GMAT Problem Solving Discussions

Hello Guys..

Need your help in the answers for the following questions:

Q1. 6 hrs from now, the population of a colony of bacteria will be 2.56 x 10 to the power 7. If the population of the bacteria colony doubles every 3 hrs, how many hours ago did the population surpass 100,000 ?
A. 9
B. 18
C. 21
D. 27
E. 33

Q2. If r+s+p > 1, is p > 1 ?
(1) p > r+s-1
(2) 1 -(r+S) > 0

i seem to be contradicting with the answers proposed and would like your help in confirming that.:bigear:

For both I think B.......

Hi All, analytical expln. to the problem:

See if this makes sense to you guys....
Eqn. of a circle is (x-a)^2 + (y-b)^2 = R^2 where (a,b) is the center of the circle.
(N.B. - ^ denotes to the power)
now (4,0) and (-4,0) are pts. on the circle. Therefore,
(4-a)^2 + (0-b)^2 = R^2 ........................(1)
(-4-a)^2 + (0-b)^2 = R^2 .......................(2)

(1) - (2) gives : a = 0.
therefore . eqn. 1 or 2 reduces to 16 + b^2 = R^2. Since b^2 is always a positive quantity, R will have a bigger value , bigger the value of b.

So the answer would be (E).

Srry for posting to a older problem

Hi All, analytical expln. to the problem:

See if this makes sense to you guys....
Eqn. of a circle is (x-a)^2 + (y-b)^2 = R^2 where (a,b) is the center of the circle.
(N.B. - ^ denotes to the power)
now (4,0) and (-4,0) are pts. on the circle. Therefore,
(4-a)^2 + (0-b)^2 = R^2 ........................(1)
(-4-a)^2 + (0-b)^2 = R^2 .......................(2)

(1) - (2) gives : a = 0.
therefore . eqn. 1 or 2 reduces to 16 + b^2 = R^2. Since b^2 is always a positive quantity, R will have a bigger value , bigger the value of b.

So the answer would be (E).
Hello Guys..

Need your help in the answers for the following questions:

Q1. 6 hrs from now, the population of a colony of bacteria will be 2.56 x 10 to the power 7. If the population of the bacteria colony doubles every 3 hrs, how many hours ago did the population surpass 100,000 ?
A. 9
B. 18
C. 21
D. 27
E. 33

Q2. If r+s+p > 1, is p > 1 ?
(1) p > r+s-1
(2) 1 -(r+S) > 0

i seem to be contradicting with the answers proposed and would like your help in confirming that.:bigear:


Agreed ans. are:
B). and B).
Here are my answer choices:-

1 (B)
2 (B) - doubtful
3 (D) - doubtful
4 (E)
5 (A)

What are the OAs?!


The OAs are
1 (B)
2 (B)
3 (D)
4 (E)
5 (A)

Can someone please provide the reasoning?

Regards
MSD
ashishjha100 Says
What r the OAs......if my choices r correct i'll give reasoning......

Yes, your answer choices are correct. Plz provide the explanation.

Regards
MSD

Q. A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them i a row, what is the probability that the 2 rosebushes in the middle of the row will be red?

A. 1/12 B.1/6 C.1/5 D.1/3 E.1/2

The OA is B i.e 1/6
However, I derived 1/12 as the answer. 4 rosebushes will have 4! ways of arranging. There can be 2 possible arrangements for the red rosebushes to be in the middle of the row i.e. W1, R1,R2, W2 or W1, R2, R1, W2.
Hence, number of possibilities is 2/4! = 1/12
Can anyone please point out my mistake?

Regards
MSD

Q. If x>0, then 1/ =

A.1/v(3x) B.1/2v(2x) C.1/(xv2) D.(v2-1)/vx E.(1+v2)/vx

I am getting A as the answer. However, the OA is D.
Donno how can that be arrived at? Please help.

Help needed with the following data suffienciency questions.

Q1. What is the median no. of employees assigned per project for projects at Company Z
1.25% of the projects at Company Z have 4 or more employees assigned to each project
2.25 % of the projects at Company Z have 2 or fewer employees assigned to each project

Q2.In the xy plane, point(r,s) lies on the circle with its center at the origin. What is the value of r2+s2 ?
1.The circle has radius 2
2.The point (v2, -v2) lies on the circle

Regards
MSD

New post below.......

