GMAT Problem Solving Discussions

MBA
301
yup ... elaborating on wht u said ...
if we take 24 ... then it will not satisfy for 12^2



Hi..this is my first quote..

as per the question...n^2 must be divisible by 72...

12^2=144=72*2

Hnece 144 is divisible by 72, so now, n=12...and among the choices given, 12 is the maximun number that will divide 12..

tell me if its wrong....
302
Hi, Can someone help me with this?

If M and N are positive integers that have remainders of 1 & 3 respectively when divided by 6, which of the following could not be a possible value of M+N?

A) 86
B. 52
C. 34
D. 28
E. 10

Pls post your answer with explanations


My Answer is E.......Since integers are positive so Least possible value for M is 7.(0 is not a positive interger)....Least possible value for N is 9.So 9+7=16.Hence 10 could not be the possible value for M+N.
I hope this helps........Naveen
303
My Answer is E.......Since integers are positive so Least possible value for M is 7.(0 is not a positive interger)....Least possible value for N is 9.So 9+7=16.Hence 10 could not be the possible value for M+N.
I hope this helps........Naveen

least value is not 16 10 is possible
3 + 7
infact ans will of the form 6n+4 :)
Hope I m clear
304
least value is not 16 10 is possible
3 + 7
infact ans will of the form 6n+4 :)
Hope I m clear


You are right. The answer is A-84.
This is the only option which when divided by 6 doesnt give the remainder 4.

Here is another one.

Which is the greatest possible area of the a triangular region with one vertex at the center of the circle and the other two vertices on the circle?
A. 3^1/2 /4
B. 1/2
C. pi/4
D. 1
E. 2^1/2
305

This is a DS question:

If K is a positive integer, is K the square of an integer?
1) K is divisible by 4
2) K is divisible by exactly four different prime numbers

306

Which is the greatest possible area of the a triangular region with one vertex at the center of the circle and the other two vertices on the circle?
A. 3^1/2 /4
B. 1/2
C. pi/4
D. 1
E. 2^1/2

if the angle between the two radii is x and radius is r
area of triangle is .5 r^2 sinx
hence it is max when x = 90
assuming radius = 1 answer is 1/2
307
This is a DS question:

If K is a positive integer, is K the square of an integer?
1) K is divisible by 4
2) K is divisible by exactly four different prime numbers



E

statement 1 just tells that its a multiple of 4, so inconclusive

statement 2 says it is something like *** depending on w,x,y and z number can take anyform even if p1-4 are fixed.

1-2 combined only says p1 is 2 and w is greater than or equal to 2

so answer is E.
308
Post 7
I think the answer should be E



Hi, It would be much better if you can give the answer along with the question...there wont be any need to scroll up and down for the question and the answer.
309

Guys can u help me ouit with these??

1) The sides of a square region, measured to the nearest centimeters, are 6 centimeters long.
The least possible value of the actual area of the square region is
A. 36.00 sq cm
B. 35.00 sq cm
C. 33.75 sq cm
D. 30.25 sq cm
E. 25.00 sq cm

2) When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7,
the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when
y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of
x - y?
A. 12
B. 15
C. 20
D. 28
E. 35

3)A certain company that sells only cars and trucks reported that revenues from car sales in
1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from
truck sales in 1996?
A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3

4)On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded
annually, and Lana invested $2,000 at 5 percent annual interest, compounded annually.
The total amount of interest earned by Tims investment in the first 2 years was how
much greater than the total amount of interest earned by Lanas investment in the first 2
years?
A. $5
B. $15
C. $50
D. $100
E. $105

5)For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for
each additional person. What is the charge for each additional person?
(1) The daily cost per person for 4 people sharing the cost of a room equally is $45.
(2) The daily cost per person for 2 people sharing the cost of a room equally is $25
more than the corresponding cost for 4 people.

