GMAT Problem Solving Discussions

MBA
2881
IMO: C

1. Given p/q = r/s Lets pick numbers here, p=140, q = 10, r = 14, s = 1. Suffices p/q=r/s, but r is not divisible by 5.

Au Contraire': 140,7,20,1 suffices p/q=r/s and r is divisible by 5.
So, NOT SUFF

2. q = 7^x, => q can be 1, 7,49,....
does not help by itself. NOT SUFF

1 and 2 together: p/q will be 140 X n / 7^x. for n = 1 and x = 1 lets say, p/q will be 140. For any combination of n and x, there will always be a number r which will be a multiple of 5 as 140 is 7 X 20.
So Together SUFF.


Hi Vikram,

Please correct me if I am wrong......for n=2 and x=2 the number will be 40/7.....hw come it be a multiple of 5????

:shocked:
2882
My take is C
Waiting for OA



Dude......the OA is E

Here it goes....

Let Henry's Income be - n
If he saves - s
He'll spend - (n-s)

Next yr ->
For every 1 $ - $ to spend
So, for s $ - ?

= s which is equal to 1/2(n-s) {half he spends this yr}

We need to find what fraction of his income shd he save this yr..
i.e s/n = ??

Solving -

s = 1/2
2 = /s
2+2r = n/s - 1

2r+3 = n/s

s/n = 1/

2883
Hi Vikram,

Please correct me if I am wrong......for n=2 and x=2 the number will be 40/7.....hw come it be a multiple of 5????

:shocked:


Hi motivation,
Here is the Question again...

p,q,r.s are +ve integers, if p/q = r/s, is r divisible by 5?

1) p is a multiple of 140
2) Q = 7^x


for n=2, and x=2, r/s as you stated will be 40/7. We are NOT looking for that to be a multiple of 5, the Question asks if "r" is a multiple of 5, and r is 40 which is divisible by 5.
2884
Hi motivation,
Here is the Question again...

p,q,r.s are +ve integers, if p/q = r/s, is r divisible by 5?

1) p is a multiple of 140
2) Q = 7^x


for n=2, and x=2, r/s as you stated will be 40/7. We are NOT looking for that to be a multiple of 5, the Question asks if "r" is a multiple of 5, and r is 40 which is divisible by 5.


Thanx vikram,,

I got that.....:)
2885

Originally Posted by amsey1382 View Post
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the stores revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?
A. 100p / (125 p)
B. 150p / (250 p)
C. 300p / (375 p)
D. 400p / (500 p)
E. 500p / (625 p)


Total no.of copies sold = Copies of A + Copies of B------ (1)
Total revenues = Revenue of A + Revenue of B --------(2)

Copies sold = a+b
Revenues(m) = 1*a + 1.25*b

So , a/(a+b) *100 = p

a/(a+1.25b) = r

From the options only option 4 correctly represents r interms of p.So I will go with option 4

Ans is D...

I made the equations and tried to solve it....and then later tried to do with answer matching...i guess thats the best approach....got this a test paper...


Hi Deepak,

Can you please how come you arrive at option D

I think i stuck somewhere and not moving forward......
2886

Hi Motivation,
I also formed the eqn and went thru the substitution of the options.That will save a lot of time.

2887
Guys... i know this is a reply to old post... but i was not able to solve this and the guy who solved this ,I couldnt understand his analysis...

Can anyone throw some light on this problem?

Originally Posted by nairpraveenk View Post
Fundoo problem
-------------------

Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.

(2) The distance between New York and Boston is greater than 140 miles.

(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.


The answer should be D (Each statement ALONE is sufficient.)
Guys, here is the detailed explanation.

Train A leaves New York at 3 PM and passes Train B an hour later. i.e. 4 PM.

Let us say the speed of Train B is S m/h.
And the distance travelled by Train B before it meets Train A is D miles.

Since, Train A takes 1 hr to meet Train B, it travels 100 miles before the meeting point.
So, total distance between New York and Boston is (100+D) miles.

New York Boston
.......................100 miles...............Meet........D miles
...................................................4 PM

Since Train B leaves Boston at 3.50 PM, it takes 10 mins to meet Train A.

=> S=D/(10 mins)
=> S=(60*D)/10 (converting to hours)
=> S=(6*D) -------------- (1)

Also it is given that the combined travel time is 2 hrs.

Travel time for Train A = (100+D)/100
Travel time for Train B = (100+D)/S

Travel time for Train A + Travel time for Train B = 2 hrs
=> ((100+D)/100) + ((100+D)/S) = 2 -------------- (2)

Solving equation (1) and (2),
=> 3D^2 - 250*D + 5000 = 0
=> D = 50 or D = 100/3
and
=> S = 300 or S = 200 repectively.

Now coming to the options,

(1) Train B arrived in New York before Train A arrived in Boston.
If D=50, S=300 and Total Distance = 150 m.
So, Train B takes total 30 mins to reach New York. i.e. It reaches at 4.20 PM
And Train A takes total 90 mins to reach Boston. i.e. It reaches at 4.30 PM

If D=100/3, S=200 and Total Distance = 400/3 m.
So, Train B takes total 40 mins to reach Boston. i.e. It reaches at 4.30 PM
And Train A takes total 80 mins to reach Boston. i.e. It reaches at 4.20 PM

Since, Train B arrived in New York before Train A arrived in Boston, Train B must have reached New York at 4.20 PM.
SUFFICIENT.

