GMAT Problem Solving Discussions

MBA
1387

Hi, I thought the Answer is (C) --> 1/2... can someone plz tell me where i went wrong?! this is what i did :-

n(n+1)(n+2) will be divisible by all even numbers, multiples of 8 and numbers which are of the form 8k-1. Here's my reasoning:-

Total no. of integers from 1 to 96 = 96.

Count all multiples of 8 between 1 & 96 --> 8, 16, 24 ... 96 (there will be 12 in all)

Next, count all even numbers between 1 & 96 (inclusive) -> there will be 48 in all. To ensure there is no double counting of integers, the total no. of integers divisible by 8 so far will be 48-12 = 36.

Note that when n = 7, n+1 = 8 (which makes n(n+1)(n+2) divisible by 8 ). Therefore, I counted all numbers of the form 8k-1 --> 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95. That makes a total of 12 numbers.

Summing them up -> the total no. of integers divisible by 8 = 36+12 = 48.

Therefore, probability = 48/96 = 1/2.


If an integer n is to be chosen at random from the integers 1 to 96 inclusive, what is the probability that n(n+1)(n+2) will be divisble by 8?

A . 1/4
B. 3/8
C. 1/2
D. 5/8
E. 3/4
1388
yeah the answer is D. 5/8
can u pls explain it?

For every n which is even n(n+1)(n+2) is divisible by 8 --->so 48 no: of n's

Also the odd n(7,15,23...) which is just above the multiple of 8(8,16,24....) n(n+1)(n+2) is divisible by 8 -----> so 12 no: of n's

so total probability = (12+4/96 =5/8
1389

Oh! I get it.. thinking that I was double counting the multiples of 8 from 1-96 i subtracted them from the total number of even integers!.. So i was 12 short. Thanks!

For every n which is even n(n+1)(n+2) is divisible by 8 --->so 48 no: of n's

Also the odd n(7,15,23...) which is just above the multiple of 8(8,16,24....) n(n+1)(n+2) is divisible by 8 -----> so 12 no: of n's

so total probability = (12+4/96 =5/8
1390
Please help with the following DS questions from Gmat Prep:

Q.I In a xy-plane, does the line with equation y=3x+2 contain the point (r,s)?
1. (3r+2-s) (4r+9-s) = 0
2. (4r-6-s) (3r+2-s) = 0

Q.II A manufacturer conducted a survey to determine how many people buy products P & Q. What fraction of people surveyed said that they buy neither product P nor product Q?
1. 1/3 of the people surveyed said that they buy product P but not Product Q
2. 1/2 of the people survey said that they buy product Q

Q.III During a 80 mile trip Marla travelled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x miles per hour for the last 40-y miles of the trip. The time that Marla too to travel the 40 miles was what percent of the time it would have taken her if she had traveled at an average speed of x miles per hour for the entire trip?
1. x = 48
2. y = 20

Regards
MSD

OA to ques no 2 is E

Let x be the no of ppl surveyed
Stem 1: only P = x/3........not suff
Stem 2: n(Q)= x/2...........not suff

Combining both:

Since we do not know how many ppl bought both pdt P and Q, it's not possible to find the no. of ppl who bought neither.


MSD: While we post replies to other problems, can u let us know the OA for this ques at least....

Regards,
1391
OA to ques no 2 is E

Let x be the no of ppl surveyed
Stem 1: only P = x/3........not suff
Stem 2: n(Q)= x/2...........not suff

Combining both:

Since we do not know how many ppl bought both pdt P and Q, it's not possible to find the no. of ppl who bought neither.


MSD: While we post replies to other problems, can u let us know the OA for this ques at least....

Regards,


Srikanth,

The question doesnt ask for the number of people. It asks for the fraction of the people of those surveryed who dont buy either product. Since the number of people is not required, we can get the answer by combining the two statements. Hence, C is the answer.
1392
Please help with the following DS questions from Gmat Prep:

Q.I In a xy-plane, does the line with equation y=3x+2 contain the point (r,s)?
1. (3r+2-s) (4r+9-s) = 0
2. (4r-6-s) (3r+2-s) = 0

Q.II A manufacturer conducted a survey to determine how many people buy products P & Q. What fraction of people surveyed said that they buy neither product P nor product Q?
1. 1/3 of the people surveyed said that they buy product P but not Product Q
2. 1/2 of the people survey said that they buy product Q

Q.III During a 80 mile trip Marla travelled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x miles per hour for the last 40-y miles of the trip. The time that Marla too to travel the 40 miles was what percent of the time it would have taken her if she had traveled at an average speed of x miles per hour for the entire trip?
1. x = 48
2. y = 20

Regards
MSD

For 3 i think ans is B.
1393
ashishjha100 Says
For 3 i think ans is B.

