GMAT Problem Solving Discussions

MBA
2217
A man cycling along the road noticed that every 12 minutes a bus overtakes him while every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at constant speed, what is the time interval between consecutive buses?

* 5 minutes
* 6 minutes
* 8 minutes
* 9 minutes
* 10 minutes

Option C
8 minutes

what's the answer..??..
2218
vikas130678 Says
5 minutes?

Option C
8 minutes

what's the answer..??..


Two answers and NO explanations ....

sorry to say guys, both are wrong

here is the solution

bus speed = b
cyclist speed = c
time difference between buses = t
distance between the buses = bt

in same direction : bt = 12 * (b-c)
in opposite direction : bt = 4 * (b+c)
12(b-c) = 4(b+c)
3b - 3c = b + c
b = 2c

bt = 2ct = 12 (2c - c)

t = 6 ... option B
2219
Two answers and NO explanations ....

sorry to say guys, both are wrong

here is the solution

bus speed = b
cyclist speed = c
time difference between buses = t
distance between the buses = bt

in same direction : bt = 12 * (b-c)
in opposite direction : bt = 4 * (b+c)
12(b-c) = 4(b+c)
3b - 3c = b + c
b = 2c

bt = 2ct = 12 (2c - c)

t = 6 ... option B


very nice questions n nicely explained as well:clap:
2220
An unusually strong cyclist can, it is hoped, provide enough power to set

Ancient Romans found it therapeutic to bathe in cold milk, in strawberries that had been crushed, or in bathtubs filled with black caviar.
(A) to bathe in cold milk, in strawberries that had been crushed, or in bathtubs filled with black caviar
(B) that they bathe in cold milk, in strawberries that had been crushed, or in caviar that was black-awkward
(C) to bathe in cold milk, crushed strawberries, or black caviar - Maintains Prallelism
(D) that they bathe in cold milk, crushed strawberries, or black caviar-Awkward
(E) to bathe in milk , strawberries, or caviar -COLD is missing, thus the original intent is changed

PPL, PLZZZZ Post the Correct answers, so That I could validate my clap-trap ;)


I doubt if paralleslism is maintained in C,..So to bring the proper comparision.."in" preposition is needed before each of the options..to take the whole phrase followed by the Verb..
else with C, the first 2 means the fruits together..& 3rd as an alternate to the 2nd..
Although I am not sure of the correct answer.
2221

Hey Puys
Can someone please help on preparation of Probability..I am just not getting hold on it...
appearing in Gmat on 30th June...

2222

Take rough values and you will conclude that both the statements together are not sufficient to answer it..
take AB as 9 and 3 and analyse seperately.

2223

Geertrudes grandmother has two grandfather clocks. One loses 3 minutes every hour; it will show that 57
minutes have elapsed when in fact exactly one hour has gone by. The other gains 5 minutes every hour.
Geertrude and her grandmother always open a bottle of champagne when the two clocks strike 12 at midnight on
the same night. On all other nights, they open a bottle of apple cider. Last night, they opened a bottle of
champagne. How many full weeks must go by before they can do so again?
A. none
B. one
C. two
D. three
E. more than three

The answer is E - at least as per the exam. But I have a doubt in mind - can this problem be solved at all without knowing when both the clocks started off? Can anyone please explain?

2224

When 777 is divided by positive integer n, the remainder is 77. How many possibilities are there for n?
A. 2
B. 3
C. 4
D. 5
E. 6
(D) If the remainder is 77, then n > 77
Also, there must be a positive integer q such that 777= nq + 77. i.e. nq = 700.
Therefore, the factors of 700 greater than 77 comprise the possible values of n.
Instead of counting the factors of 700 that are greater than 77, lets count the ones that are less than 700/77.
As 700 = 5^2 2^2 7, we can see that there are 5 factors of 700 that are less than 700: 1 , 2 , 4 , 5 , and 7.
Thus there are 5 possible values of n (i.e. factors of 700) greater than 77.

This is question + answer from an exam. I got this right but I was looking for factors of 700 greater than 77. That took a long time. But I am unclear about the argument that we should be "instead of counting the factors of 700 that are greater than 77, lets count the ones that are less than 700/77". Can someone please elaborate?