6)2x + y = 12
y For how many ordered pairs (x , y) that are solutions of the system above are x
and y both
integers?
A. 7
B. 10
C. 12
D. 13
E. 14

7)A certain circle in the xy-plane has its center at the origin. If P is a point on the circle,
what is the sum of the squares of the coordinates of P?
(1) The radius of the circle is 4.
(2) The sum of the coordinates of P is 0.

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.

9)One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y
kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C =
6.5x + 8.5y. Is x (1) y > 0.15
(2) C >=7.30

Plz explain methods

310

1) The sides of a square region, measured to the nearest centimeters, are 6 centimeters long.
The least possible value of the actual area of the square region is
A. 36.00 sq cm
B. 35.00 sq cm
C. 33.75 sq cm
D. 30.25 sq cm
E. 25.00 sq cm

The trick here is that the answer has to be a perfect square. Hence the only possible answers are 36, 30.25 or 25. Answer cannot be 25 as then the nearest possible cm is 5. Hence the answer is the 30.25 having square root 5.6. (D)

2) When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7,
the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when
y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of
x - y?
A. 12
B. 15
C. 20
D. 28
E. 35

Take two numbers satsfying the conditions. One is 18 and the other 53. Now, 53 - 18 = 35. Only one of the options is a factor of 35 i.e. 35. Hence (E).

3)A certain company that sells only cars and trucks reported that revenues from car sales in
1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from
truck sales in 1996?
A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3

Simple case of forming equations based on the data. And you get the answer as (A).

4)On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded
annually, and Lana invested $2,000 at 5 percent annual interest, compounded annually.
The total amount of interest earned by Tim's investment in the first 2 years was how
much greater than the total amount of interest earned by Lana's investment in the first 2
years?
A. $5
B. $15
C. $50
D. $100
E. $105

The answer is (A). Simple calculations which can be done even in the head.

5)For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for
each additional person. What is the charge for each additional person?
(1) The daily cost per person for 4 people sharing the cost of a room equally is $45.
(2) The daily cost per person for 2 people sharing the cost of a room equally is $25 more than the corresponding cost for 4 people.

I am assuming this is a DS question. We can solve it using anyone of the two options. An equation in only one variable can be formed using anyone of the two statements.

6)2x + y = 12
y For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?
A. 7
B. 10
C. 12
D. 13
E. 14

Answer is (D) : 13. x varies from 0 - 12. Correspondingly y varies from 12 - (-12).

7)A certain circle in the xy-plane has its center at the origin. If P is a point on the circle,
what is the sum of the squares of the coordinates of P?
(1) The radius of the circle is 4.
(2) The sum of the coordinates of P is 0.

Another DS question. Answer is Using only statement (1). The data about the radius has to present and is sufficient to answer the question.

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.

Cannot be answered. Depending on the number of projects with 3 employees assigned, the median can be 3 or 4.

9)One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y
kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C =
6.5x + 8.5y. Is x (1) y > 0.15
(2) C >=7.30

Statement (1) alone doesnt tell us anything other than x Statement (2) alone can be used for the answer. Using C = 6.5x + 8.5y, we can see that x has to be less than 0.8 else the condition x + y = 1 doesnt satisfy.

Phew!! typing all that was tiring. 😃
311
This is a DS question:

If K is a positive integer, is K the square of an integer?
1) K is divisible by 4
2) K is divisible by exactly four different prime numbers

Cannot be answered.

Statement 1 doesnt tell us anything. Eg. 25 not divisible by 4 while 36 divisible by 4.

Statement 2 is also inconclusive. Eg. (2X2) X (3X3) X (5X5) X (7X7) is a perfect square while 2 X 3 X 5 X 7 is not.

Taking the two together we can use the same logic as above and prove that it is inconclusive.

Please do post answers with explanations.
312
if the angle between the two radii is x and radius is r
area of triangle is .5 r^2 sinx
hence it is max when x = 90
assuming radius = 1 answer is 1/2

Hey Krsh...
Why did you assume that the raduis is 1? Is this also an assumption unless given otherwise like the face value of shares to be assumed 100 unless given otherwise?
313
Hi, Can someone help me with this?