Ya, I agree with B...
1394
Please help with the following DS questions from Gmat Prep:

Q.I In a xy-plane, does the line with equation y=3x+2 contain the point (r,s)?
1. (3r+2-s) (4r+9-s) = 0
2. (4r-6-s) (3r+2-s) = 0

Q.II A manufacturer conducted a survey to determine how many people buy products P & Q. What fraction of people surveyed said that they buy neither product P nor product Q?
1. 1/3 of the people surveyed said that they buy product P but not Product Q
2. 1/2 of the people survey said that they buy product Q

Q.III During a 80 mile trip Marla travelled at an average speed of x miles per hour for the first y miles of the trip and at an average speed of 1.25x miles per hour for the last 40-y miles of the trip. The time that Marla too to travel the 40 miles was what percent of the time it would have taken her if she had traveled at an average speed of x miles per hour for the entire trip?
1. x = 48
2. y = 20

Regards
MSD


I'll try to give my answers and explanations for 1st and 2nd -

I. does the line with equation y=3x+2 contain the point (r,s) ? The point (r,s) will be on the line iff this point satisfy the line's equation i.e. s = 3r+2 => 3r+2-s = 0.

Considering option A : (3r+2-s) (4r+9-s) = 0. Any of the expression (3r+2-s) or (4r+9-s) could be zero so Not sufficient.

Considering option B : (4r-6-s) (3r+2-s) = 0 Again, any of the expression could be zero so Not sufficient.

Considering option A and B : If (3r+2-s) is not zero then both (4r+9-s) and (4r-6-s) should be zero and hence they should be equal => (4r+9-s) = (4r-6-s) and thats not possible so, (3r+2-s) has to be zero. Sufficient.

Answer should be C.
II. We just have to calculate the fraction of people who neither buy product P nor product Q.
option A and B are not sufficient by themselves but when we'll consider them both together, we can calculate fraction of people who buy P, Q and both (x/3 + x/2 = 5x/6). So, the remaining x/6 people neither buy P nor Q.
Answer should be C.

Please let us know the OAs.
1395

Pls help:huh:

1396
ashishjha100 Says
Pls help:huh:

GMP1 - Here are my answers with explanations -

I. considering option A : number of cups of flour = 2.5(number of cups of sugar) So, the ratio of number of cups of flour to the numbse of cups of sugar is 2.5 . Sufficient.
Considering option B : number of cups of flour = number of cups of sugar + 3/2 . this will only give the difference between number of cups but not the ratio. Not sufficient.

Answer should be A.
II. Considering option A : r+s=1. There is no information about coordinate (u,v) so can not decide anything. Not sufficient.
Consider option B : r+u=1 and s+v=1. That means if the coordinate (r,s) = (2,-1) then (u,v) = (-1,2). And both these points are equi-distant from the origin. Sufficient.

Answer should be B.
III. Considering option A : n^2/36 = integer => the least value of n^2 will be 36 i.e n = 6 which is divisible by 3. All higher values of n^2 should have atleast 2 3's (because divisor 36 has 2 3's). Sufficient
Consider option B : 144/n^2 = integer => (2^4.3^2)/n^2 = integer. n could be 2 and the expression will give an integer but 2 is not divisible by 3. Whereas n = 3 also satisfies this expression. hence, we can not reach to a definite answer. not sufficient.

Answer should be A.
IV. When y intercept of line is 4 (i.e positive) and line has negative slope then x intercept has to be positive only.
Please refer to figure attached, all the lines drawn satisfy the criteria (y intercept = 4 and slope = -ve) and everyone should cut X axis in positive direction only. So x intercept has to be greater than zero.

Hence answer should be C i.e. III only.

V. Options are not suffcient individually but when you'll combine them -
Total cost = 8P + 25H (where P and H are number of paper and hardcover books respectively)
Paperback books should be more than 10 (P>10)
Total cost of hardover books was atleast 150 (i.e H >=6)
total cost of all books is less than 260 i.e. (8P + 25H Only one criteria - H = 6 can satisfy all these conditions, no. of paper books (P) can be 10 or 11 but H can not exceed 6. So, Juan bought 6 hardcover books.

Answer should be C.

Please let us know the OAs.
Ashutosh
1397
GMP1 - Here are my answers with explanations -

I. considering option A : number of cups of flour = 2.5(number of cups of sugar) So, the ratio of number of cups of flour to the numbse of cups of sugar is 2.5 . Sufficient.
Considering option B : number of cups of flour = number of cups of sugar + 3/2 . this will only give the difference between number of cups but not the ratio. Not sufficient.

Answer should be A.
II. Considering option A : r+s=1. There is no information about coordinate (u,v) so can not decide anything. Not sufficient.
Consider option B : r+u=1 and s+v=1. That means if the coordinate (r,s) = (2,-1) then (u,v) = (-1,2). And both these points are equi-distant from the origin. Sufficient.

Answer should be B.
III. Considering option A : n^2/36 = integer => the least value of n^2 will be 36 i.e n = 6 which is divisible by 3. All higher values of n^2 should have atleast 2 3's (because divisor 36 has 2 3's). Sufficient
Consider option B : 144/n^2 = integer => (2^4.3^2)/n^2 = integer. n could be 2 and the expression will give an integer but 2 is not divisible by 3. Whereas n = 3 also satisfies this expression. hence, we can not reach to a definite answer. not sufficient.

