GMAT Problem Solving Discussions

MBA
4386
coolrahine Says
Correct answer Sausi .... Now lemme know have yu already gven GMAT and if so then what is yur score ... My prep tests are workin somwat fine with avgs varying between 700 to 750 ... :)


I just started my preps 2 weeks back after thinking about it for more than 3-4 months !
6th Sept is the D-Day !!
4387

So which all are the inst whre yu'll apply as IIMAPGPX last day for submission is 16th august ..

4388
coolrahine Says
So which all are the inst whre yu'll apply as IIMAPGPX last day for submission is 16th august ..


I think its best that we talk over pm........
4389

Hi Puys,
Pls solve the below Qs. I am lost in middle of these problems...
1.IF an unbiased coin is flipped 7 times,the probability of getting the same face on exactly 5 consecutive trials is
a.) 3/128
b.) 5/64
c.) 1/16
d.) 1/64
e.) 3/64

2.Six letters are to be placed in six addressed envelopes. If the letters are placed at random into the envelopes, the probability that none of the six letters are placed into their corresponding envelopes is
a.) 1/6!
b.) 0
c.) 1-(1/6!)
d.) 1 -(5/6!)
e.) None of these

4390
Hi Puys,
Pls solve the below Qs. I am lost in middle of these problems...
1.IF an unbiased coin is flipped 7 times,the probability of getting the same face on exactly 5 consecutive trials is
a.) 3/128
b.) 5/64
c.) 1/16
d.) 1/64
e.) 3/64

2.Six letters are to be placed in six addressed envelopes. If the letters are placed at random into the envelopes, the probability that none of the six letters are placed into their corresponding envelopes is
a.) 1/6!
b.) 0
c.) 1-(1/6!)
d.) 1 -(5/6!)
e.) None of these


My takes:

1. b
There are 3 ways in which the 5 consecutive heads or tails can come up.
i) XTHHHHH ii) THHHHHT iii) HHHHHTX,

Case(i) X can be H or T and 5 H's could be T's, so total = 2*2 = 4 ways
Case (ii) The 5 H's could be T's , so total = 2 ways
Case (iii) X can be H or T and 5 H's could be T's, so total = 2*2 = 4 ways

Thus total possible ways = 4+2+4=10
Total possible outcomes = 2^7
P = 10/(2^7) = 5/64

2.e
From the inclusion exclusion principle:

With n letters and envelopes, the probability that none is correctly
placed is:

= 1/2! - 1/3! + 1/4! - 1/5! + ....... + *(1/n!)

Thus we get ,
P = 1/2! - 1/3! + 1/4! - 1/5! + 1/6!
P = 53/144

For Inclusion-Exclusion principle, read this: Math Forum - Ask Dr. Math
Incidently, the same question is tackled in this post !
4391

Hi Sausi,
Thanks for the explanations.
I am unaware of this inclusion-exclusion principle.Hope I am clear now.
Thanks again.

4392
We essentially have two equations
a+b+c = 80
ab/2 c/4 = 34.5
Solving we get 6b+5c =182 => 5c = 182 6b => c is even
Therefore b can take values 2, 7, 12, 17, 22, 27 (for 32, c And (a,c )can take corresponding values (44,34), (45, 28 ), (46, 22), (47, 16),(48, 10), (49, 4)
We have 6 possible sets so its option D


An easy way to solve the problem would be to substitute the first eqn. in the 2nd eqn. keeping intact the variable that needs to be solved. (Correct no. of questions)

Therefore, c = (80-a-b)
Substitute in eqn. 2,
a-b/2-(80-a-b)/4 = 34.5 => 5a/4 - b/4 = 54.5
On reduction, we get:
5a - b = 218 => b = (5a-21
A quick look tells us that a is > 43 (bcos 43*5=215 and questions answered cant be negative.)
Jus substitute the given 2 options and see if it fits.
4393
An easy way to solve the problem would be to substitute the first eqn. in the 2nd eqn. keeping intact the variable that needs to be solved. (Correct no. of questions)

Therefore, c = (80-a-b)
Substitute in eqn. 2,
a-b/2-(80-a-b)/4 = 34.5 => 5a/4 - b/4 = 54.5
On reduction, we get:
5a - b = 218 => b = (5a-21
A quick look tells us that a is > 43 (bcos 43*5=215 and questions answered cant be negative.)
Jus substitute the given 2 options and see if it fits.


I would naturally go for substitution on a timed test for a question like this. I just solved for the whole set of variables (a,b,c) that satisfy the given equations as if the Q were to find all possible values.
4394
I was giving the exam oriented approach.
4395
A----------B---------C----------D

Is
CD > BC ?
(1) AD = 20
(2) AB = CD


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) is it correct???
4396

Both statements together are insufficient. whr's the 5th option? :@

4397

Hi fellas, there's this particular question I have a doubt in. This is from a MGMAT test.