Help needed with the following data suffienciency questions.

Q1. What is the median no. of employees assigned per project for projects at Company Z
1.25% of the projects at Company Z have 4 or more employees assigned to each project
2.25 % of the projects at Company Z have 2 or fewer employees assigned to each project

Q2.In the xy plane, point(r,s) lies on the circle with its center at the origin. What is the value of r2+s2 ?
1.The circle has radius 2
2.The point (v2, -v2) lies on the circle

Regards
MSD

1.C

let that company has 20 projects.....

1.25% of the projects at Company Z have 4 or more employees assigned to each project
ie 5 projects have 4 or more employees. Not sufficient so BCE

2.25 % of the projects at Company Z have 2 or fewer employees assigned to each project
ie 5 projects have 2 or fewer employees. Not sufficient so CE

Combining, the rest of the projects have 3 employees each......ie projects from 6-15
so median is the average no: of employees in 10& 11th project and it is 3 employees...... SO ans C

2.is r^2+s^2?
Q. A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them i a row, what is the probability that the 2 rosebushes in the middle of the row will be red?

A. 1/12 B.1/6 C.1/5 D.1/3 E.1/2

The OA is B i.e 1/6
However, I derived 1/12 as the answer. 4 rosebushes will have 4! ways of arranging. There can be 2 possible arrangements for the red rosebushes to be in the middle of the row i.e. W1, R1,R2, W2 or W1, R2, R1, W2.
Hence, number of possibilities is 2/4! = 1/12
Can anyone please point out my mistake?

Regards
MSD

OA is correct......

Your mistake is ....u dont considered 2 more possible arrangements ie total 4 arrangements....(W1, R1,R2, W2), (W1, R2, R1, W2), (w2,R1,R2,W1) & (w2,R2,R1,W1)

So total probability = 4/4!= 1/6

Hope this clears ur doubt...........

I think the arrangement we are looking for here is W R R W

Probability of picking 1 W out of the 4 rose bushes = 2/4
Probability of picking 1 R out of the remaining 3 rose bushes = 2/3
Probability of picking 1 R out of the remaining 2 rose bushes = 1/2
Probability of picking 1 W out of 1 rose bush left = 1/1

Therefore total probability of this arrangement occurring =

W R R W = (2/4) * (2/3) * (1/2) * (1/1) = 1/6

Plz correct me if i'm wrong!

Q. A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them i a row, what is the probability that the 2 rosebushes in the middle of the row will be red?

A. 1/12 B.1/6 C.1/5 D.1/3 E.1/2

The OA is B i.e 1/6
However, I derived 1/12 as the answer. 4 rosebushes will have 4! ways of arranging. There can be 2 possible arrangements for the red rosebushes to be in the middle of the row i.e. W1, R1,R2, W2 or W1, R2, R1, W2.
Hence, number of possibilities is 2/4! = 1/12
Can anyone please point out my mistake?

Regards
MSD

1) There are 4^3 ways of posting 3 letters in 4 letter boxes = 64 ways. But 64 includes the number of ways by which all the letters can be put in 1 letter box. There are 4 ways in which all letters can be put into each of the letter boxes. Therefore 64-4 = 60 is your answer.

2) Probability of selecting a red marble first = 4/16
Probability of selecting a blue marble next = 3/15

Therefore total probability of selecting a red marble first followed by a blue marble = (4/16)*(3/15) = 1/20

3) The number of unique signals that can be made using 4 flags - refers to the number of possible unique arrangements of the 4 flags. This can be given by 4! = 24. Therefore there are 24 ways of arranging 4 flags.

4)
--> Given: Y takes "d" days to produce "w"
--> Given: X takes "d+2" days to produce "w"
--> Given: X+Y take 3 days to produce 5w/4
--> Therefore, X+Y take 12/5 days to produce "w"
(ensure that the quantity produced is the same by X & Y working together and alone)

1/(X+Y) = (1/X) + (1/Y) (Solve to get d = 4 days)

X days "d+2" days to produce "w" --> 6 days to produce "w"
Therefore to produce "2w" it will take 6*2 = 12 days.