(2) The distance between New York and Boston is greater than 140 miles.
If D=50, total distance is 150 m. (>140 m)
If D=100/3, total distance is ~133.33 m. (This means that D=50, S=300 and total distance is 150 m.
So, Train B takes total 30 mins to reach New York. i.e. It reaches at 4.20 PM
SUFFICIENT.

Cheers! 😃
2888
The answer should be D (Each statement ALONE is sufficient.)
Guys, here is the detailed explanation.

Train A leaves New York at 3 PM and passes Train B an hour later. i.e. 4 PM.

Let us say the speed of Train B is S m/h.
And the distance travelled by Train B before it meets Train A is D miles.

Since, Train A takes 1 hr to meet Train B, it travels 100 miles before the meeting point.
So, total distance between New York and Boston is (100+D) miles.

New York Boston
.......................100 miles...............Meet........D miles
...................................................4 PM

Since Train B leaves Boston at 3.50 PM, it takes 10 mins to meet Train A.

=> S=D/(10 mins)
=> S=(60*D)/10 (converting to hours)
=> S=(6*D) -------------- (1)

Also it is given that the combined travel time is 2 hrs.

Travel time for Train A = (100+D)/100
Travel time for Train B = (100+D)/S

Travel time for Train A + Travel time for Train B = 2 hrs
=> ((100+D)/100) + ((100+D)/S) = 2 -------------- (2)

Solving equation (1) and (2),
=> 3D^2 - 250*D + 5000 = 0
=> D = 50 or D = 100/3
and
=> S = 300 or S = 200 repectively.

Now coming to the options,

(1) Train B arrived in New York before Train A arrived in Boston.
If D=50, S=300 and Total Distance = 150 m.
So, Train B takes total 30 mins to reach New York. i.e. It reaches at 4.20 PM
And Train A takes total 90 mins to reach Boston. i.e. It reaches at 4.30 PM

If D=100/3, S=200 and Total Distance = 400/3 m.
So, Train B takes total 40 mins to reach Boston. i.e. It reaches at 4.30 PM
And Train A takes total 80 mins to reach Boston. i.e. It reaches at 4.20 PM

Since, Train B arrived in New York before Train A arrived in Boston, Train B must have reached New York at 4.20 PM.
SUFFICIENT.

(2) The distance between New York and Boston is greater than 140 miles.
If D=50, total distance is 150 m. (>140 m)
If D=100/3, total distance is ~133.33 m. (This means that D=50, S=300 and total distance is 150 m.
So, Train B takes total 30 mins to reach New York. i.e. It reaches at 4.20 PM
SUFFICIENT.

Cheers! :)


Wow...
Excellent Explanation dude !!!
2889

Old Problem: I was not abel to solve this... want to have discussion on this..
A certain city wid a population of 132000 is to be didvided into 11 districts and no district shuould have a populatn that is 10% greater than population of any other district wat is the min populn that the least populated district could have ?


A)10700
B)10800
C)10900
D)11000
E)11100

2890

Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

a. 78
b. 77 1/5
c. 66 1/7
d. 55 1/7
e. 52

2891

If n is a non-negative integer such that 12^n is a divisor of 3,176,793, what is the value of n^12 - 12^n ?

a. -11
b. -1
c. 0
d. 1
e. 11

2892
If n is a non-negative integer such that 12^n is a divisor of 3,176,793, what is the value of n^12 12^n ?

a. -11
b. -1
c. 0
d. 1
e. 11



IMO B

because

for 3/12^n can only be satisfied when we have n=0.

so 0-1=-1.
2893
IMO B

because

for 3/12^n can only be satisfied when we have n=0.

so 0-1=-1.


Why u want to satisfy 3/12^n?
2894

Ans D
Let the population of the least populated district be x. And that of remaining be 1.1x. Forming tha equation we get 12x = total population. Hence x is 11000


Old Problem: I was not abel to solve this... want to have discussion on this..
A certain city wid a population of 132000 is to be didvided into 11 districts and no district shuould have a populatn that is 10% greater than population of any other district wat is the min populn that the least populated district could have ?


A)10700
B)10800
C)10900
D)11000
E)11100
2895
Ans D
Let the population of the least populated district be x. And that of remaining be 1.1x. Forming tha equation we get 12x = total population. Hence x is 11000


Thats the correct answer !!!
2896
Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

a. 78
b. 77 1/5
c. 66 1/7
d. 55 1/7
e. 52


My take is B

here for max possible range the numbers should be.
x,x+1, 55,56,3x+20

as the mean is 55
5x+132/5 =55
=> x=28.6

so rage is x---------3x+20
=> 2x+20 =77.2= 77 1/5
2897
If n is a non-negative integer such that 12^n is a divisor of 3,176,793, what is the value of n^12 12^n ?

a. -11
b. -1
c. 0
d. 1
e. 11


Hey is the question correct..???
12^n is always an even number & 3,176,793 is an odd number.

now how is that possible that an even No is a factor of an odd no.......??:banghead:
2898

Need Some help -

I get a lil confused with 3 sets.
Is the below formula correct
n(AUBUC)=n(A)+n(B)+n(C)-n(AnB)-n(AnC)-n(BnC)+n(AnBnC)???

It'd be nice if someone can explain!!

Thanks in advance!

2899

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

A) x = w
B) x > w
C) x/y is an integer
D) w/z is an integer
E) x/z is an integer

2900

For the below q ,I solved them as AP and took the nos as 55-2d,55-d,55,55+d,55+2d.
so 55+2d = 3(55-2d) + 20
d = 16.25

so the nos are 22.75,38.75,55,71.25,87.5.
so range i'm getting is 64.75.
Wats wrong in the above workout?