Answer should be A.
IV. When y intercept of line is 4 (i.e positive) and line has negative slope then x intercept has to be positive only.
Please refer to figure attached, all the lines drawn satisfy the criteria (y intercept = 4 and slope = -ve) and everyone should cut X axis in positive direction only. So x intercept has to be greater than zero.

Hence answer should be C i.e. III only.

V. Options are not suffcient individually but when you'll combine them -
Total cost = 8P + 25H (where P and H are number of paper and hardcover books respectively)
Paperback books should be more than 10 (P>10)
Total cost of hardover books was atleast 150 (i.e H >=6)
total cost of all books is less than 260 i.e. (8P + 25H Only one criteria - H = 6 can satisfy all these conditions, no. of paper books (P) can be 10 or 11 but H can not exceed 6. So, Juan bought 6 hardcover books.

Answer should be C.

Please let us know the OAs.
Ashutosh

OAs are in the question with a blue quare marking on it.......Thanks Dopa for ur explanation.....only 2nd question has a different OA.(C)
1398
ashishjha100 Says
For 3 i think ans is B.


Yes. The answer is indeed B for Q III. Can you please provide an explanation?

Regards
MSD
1399
I'll try to give my answers and explanations for 1st and 2nd -

I. does the line with equation y=3x+2 contain the point (r,s) ? The point (r,s) will be on the line iff this point satisfy the line's equation i.e. s = 3r+2 => 3r+2-s = 0.

Considering option A : (3r+2-s) (4r+9-s) = 0. Any of the expression (3r+2-s) or (4r+9-s) could be zero so Not sufficient.

Considering option B : (4r-6-s) (3r+2-s) = 0 Again, any of the expression could be zero so Not sufficient.

Considering option A and B : If (3r+2-s) is not zero then both (4r+9-s) and (4r-6-s) should be zero and hence they should be equal => (4r+9-s) = (4r-6-s) and thats not possible so, (3r+2-s) has to be zero. Sufficient.

Answer should be C.
II. We just have to calculate the fraction of people who neither buy product P nor product Q.
option A and B are not sufficient by themselves but when we'll consider them both together, we can calculate fraction of people who buy P, Q and both (x/3 + x/2 = 5x/6). So, the remaining x/6 people neither buy P nor Q.
Answer should be C.

Please let us know the OAs.


You've got them correct. The OAs for both the questions are C.
1400
ashishjha100 Says
For 3 i think ans is B.



total time for journey = t1+t2

t1= y/x
t2=(40-y)/1.25x

required fraction= (t1+t2)/t

t=40/x

substituting

required fraction= (y/x + (40-y)/1.25x)/(40/x)
= (y + (40-y)/1.25)/40

so only y is required......:-o
1401

Hey.. can you plz help me with these questions? Thanks a ton!

1. A new fast growing strain of yeast cells reproduces every two minutes. Thus, one yeast cell becomes two yeast cells after 2 mins, four after 4 mins, eight after 8 mins and so on. If one newly divided cell is placed in a rectangular vat 6 inches by 8 inches by 12 inches, and after one hour, the vat i full of yeast, how long did it take to fill half the vat?

A) 15 min B) 24 min C) 30 min D) 48 min E) 58 min
------------------------------------------------------------------------
2. A group of investors purchased an apartment building that returned total net income over a 10 year period equal to the original $414000 investment. If expenses consumed 25% of the annual gross income from the building, what was the average annual gross income for the building over the 10 year period?

A) $10350 B) $41400 C)$51750 D) $55200 E) $103500
------------------------------------------------------------------------

1402

1. A new fast growing strain of yeast cells reproduces every two minutes. Thus, one yeast cell becomes two yeast cells after 2 mins, four after 4 mins, eight after 8 mins and so on. If one newly divided cell is placed in a rectangular vat 6 inches by 8 inches by 12 inches, and after one hour, the vat i full of yeast, how long did it take to fill half the vat?

A) 15 min B) 24 min C) 30 min D) 48 min E) 58 min


arch,
is it 6 or 8 min.....if it is 6 i think 58 min....wats OA?

1403

2. A group of investors purchased an apartment building that returned total net income over a 10 year period equal to the original $414000 investment. If expenses consumed 25% of the annual gross income from the building, what was the average annual gross income for the building over the 10 year period?

A) $10350 B) $41400 C)$51750 D) $55200 E) $103500

wats OA?

1404

Hi,

Ashish..How did u get 51750..Can u provide exp for this......


Regards
Phani Madhav

1405

Hey.. OA's are:-
Q 1 (E)
Q 2 (D)

Can you plz provide explanation for Q1? Thanks!

2. A group of investors purchased an apartment building that returned total net income over a 10 year period equal to the original $414000 investment. If expenses consumed 25% of the annual gross income from the building, what was the average annual gross income for the building over the 10 year period?

A) $10350 B) $41400 C)$51750 D) $55200 E) $103500

wats OA?
1406
Hey.. OA's are:-
Q 1 (E)
Q 2 (D)

Can you plz provide explanation for Q1? Thanks!

After 1 hr no: of yeast cells are 2^30 (since xplying every 2 minutes)

so half of 2^30 = 2^29

it will be in 58th minutes(29*2)