Thanks in advance!

btw..I am posting these questions from a particular exam. Please let me know if I should mention the name of the exam - not very sure about the copyright policy.

2225

Hi!
Been quite some time I did quant. But it is always fun!
To begin with yr ques...once u noticed that u need factors of 700 greater than 77, the first thing that should click u is 100 is one of the factors!! Is there any factor of 700 betn 100 and 78? None! (this shudn't take u more than a few secs!)
After this, 700/100=7...so at max there can b 7 factors...keep tryin for each n betn 1 and 7
700%1=0
700%2=0
700%3= xx (not a factor)
700%4= 0
700%5= 0
700%6= yy (not a factor)
700%7=0 ...
voila!! yr answer is 5! How much tym did it take?? Not more than a 30 secs if u get the crux of the pblm pretty soon 😃

2226
Geertrudes grandmother has two grandfather clocks. One loses 3 minutes every hour; it will show that 57
minutes have elapsed when in fact exactly one hour has gone by. The other gains 5 minutes every hour.
Geertrude and her grandmother always open a bottle of champagne when the two clocks strike 12 at midnight on
the same night. On all other nights, they open a bottle of apple cider. Last night, they opened a bottle of
champagne. How many full weeks must go by before they can do so again?
A. none
B. one
C. two
D. three
E. more than three

The answer is E - at least as per the exam. But I have a doubt in mind - can this problem be solved at all without knowing when both the clocks started off? Can anyone please explain?


hello buddy ....unfortunately we cannot solve this problem without knowing their relative positions ...i.e it is not necessary to know, when did they strike at 12 midnight last, but is necessary to know that at any give time, what are the respective positions of 2 clocks ....

eg. if 2 boys are running at a given speed on a circular track , when will they meet at the starting position ? without knowing the positions of 2 boys we cannot tell when will they meet next ? they could be just a couple of mins from meeting next or they could have just met a couple of mins back ....

Similarly ,
For slower watch, it takes 60/57 hrs to complete 1 hr
and for faster watch it takes 60/65 hr to complete 1 hr ...

they meet at starting position at LCM of individual times to complete one entire cycle i.e 24 hrs

Now, 65 and 57 are coprime, hence LCM is product of these nos ..

So no of weeks before they strike at midnight = (65*57)/(24*7)....which is clearly greater than 3 ....

hope this answers you query !!
2227
When 777 is divided by positive integer n, the remainder is 77. How many possibilities are there for n?
A. 2
B. 3
C. 4
D. 5
E. 6
(D) If the remainder is 77, then n > 77
Also, there must be a positive integer q such that 777= nq + 77. i.e. nq = 700.
Therefore, the factors of 700 greater than 77 comprise the possible values of n.
Instead of counting the factors of 700 that are greater than 77, let's count the ones that are less than 700/77.
As 700 = 5^2 2^2 7, we can see that there are 5 factors of 700 that are less than 700: 1 , 2 , 4 , 5 , and 7.
Thus there are 5 possible values of n (i.e. factors of 700) greater than 77.

This is question + answer from an exam. I got this right but I was looking for factors of 700 greater than 77. That took a long time. But I am unclear about the argument that we should be "instead of counting the factors of 700 that are greater than 77, let's count the ones that are less than 700/77". Can someone please elaborate?

Thanks in advance!

btw..I am posting these questions from a particular exam. Please let me know if I should mention the name of the exam - not very sure about the copyright policy.


Let me try to explain your doubt...

once you know we need to find out those factors of 700 which are greater than 77.

For any number, Number = one factor X Some other factors

So if we know the smaller factors of any number (easier to find after dividing the number into its prime factors) we can find the corresponding bigger factors

700 = 1X700
700 = 2X350
700 = 4X175
700 = 5X140
700 = 7X100
700 = 10X70 ---> stop here as 70 is less than 77...

answer 5

hope it helps
2228

If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?

a) 3
b) 6
c) 11
d) 22
e)222

2229
If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?

a) 3
b) 6
c) 11
d) 22
e)222


My Answer is 222 (E)

Plz confirm if its correct ?? then i will post the explanation
2230
My Answer is 222 (E)

Plz confirm if its correct ?? then i will post the explanation


yes sir, it is correct, but i dont get the logic of ppl saying that they post the explanation only after confirmation of correct answer..

