32
c) 36
d) 44
e) 48
9) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.
She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.
The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.
If Jane wears a brown skirt and a white blouse, she could:
a) not wear blue stockings.
b) not wear brown shoes.
c) not wear black shoes.
d) wear blue stockings.
e) wear red stockings.
10) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.
She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.
The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.
Jane buys a gray scarf. If she wears the new scarf, then she could:
a) not wear blue stockings.
b) not wear brown stockings.
c) not wear black shoes.
d) wear a white blouse.
e) wear black stockings.
11) Jane works at a fashion design company, and is having problems getting dressed for work. She refuses to wear any color combination that does not go well together as many of her clients may look down upon this.
She has two pairs of skirts, brown and blue; three blouses, white, sky blue, and gray; four pairs of stockings, red, black, brown, and blue; and two pairs of shoes, black and brown.
The blue skirt cannot be worn with red or brown stockings.
Gray does not go well with brown.
Black does not go well with brown.
Jane will never wear:
a) blue and red together.
b) white and red together.
c) gray and blue together.
d) white and black together.
e) white and red together.
12) Two men, Barry and David, and two women Ann and Cathy are doctors. One is a surgeon, one a dentist, one an optometrist, and one is a general practitioner. They are seated around a square table, with one person on each side.
1) Barry is across from the dentist.
2) David is not across from the surgeon.
3) The optometrist is on Ann's immediate left.
4) Cathy is the general practitioner.
5) The surgeon and general practitioner are married to each other.
6) The general practitioner is not on Cathy's immediate left.
7) The general practitioner is across from the optometrist.
Which of the following must be true?
a) Barry is the dentist.
b) The surgeon and general practitioner are women.
c) The dentist is across from the surgeon.
d) David is the surgeon.
e) Cathy is across from Ann.
13) Two men, Barry and David, and two women Ann and Cathy are doctors. One is a surgeon, one a dentist, one an optometrist, and one is a general practitioner. They are seated around a square table, with one person on each side.
1) Barry is across from the dentist.
2) David is not across from the surgeon.
3) The optometrist is on Ann's immediate left.
4) Cathy is the general practitioner.
5) The surgeon and general practitioner are married to each other.
6) The general practitioner is not on Cathy's immediate left.
7) The general practitioner is across from the optometrist.
If both women leave the table, the
a) optometrist and dentist remain.
b) surgeon and optometrist remain.
c) surgeon and general practitioner remain.
d) general practitioner and dentist remain.
e) general practitioner and optometrist remain.


abt ques from 13 onwards, the condition 4) state that Cathy is general practitioner
6) The general practitioner is not on Cathy's immediate left.

aren't both the conditions contradictory?
abt ques from 13 onwards, the condition 4) state that Cathy is general practitioner
6) The general practitioner is not on Cathy's immediate left.

aren't both the conditions contradictory?

nope...i hope u understand from the following diagram :
Is y an integer?

A.y3 is an integer
B.3y is an integer

need help in solving this...

using st.1 alone,

y3 is an integer...this holds true for both y = any integer eg. 2, 3,4 and y = cuberoot(2), cuberoot(3) etc...
hence, st.1 alone is not sufficient...


using st.2 alone,
3y is an integer.... y can either be 2,3,4 etc... or 1/3, 2/3, 4/3 etc...

hence, st.2 alone is also not sufficient....

using both st. together,

y has to be an integer..cuz if y=cuberoot(2), then st.2 is not satisfied, and if y=1/3, then st.1 is not satisfied...

hence, answer is C..
"For the past x laps around the track, Steven's average time per lap was 51 seconds. If a lap of 39 seconds would reduce his average time per lap to 49 seconds, what is the value of x?"
A) 2
B) 5
C) 6
D) 10
E) 12

I would appreciate if you can solve this without using Plug in numbers so that I 'll see the concepts better. Tks!.
"For the past x laps around the track, Steven's average time per lap was 51 seconds. If a lap of 39 seconds would reduce his average time per lap to 49 seconds, what is the value of x?"
A) 2
B) 5
C) 6
D) 10
E) 12

I would appreciate if you can solve this without using Plug in numbers so that I 'll see the concepts better. Tks!.

see, for x laps, steven's avg. time per lap was 51 sec...that means he has run for a total of 51x seconds till now..when he completes another lap of 39 seconds, total time steven has run = 51x + 39
and total laps steven has run = x+1

now, his avg. time per lap = (51x+39)/(x+1) which is given to be equal to 49 seconds

hence,
(51x+39)/(x+1) = 49
51x+39 = 49x + 49
2x = 10
x=5...

hope u understood it...
If x is 1/2 , then 6x2+11x 7 / 2x-1=
I would appreciate some algebra solving, tks!
"For the past x laps around the track, Steven's average time per lap was 51 seconds. If a lap of 39 seconds would reduce his average time per lap to 49 seconds, what is the value of x?"
A) 2
B) 5
C) 6
D) 10
E) 12

I would appreciate if you can solve this without using Plug in numbers so that I 'll see the concepts better. Tks!.

A lap of 39 seconds takes out (51-39)12 seconds...whereas the actual reduction in average is 2 (51 to 49)...so there should be 6 laps including the last one of 39...

x=5
If x is - 1/2 , then 6x2+11x - 7 / 2x-1=
I would appreciate some algebra solving, tks!

Can you post the equation again...sorry but I didnt get anything out of ur post...

Ok (I have trouble pasting my ecuations here)
X is different from - 1/2
Then 6x2+11x - 7
2x-1
=
(X is different from minus one half; then six (X elevated to the 2 power), plus 11X, minus 7 all this divided by 2x minus 1, equals...)

Ok (I have trouble pasting my ecuations here)
X is different from - 1/2
Then 6x2+11x - 7
2x-1
=
(X is different from minus one half; then six (X elevated to the 2 power), plus 11X, minus 7 all this divided by 2x minus 1, equals...)

Ans : 3x+7
If x is 1/2 , then 6x2+11x 7 / 2x-1=
I would appreciate some algebra solving, tks!

hi..first of all, i think the condition is x is not equal to +1/2....cuz if thts the case, then the equation becomes equal to infinity since the denominator equals zero....so considering tht case,

6x2+11x-7 can be written as (3x+7)(2x-1)...(2x-1) cancels with the denominator...so we are left with (3x+7).
If x is 1/2 , then 6x2+11x 7 / 2x-1=
I would appreciate some algebra solving, tks!


6x^2 +11x -7=(2x-1)(3x+7). since x!=1/2 hence (6x^2+11x-7)/(2x-1)=3x+7. if the condiotion of x!=1/2 was not given then answer would have been infinity