GMAT Problem Solving Discussions

Is this the only Data given??
Seems a rather odd question, esp for GMAT!!

Anyways.. shall attempt to paraphrase and solve it.

Given Data: There are only 2 people in consideration.

Since everyone's birthday has to be on one of the 7 days, the probability that first person's b'day is not on a Monday = 6/7.

Similarly, probability of second person not being born on a Monday is = 6/7

Therefore probability that both are not born on Monday = 6/7 * 6/7 = 36/49

Probability that atleast one of them is born on a Monday is
= 1 - (36/49)
= 13/49


Cheers



Q. What is the probability that at least one of two people was born on a Monday...

guys please help..

hey jawaharnr,

The answer is right and i also solved it exactly the same way but i am not completely convinced with the answer explaination...

it says 1/7(prob of person A to born on monday) + 1/7(prob of person B to born on Monday) - 1/49(P (A nd B)) = 13/49.

so actually it is using P(A) + P(B) -P(A and B)

according to me P(A and B) should be 0 .

Why should P(A ^ B) be 0??
That would imply, that there is no possibility of both of them being born on Monday!! Is that the case??

Actually, the births of 2 people are independent events (Hoping that they are not twins )
So probability if anyone being born on Monday is P(A) = P(B) = 1/7
Since the Events are independent, laws of probability state that
P (A ^ B) = P(A)*P(B)
= 1/7 * 1/7
= 1/49


Hope this clears ur doubt


hey jawaharnr,

The answer is right and i also solved it exactly the same way but i am not completely convinced with the answer explaination...

it says 1/7(prob of person A to born on monday) + 1/7(prob of person B to born on Monday) - 1/49(P (A nd B)) = 13/49.

so actually it is using P(A) + P(B) -P(A and B)

according to me P(A and B) should be 0 .

Hi Guys,

I saw two similar questions have different explanation and two different answers.

Q1. How many ways 5 boys and 6 girlsbe arranged in a row so that no two boys are together. Below are the answer choices:
a. 7 * 6! b. 6!*5!*2 c. 6!*5!
P
5

d. 7 * 5!
P
5
e.6 * 6!
P
5
Answer is a.

Q2. How many ways can 6 positive and 5 negative sings be arranged in a row so that no two negative sings are together. Below are the answer choices:

a. 21 b. 15120 c. 30 d. 6!*5! e. 6* (7!/2!)

Answer is a i.e. 21.

Two different answer explanations are given for above two qs and i think answer explanation should be same as well as the answer.

Can you guys pls help me understanding the explanation and the correct answer.

Thank you.

Sujoy

Hi, please note that the first one is a permutation question while the second one is combination.

1. 6 girls can be arranged in 6! Ways, now we have total 7 slots for 5 boys so they can be arranged in 7P5 ways.

2. Applying the same concept here:6 positive signs that can be arranged in only
One way, now we have 7 slots for 5 negative signs...applying the combination formula..its 7C5 =21.

Q.1
___ G1 ___ G2 ___ G3 ___ G4 ___ G5 ___ G6 ___
..1....... 2........ 3....... 4........ 5........ 6....... 7

Note that order in which boys or girls sit is important.
Hence, Permutation
G1 to G6 can be arranged in 6! ways.
Seven slots can be alloted to 5 boys in 7P5 ways.
The answer is 6! x 7P5

Q.2

___ + ___ + ___ + ___ + ___ + ___ + ___
..1..... 2.......3.......4.......5.......6........7

7 gaps are available and we have 5 negative signs.
All positive/ negative signs are the same and order of arrangement is not important.
Hence, combinations, 7C5 = 42/2 = 21 ways

Hi Guys,

I saw two similar questions have different explanation and two different answers.

Q1. How many ways 5 boys and 6 girlsbe arranged in a row so that no two boys are together. Below are the answer choices:
a. 7 * 6! b. 6!*5!*2 c. 6!*5!
P
5

d. 7 * 5!
P
5
e.6 * 6!
P
5
Answer is a.

Q2. How many ways can 6 positive and 5 negative sings be arranged in a row so that no two negative sings are together. Below are the answer choices:

a. 21 b. 15120 c. 30 d. 6!*5! e. 6* (7!/2!)

Answer is a i.e. 21.

Two different answer explanations are given for above two qs and i think answer explanation should be same as well as the answer.

Can you guys pls help me understanding the explanation and the correct answer.

Thank you.

Sujoy

(Q) What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?

a) 1/6
b) 1/4
c) 1/2
d) 21/216
e) 32/216

Can somebody explain?

The official answer is (a)

Thank you silverlineinsky and euros. I got the explanation.

(Q) What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?

a) 1/6
b) 1/4
c) 1/2
d) 21/216
e) 32/216

Can somebody explain?

The official answer is (a)


Two cases:

1 - for sum 8

Possible combinations:
1 1 6 - 3!/2! ways = 3 ways
1 2 5 - 3! = 6 ways
1 3 4 - 6 ways
2 2 4 - 3 ways
2 3 3 - 3 ways
Total = 21 ways

P(any digit) = 1/6

P(sum = 8 ) = * 21 --------- eq 1

2 - for sum 14

Possible combinations:
2 6 6 - 3 ways
3 6 5 - 6 ways
4 4 6 - 3 ways
4 5 5 - 3 ways

Total = 15 ways

P(sum=14) = * 15 --------- eq 2

Add eq 1 and eq 2

P(sum = 8 or sum = 14) = 36/216 = 1/6

HTH!