if you are confident about it, shoot .... if there is problem in your method, I;m sure someone here will be glad to to correct it...
2231
yes sir, it is correct, but i dont get the logic of ppl saying that they post the explanation only after confirmation of correct answer..

if you are confident about it, shoot .... if there is problem in your method, I;m sure someone here will be glad to to correct it...


abc can be combined as three digit number in 6 ways.
Now sum of the numbers is 2(100+10+1)a+2(100+10+1)b+2(100+10+1)c
=222(a+b+c)hence even if abc is 101 then the sum of numbes that is x shuold be divisible by 222 atleast.
Henc 222 is the answer.
Hope these helps.
2232
yes sir, it is correct, but i dont get the logic of ppl saying that they post the explanation only after confirmation of correct answer..

if you are confident about it, shoot .... if there is problem in your method, I;m sure someone here will be glad to to correct it...


arey bhai !!! plz dont say sir n all....

i just said that explanation thing like that. dont knw abt the other ppl.

anyways, cuming to the explanation

we have 3 digits, lets say a,b,c.
so the nos formed are abc,acb, bca, bac, cab, cba.

the sum of all these nos will be
100a+10b+c-->abc
100a+10c+b-->acb
100b+10c+a-->bca
100b+10a+c-->bac
100c+10a+b-->cab
100c+10b+a-->cba

now the sum of all these 6 nos is X = 222(a+b+c).

So the largest integer is 222.

I hope my explanation is clear!!!:cheerio:
2233
1. If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?


2. 2 couples and a single person are seated at random in a row of 5 chairs. What is the probability that neither of the couples sit together in adjacent chairs.

3. 9 people, including 3 couples, are to be seated in a row of 9 chairs.

What is the probability that


a. None of the Couples are sitting together


b. Only one couple is sitting together


c. All the couples are sitting together

Plz post explanations along with answers.


1. 10*8*6 = 240.

2. 5! - (3!x2x2) = 96
3.
a)Total number of possibilities - (number of possibilities of couples sitting together).

Ans: 9! - (6!x2x2x2) = 6!x496

b) I dunno how to solve for this one.

c) 6!x2x2x2 = 8x6!



Let me know if you need explanation.
2234

A circle is centered on the origin in the coordinate plane. Point (A, B) is randomly selected inside of the circle.
What is the probability that A > B > 0?
A. 1/8
B. 1/4
C. 3/8
D. 1/2
E. 3/4

The exam says it is 1/8. But I think it should be 3/8 considering the third and fourth quadrant. Can anyone please explain?

Thanks in advance!

2235
A circle is centered on the origin in the coordinate plane. Point (A, B) is randomly selected inside of the circle.
What is the probability that A > B > 0?
A. 1/8
B. 1/4
C. 3/8
D. 1/2
E. 3/4

The exam says it is 1/8. But I think it should be 3/8 considering the third and fourth quadrant. Can anyone please explain?

Thanks in advance!


You can observe that only in the first quadrant the coordinates are positive ie. A>0 and B>0 as given in the condition.
Also there are total 8 patitions in which we can divide the xy plane which i cant draw here to explain.
Also A>B in I quadrant below line x=y.
Hence probability is 1/8 obviously.I think u have not checked for the condition th is both coordiantes should be positive.
2236
A circle is centered on the origin in the coordinate plane. Point (A, B) is randomly selected inside of the circle.
What is the probability that A > B > 0?
A. 1/8
B. 1/4
C. 3/8
D. 1/2
E. 3/4

The exam says it is 1/8. But I think it should be 3/8 considering the third and fourth quadrant. Can anyone please explain?

Thanks in advance!


I am not sure of the answer choice I would have marked.. but I can try..

Centered @ (0, 0)... and also A > B > 0
this means both A and B are positive and both lie inside the Quad I

so we dont care for the remaining Quads and we get the probability of both being positive as (1/4).

prob of A > B, this I am not sure how to figure out..

very frankly.. if I would have not known the correct answer from you, I would have suggested option B only, since A > B > 0 can be percieved as a way of saying that both A and B are greater than 0.

Lemme know if you get the means to figure out the correct answer..