If M and N are positive integers that have remainders of 1 & 3 respectively when divided by 6, which of the following could not be a possible value of M+N?

A) 86
B. 52
C. 34
D. 28
E. 10

Pls post your answer with explanations

By forming equations we can see that the values of M + N will be of the form
6x+4. (86 - 4) = 82 is not divisible by 6. Hence the answer is (A).
314

To elucidate,
If 6(K1)+1 = M and 6(K2)+3 = N , K1, K2 some constants.
M+N = 6(K1+K2) + 1 + 3 = 6(K)+4
where, K1+K2 = K , some constant.

86 should be 4 + a multiple of 6, implies 82 is a multiple of 6, which is not.
Hence answer 86.

315
Hey Krsh...
Why did you assume that the raduis is 1? Is this also an assumption unless given otherwise like the face value of shares to be assumed 100 unless given otherwise?

No .... I doubt the credibility of the question ... But the way we approach is the same as mentioned in my post
316

Take two numbers satsfying the conditions. One is 18 and the other 53. Now, 53 - 18 = 45. Only one of the options is a factor of 45 i.e. 15. Hence (B).

53-18 is 35. So I guess answer is 35. And also since we are subtracting, the remainders get cancelled and the answer should be a multiple of 7 and 5.

317
The trick here is that the answer has to be a perfect square. Hence the only possible answers are 36, 30.25 or 25. Answer cannot be 25 as then the nearest possible cm is 5. Hence the answer is the 30.25 having square root 5.6. (D)

Take two numbers satsfying the conditions. One is 18 and the other 53. Now, 53 - 18 = 45. Only one of the options is a factor of 45 i.e. 15. Hence (B).

53-18 is 35....So Answer for 2nd one is D........
318

53-18 is 35....So Answer for 2nd one is D........

Hey Saini...
Thanks for pointing out the mistake. 😃 But then answer will be (E) 35 and not (D). I am editing my original answer.
319
if the angle between the two radii is x and radius is r
area of triangle is .5 r^2 sinx
hence it is max when x = 90
assuming radius = 1 answer is 1/2



I missed to add the info that the radius of the circle is 1. This is a question that I got in GMATprep
320
Guys can u help me ouit with these??

1) The sides of a square region, measured to the nearest centimeters, are 6 centimeters long.
The least possible value of the actual area of the square region is
A. 36.00 sq cm
B. 35.00 sq cm
C. 33.75 sq cm
D. 30.25 sq cm
E. 25.00 sq cm

2) When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7,
the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when
y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of
x - y?
A. 12
B. 15
C. 20
D. 28
E. 35

3)A certain company that sells only cars and trucks reported that revenues from car sales in
1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from
truck sales in 1996?
A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3

4)On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded
annually, and Lana invested $2,000 at 5 percent annual interest, compounded annually.
The total amount of interest earned by Tims investment in the first 2 years was how
much greater than the total amount of interest earned by Lanas investment in the first 2
years?
A. $5
B. $15
C. $50
D. $100
E. $105

5)For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for
each additional person. What is the charge for each additional person?
(1) The daily cost per person for 4 people sharing the cost of a room equally is $45.
(2) The daily cost per person for 2 people sharing the cost of a room equally is $25
more than the corresponding cost for 4 people.

6)2x + y = 12
y For how many ordered pairs (x , y) that are solutions of the system above are x
and y both
integers?
A. 7
B. 10
C. 12
D. 13
E. 14

7)A certain circle in the xy-plane has its center at the origin. If P is a point on the circle,
what is the sum of the squares of the coordinates of P?
(1) The radius of the circle is 4.
(2) The sum of the coordinates of P is 0.

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.

9)One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y
kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C =
6.5x + 8.5y. Is x (1) y > 0.15
(2) C >=7.30

Plz explain methods




OA's are

1) D
2) E
3) A
4) A
5) D
6) D
7) A
C
9) B