5) Plz refer to page 104 in this forum where the question has been discussed in detail.

The OAs are
1 (B)
2 (B)
3 (D)
4 (E)
5 (A)

Can someone please provide the reasoning?

Regards
MSD

I also tend to agree with B as the answer for Question 1, but for q2, why not E.
E.g. if r+s =0.7 which satisfies the condition r+s 1 or p could be 1.5 which again satisfied p+r+s > 1. So we cannot say for sure that condition 2 is sufficient. What do you think ?

ashishjha100 Says
For both I think B.......

I also tend to agree with B as the answer for Question 1, but for q2, why not E.
E.g. if r+s =0.7 which satisfies the condition r+s 1 or p could be 1.5 which again satisfied p+r+s > 1. So we cannot say for sure that condition 2 is sufficient. What do you think ?
ashishjha100 Says
New post below.......


Quote:
Originally Posted by msd_2008 View Post
Help needed with the following data suffienciency questions.

Q1. What is the median no. of employees assigned per project for projects at Company Z
1.25% of the projects at Company Z have 4 or more employees assigned to each project
2.25 % of the projects at Company Z have 2 or fewer employees assigned to each project

Q2.In the xy plane, point(r,s) lies on the circle with its center at the origin. What is the value of r2+s2 ?
1.The circle has radius 2
2.The point (v2, -v2) lies on the circle

Regards
MSD


1.Ans is C

lets consider this situation with 20 projects so

1.25% of the projects at Company Z have 4 or more employees assigned to each project
ie 5 projects have 4 or more employees . Not sufficient so BCE

2.25 % of the projects at Company Z have 2 or fewer employees assigned to each project
ie 5 projects have 2 or fewer employees. Not sufficient so CE

Combining the rest(middle) 15 projects of company has 3 employees each....
So median value is the employee in 10th project it is obviously 3

So ans is C

ashishjha100, I guess the answer should be E
as if take your case as total number is even the median will be mean of 10th and 11th project which will be (3+(4+n))/2. as we dont know n so we can not find median number of employees

Please correct me if i am not
Quote:
Originally Posted by msd_2008 View Post
Help needed with the following data suffienciency questions.

Q1. What is the median no. of employees assigned per project for projects at Company Z
1.25% of the projects at Company Z have 4 or more employees assigned to each project
2.25 % of the projects at Company Z have 2 or fewer employees assigned to each project

Q2.In the xy plane, point(r,s) lies on the circle with its center at the origin. What is the value of r2+s2 ?
1.The circle has radius 2
2.The point (v2, -v2) lies on the circle

Regards
MSD


1.Ans is C

lets consider this situation with 20 projects so

1.25% of the projects at Company Z have 4 or more employees assigned to each project
ie 5 projects have 4 or more employees . Not sufficient so BCE

2.25 % of the projects at Company Z have 2 or fewer employees assigned to each project
ie 5 projects have 2 or fewer employees. Not sufficient so CE

Combining the rest(middle) 15 projects of company has 3 employees each....
So median value is the employee in 10th project it is obviously 3

So ans is C

ashishjha100, I guess the answer should be E
as if take your case as total number is even the median will be mean of 10th and 11th project which will be (3+(4+n))/2. as we dont know n so we can not find median number of employees

Please correct me if i am not

Dear Inder,
i used an example for easier understanding.......consider case as such....from the combination of 2 statements we can know the no: of employees in remaining 50% projects is 3 (b/c 25% has 2 or fewer and 25 % has 4 or more)
By considering any ways the median comes in the group of 50% projects and the only no: of employees in this 50% group is 3 so median is 3.....just consider with odd or even no: of projects.....

Hope this will help........

A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related
linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of
30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100
on the S-scale?
A. 20
B. 36
C. 48
D. 60
E. 84

Ans is C.48

S=aR + c

Put S=60,R=24 & S=30,R=6 to get two linear equations in two variables.

a=5/3 c=20

Then S=(5/3)*R + c
for S=100, R comes as 48

How did u come to S=aR + c.?.........didn't understand......pls help..