Q. If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75

The solution is as follows :


This question can be restated in several ways. Let Work = amount earned (i.e., amount needed to purchase the jacket). Recall, Work = Rate x Time. Since the number of hours that either Jim or Tom need to work in order to purchase the jacket is given, we need only know either person's rate of pay to determine the cost of the jacket; hence, the question can be restated as either: "What is x?" or "What is y?".

Also, since the amount of time needed for either Jim or Tom to purchase the jacket is given, it can be shown that the amount of time needed for them working together to purchase the jacket can also be calculated. The formula Work = Rate x Time also applies when Jim and Tom work together; hence, only the combined rate of Jim and Tom working together is required. Since the combined rate of two people working together is equal to the sum of their individual rates, the question can also be restated as: "What is X + Y?"

(1) INSUFFICIENT: This statement gives only the relative earning power of Jim and Tom. Since the original question states the amount of time needed for either Jim or Tom to earn enough money to purchase the jacket, it also gives us the relative earning power of Jim and Tom. Hence, statement (1) does not add any information to the original question.

(2) SUFFICIENT: Let Z = 1 jacket. Since Tom and Jim must 4 and 5 hours, respectively, to earn enough to buy 1 jacket, in units of "jacket per hour," Jim works at the rate of 1/4 jackets per hour and Tom works at the rate of 1/5 jackets per hour. Their combined rate is 1/4 + 1/5 = 5/20 + 4/20 = 9/20 jackets per hour. Since Time = Work/Rate, Time = 1 jacket/(9/20 jackets per hour) = 20/9 hours.

Since the combined pay rate of the Jim and Tom is equal to the sum of the individual pay rates of the two; hence, the combined pay rate in dollars per hour is X + Y. When the two work together, AmountEarned = CombinedPayRate x Time = (X + Y) x 9/20. Since statement (2) states that X + Y = $43.75, this statement is sufficient to compute the cost of the jacket (it is not necessary to make the final calculation).

The correct answer is B.

Note: It is also not necessary to explicitly compute the time needed for Jim and Tom working together to earn the jacket (20/9 hours). It is only necessary to recognize that this number can be calculated in order to determine that (2) is sufficient.

----

I feel the answer is D.
Let the price of the Jacket be Z. So, 4x=z=5y. In effect, 4x=5y. So, 4x-5y=0 is the 1st equation. Both A) and B) will give another equation, thus allowing us to find values of x and y. And hence Z. I don't understand the logic given in the solution though. Am I missing something?

4398

Sorry. my bad! 5th option was this only that both together are insufficient...

4399

4 letters, A,B,C,D should go to 4 independent houses, 1,2,3, and 4, respectively. What's the no. of possible ways so that no letter goes to the correct address.

Please explain your answer. I am not looking for a listing approach.

4400
Hi fellas, there's this particular question I have a doubt in. This is from a MGMAT test.

Q. If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75

The solution is as follows :


This question can be restated in several ways. Let Work = amount earned (i.e., amount needed to purchase the jacket). Recall, Work = Rate x Time. Since the number of hours that either Jim or Tom need to work in order to purchase the jacket is given, we need only know either person's rate of pay to determine the cost of the jacket; hence, the question can be restated as either: "What is x?" or "What is y?".

Also, since the amount of time needed for either Jim or Tom to purchase the jacket is given, it can be shown that the amount of time needed for them working together to purchase the jacket can also be calculated. The formula Work = Rate x Time also applies when Jim and Tom work together; hence, only the combined rate of Jim and Tom working together is required. Since the combined rate of two people working together is equal to the sum of their individual rates, the question can also be restated as: "What is X + Y?"

(1) INSUFFICIENT: This statement gives only the relative earning power of Jim and Tom. Since the original question states the amount of time needed for either Jim or Tom to earn enough money to purchase the jacket, it also gives us the relative earning power of Jim and Tom. Hence, statement (1) does not add any information to the original question.

(2) SUFFICIENT: Let Z = 1 jacket. Since Tom and Jim must 4 and 5 hours, respectively, to earn enough to buy 1 jacket, in units of "jacket per hour," Jim works at the rate of 1/4 jackets per hour and Tom works at the rate of 1/5 jackets per hour. Their combined rate is 1/4 + 1/5 = 5/20 + 4/20 = 9/20 jackets per hour. Since Time = Work/Rate, Time = 1 jacket/(9/20 jackets per hour) = 20/9 hours.