A challenging probability question which came to my mind...

Q) If a man climbs a staircase having 12 steps by jumping one step, two steps or three steps at a time in any order. What is the probability that he took at least two three step jumps?

The first question talks on PEOPLE (who look different) 😁 and hence PERMUTATIONS to be used :)

Ans: 6! X 7P5.

The second one talks on SIGNS (which look similar) and hence COMBINATIONS to be used :)

Ans: 6C6 X 7C5 = 21


Hi Guys,

I saw two similar questions have different explanation and two different answers.

Q1. How many ways 5 boys and 6 girlsbe arranged in a row so that no two boys are together. Below are the answer choices:
a. 7 * 6! b. 6!*5!*2 c. 6!*5!
P
5

d. 7 * 5!
P
5
e.6 * 6!
P
5
Answer is a.

Q2. How many ways can 6 positive and 5 negative sings be arranged in a row so that no two negative sings are together. Below are the answer choices:

a. 21 b. 15120 c. 30 d. 6!*5! e. 6* (7!/2!)

Answer is a i.e. 21.

Two different answer explanations are given for above two qs and i think answer explanation should be same as well as the answer.

Can you guys pls help me understanding the explanation and the correct answer.

Thank you.

Sujoy

Another question on probability

q) What is the probability of getting at-least 2 doublets ( i.e (1,1)...) in four throws with two dice?

How many 4-digit numbers can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 4536 (B) 4546 (C) 4556 (D) 9436 (E) 9556


How many even 4-digit numbers can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 2296 (B) 2396 (C) 2444 (D) 2456 (E) 2486


How many even 4-digit numbers divisible by 4 can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 336 (B) 784 (C) 1120 (D) 1804 (E) 1936



How many 4-digit numbers can be formed by using the digits 0-9, so that it contains exactly 3 distinct digits?

(A) 1944 (B) 3240 (C) 3850 (D) 3888 (E) 4216

For Q.1, I am getting (A) 4536 as the answer.
Another question on probability

q) What is the probability of getting at-least 2 doublets ( i.e (1,1)...) in four throws with two dice?


P(Atleast 2 doublets) = 1 - P(no doublet) - P(1 doublet)

36 = total number of choices when 2 dice are thrown
6 doublets, 30 non doublets

P(no doublet)= 30/36
P(1doublet) = 6/36

P(no doublet) = P(no doublet in any of the 4 throws) = (30/36) ^ 4 = 625/1296
P(1doublet) = 6/36 * (30/36)^3 = 125/1296

P(atleast 2 doublets) = 1 - (625+125)/1296 = 546/1296 = 273/632

Did I mess up somewhere?

Are the answers

1. (A) 4536
2. (A) 2296

3. (C) 1120
4. (A) 1944


???

Kindly share the answers. I shall share the solutions then :)


(

How many 4-digit numbers can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 4536 (B) 4546 (C) 4556 (D) 9436 (E) 9556


How many even 4-digit numbers can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 2296 (B) 2396 (C) 2444 (D) 2456 (E) 2486


How many even 4-digit numbers divisible by 4 can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 336 (B) 784 (C) 1120 (D) 1804 (E) 1936



How many 4-digit numbers can be formed by using the digits 0-9, so that it contains exactly 3 distinct digits?

(A) 1944 (B) 3240 (C) 3850 (D) 3888 (E) 4216

For Q.1, I am getting (A) 4536 as the answer.

Are the answers

1. (A) 4536
2. (A) 2296

3. (C) 1120
4. (A) 1944


???

Kindly share the answers. I shall share the solutions then :)




I have posted these questions here because I do not have the solutions or the answers. If I had the answers, I would have definitely posted them at the end of the post. Will appreciate if you could share the solutions. πŸ˜ƒ
How many 4-digit numbers can be formed by using the digits 0-9, so that no two digits are repeated?

(A) 4536 (B) 4546 (C) 4556 (D) 9436 (E) 9556


]


My answers below

1. 4536
2. 2296
3. 1120

-Deepak.

Guys suggest me some books on quant as i have only OG's and CAT books are difficult as per gmat standard is concern...So which book to buy...
Where do you get these questions so that i can use mine 2(brain)...this is medium cat level stuff what i believe..does GMAT standard require this?
Pls reply..

Guys suggest me some books on quant as i have only OG's and CAT books are difficult as per gmat standard is concern...So which book to buy...
Where do you get these questions so that i can use mine 2(brain)...this is medium cat level stuff what i believe..does GMAT standard require this?
Pls reply..


OGs are sufficient practice material for GMAT quant. And if you think you need more practice then there are certain documents I came across while my preparation 1000DS and 1000 PS. You can find them online. And if you are thorough with CAT stuff and the quant level used there then GMAT quant should be a cake walk for you.

Good Luck!
OGs are sufficient practice material for GMAT quant. And if you think you need more practice then there are certain documents I came across while my preparation 1000DS and 1000 PS. You can find them online. And if you are thorough with CAT stuff and the quant level used there then GMAT quant should be a cake walk for you.

Good Luck!


No iam not thorough with CAT level quant but rather i don't want to do it as it doesn't required by GMAC standard GMAT.
So if you can give me 1000PS/DS i will be delighted.b/w when you are planning to give GMAT.

Note:- pls post the books from which you have posted these q's on this forum..