Since the combined pay rate of the Jim and Tom is equal to the sum of the individual pay rates of the two; hence, the combined pay rate in dollars per hour is X + Y. When the two work together, AmountEarned = CombinedPayRate x Time = (X + Y) x 9/20. Since statement (2) states that X + Y = $43.75, this statement is sufficient to compute the cost of the jacket (it is not necessary to make the final calculation).

The correct answer is B.

Note: It is also not necessary to explicitly compute the time needed for Jim and Tom working together to earn the jacket (20/9 hours). It is only necessary to recognize that this number can be calculated in order to determine that (2) is sufficient.

----

I feel the answer is D.
Let the price of the Jacket be Z. So, 4x=z=5y. In effect, 4x=5y. So, 4x-5y=0 is the 1st equation. Both A) and B) will give another equation, thus allowing us to find values of x and y. And hence Z. I don't understand the logic given in the solution though. Am I missing something?


The answer is correct !

Stmnt 1 : Tom makes 20% less per hour than Jim does
If you make this into an eqn, you will get, y=0.8x, which is the same as what you get when you equate the price paid by each for the jacket,
i.e., 4x=5y, or, y=0.8x
So, there is no additional info provided by this statement.
4401
4 letters, A,B,C,D should go to 4 independent houses, 1,2,3, and 4, respectively. What's the no. of possible ways so that no letter goes to the correct address.

Please explain your answer. I am not looking for a listing approach.


This is a problem of de arrangement, where none of the things are at the correct place...

If n things are to be arranged such that none of the things are at correct place , then total possible de arrangements is given by formula

n! ( 1 - 1/1! + 1/2! -1/3! +1/4! -1/5! .....(-1)^n/n! )

When n=4,
total possible de arrangements = 4 ! ( 1 - 1/1! + 1/2! -1/3! +1/4!
= 24 ( 1-1 + 1/2 - 1/6 + 1/24 )
= 24 ((12-4+1)/24)
= 9

Alos, let us try the classical approach..

There are 4 envelopes ..say A B C D
Now, A can be at one of the 3 incorrect places I.e B, C Or D..
Let us evaluate each of the 3 possibilities :

1) When A is at B..
No of incorrect places for B = 3
No of incorrect places for C = 1
and D has to occupy last incorrect place..
total incorrect ways when A is at B = 3*1*1 = 3 ways..

Similarly, when A is at C, there would be 3 incorrect places for C, and a single incorrect place for B and D..
Hence, 3 ways..

similarly, 3 incorrect places when A is at D..

Total incorrect places = 3+3+3 = 9...this takes care of all incorrect possibilities.

Theory for the Inclusion-Exclusion principle/de arrangement can be read here:
Math Forum - Ask Dr. Math AND
http://www.physics.harvard.edu/academics/undergrad/probweek/sol16.pdf
4402

Hi all ,

I have come across the below problem in Probability and need your help to solve the same .

Problem

Kamal and Monica appeared for an interview for two vacancies . The probability of Kamal's selection is 1/3 and that of Monica's rejection is 4/5 . Find the probability that only one of them will be selected .

Solution suggested by the book :

Let K be the event that Kamal will be selected and M the event that Monica will be selected .
Then P(K) = 1/3 and P(M^c) = 4/5
Therefore P(M) = 1 - P(M^c) = 1-4/5 = 1/5
and P(K^c) = 1-1/3 = 2/3

Only one of them will be selected if either i.) Kamal is selected and Monica is not selected or ii.) Monica is selected and Kamal is not

In case i.) Probability = 1/3 * 4/5 = 4/15
In case ii.) Probability = 2/3 * 1/5 = 2/15

Hence the required probability , that one of them will be selected is
4/15 + 2/15 = 6/15= 2/5

My approach

Required probability = P(K) + P(M) -P(K).P(M)
= 1/3 + 1/5 - 1/15
= 7/15

Could someone tell me where I am making a mistake .

4403

My approach

Required probability = P(K) + P(M) -P(K).P(M)
= 1/3 + 1/5 - 2/15
= 6/15

Could someone tell me where I am making a mistake .


Corrections are highlighted in red.
4404

You mean P(K).P(M) = 1/3 * 1/5 = 2/15 ?

4405
bluefox1 Says
You mean P(K).P(M) = 1/3 * 1/5 = 2/15 ?


Sorry i missed out on detailing that part. Find below the expression

Required probability = P(K) + P(M) - 2P(K).P(M)
= 1/3 + 1/5 - 2/15
= 6/15


P(K) includes cases of K and M getting selected at the same time.
P(M) also includes these cases.

So we have counted P(K).P(M) twice, in the addition of P(K) + P(M)
Thats why we subtract it twice.