GMAT Problem Solving Discussions

wordings could be tricky sometimes ...but i still feel it cannot be 6P4

if the 4 choices are idli, dosa, utappa and wada ...problem wordings imply it does not matter who has ordered what ....coz it is not a different order ..


I agree it should be combinations and not permutations...

It should be 6p4.

P.S. Bhavin... idli,dosa,uttapa and wada... 😞 i feel like crying...
I am at place where i can only just think of such things... can never see it 😞

I am back with Probability...

Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?

A 1/5
B 2/5
C 3/5
D 4/5
E 3/8

I am back with Probability...

Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?

A 1/5
B 2/5
C 3/5
D 4/5
E 3/8


Let the couples be denoted as A1-A2 and B1-B2.
A1-A2 together = 4!2!
B1-B2 together = 4!2!
A1-A2 together and B1-B2 together = 3!2!2!
All A1-A2 together and/or all B1-B2 together = 2*4!2! - 3!2!2!
= 96-24 = 72

All possible arrangements without restriction = 5! = 120
Probability = 1 - (72/120)
= 2/5

I would have marked option B

I believe this question is too tough and time consuming to be asked in GMAT.. nevertheless, plz lemme know the OA πŸ˜‰

thats wrong !!! Try again..

one observation.. you guys seem to taken aback by mismatch in the actual answer the text in question stem.. plz.. read the lines below..

NEVER EXPECT GMAT (OR FOR THAT MATTER ANY OTHER APTITUDE TEST) TO BE EXPLICIT IN IT'S QUESTIONS... THE TEST IS NOT DESIGNED TO GAUGE CANDIDATE'S MATHEMATICAL SKILLS, BUT RATHER IT IS PRIMARILY DESIGNED TO GAUGE CANDIDATE'S ABILITY TO PICK THE RIGHT APPROACH IN THE LIMITED TIME AND REACH THE RIGHT ANSWER..

Dont wanna sound rude or anything, but I would really want to see a question in GMAT/CAT/GRE which explicitly asks the candidate to calculate a value using P&C; concepts.. hope that clarifies things.. ;)

have a good one!!

A family of 4 is at a restaurant with 6 choices
.
.

Pure combinations ...internal pattern of choices does not matter

6C4 = 15 ..Option A

I sooo agree with you!! but the OA is 360.. using permutations...
and i have no clue why!! :-(

fyi - the ques is from a score800 test..

wordings could be tricky sometimes ...but i still feel it cannot be 6P4
.
.
..

In this question the key is words "nobody orders the same meal". This means order, although not mentioned, is to be kept in mind while solving this question.
.
.
.
how much time you took to solve this?
BTW... your approach is correct...but answer is wrong... only one thing you missed.
What are we finding here?
The probability of couple sitting together or not sitting together? ;)


I wasjust checking whether you read the answer carefully or not.. you passed your test.. ..

thanks for pointing that out.. πŸ˜‰
Let the couples be denoted as A1-A2 and B1-B2.
A1-A2 together = 4!2!
B1-B2 together = 4!2!
A1-A2 together and B1-B2 together = 3!2!2!
All A1-A2 together and/or all B1-B2 together = 2*4!2! - 3!2!2!
= 96-24 = 72

All possible arrangements without restriction = 5! = 120
Probability = 1 - (72/120)
= 2/5

answer = 1 - 2/5 = 3/5

I would have marked option B

I believe this question is too tough and time consuming to be asked in GMAT.. nevertheless, plz lemme know the OA ;)


corrected the mistake committed above
nuttyvarun Says
corrected the mistake committed above


thats correct...
and i was not able to solve this sum... so thanks for this ...

One more for more practice:
A number sequence has 100 elements. Any of its elements (except for the first and last element) is equal to the product of its neighbors. The product of the first 50 elements, just as the product of all the elements is 27. What is the sum of the first and the second element?
a. 244/3
b. 10
c. 12
d. 28/3
e.1

Lengthy one:
There were ten friends four of whom are Sanjay, Salim, Reena and Teena. A team of six is to be formed such that Reena & Teena are never together but Sanjay and Salim are always together. How many teams can be made?

a.110
b.68
c.77
d.76
e.108

In this question the key is words "nobody orders the same meal". This means order, although not mentioned, is to be kept in mind while solving this question.

A-can order from 6 choices
B-has now only 5 choices to select from
C-has 4 after B has selected
D-has 3 choices after C has selected

Total - 6*5*4*3 = 360. So order came into play.

I hope this helps.


@nuttyvarun, in this question, "nobody orders the same meal" means that no two people order the same thing - as in one order person A & person B both can't order idli....

Thanks for your inputs!

simple one...
A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?a)27.b)36.c)72.d)112.e)422.

ndhadha Says
wats the OA?


Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5 ?
A. 1/6
B. 1/5
C. 1/3
D. 2/5
E. 2/3

sorry for the late reply
OA is D
Taking all together here. I shall post the answers tomm... Have a Good night...

simple one...
A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?a)27.b)36.c)72.d)112.e)422.

Lengthy one:
There were ten friends four of whom are Sanjay, Salim, Reena and Teena. A team of six is to be formed such that Reena & Teena are never together but Sanjay and Salim are always together. How many teams can be made?

a.110
b.68
c.77
d.76
e.108

One more for more practice:
A number sequence has 100 elements. Any of its elements (except for the first and last element) is equal to the product of its neighbors. The product of the first 50 elements, just as the product of all the elements is 27. What is the sum of the first and the second element?
a. 244/3
b. 10
c. 12
d. 28/3
e.1

simple one...
A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?a)27.b)36.c)72.d)112.e)422.

Not sure if this approach is correct....

Possibilities for 3rd digit - 3
Possibilities for 4th digit - 3
Possibilities for 6th digit - 4

5th digit will always by 3 times 6th digit, so possibility - 1

Poss credit cards -> 3*3*4 = 36

IMO b) 36...
Not sure if this approach is correct....

Possibilities for 3rd digit - 3
Possibilities for 4th digit - 3
Possibilities for 6th digit - 4

5th digit will always by 3 times 6th digit, so possibility - 1

Poss credit cards -> 3*3*4 = 36

IMO b) 36...


try again..
Approach is correct... but u missed something...

5 th DIGIT will be 3 times the 6th πŸ˜‰ 5th Digit... DIGIT...

One more for practice:
In a blue jar there are red, white and green balls. The probability of drawing a red ball is 1/5. The probability of drawing a red ball, returning it, and then drawing a white ball is 1/10. What is the probability of drawing a white ball?
a)1/5.
b).
c)1/3.
d)3/10.
e).

Last one that i could solve today:
How many 5 digit numbers can be created if the following terms apply: the leftmost digit is even, the second is odd, the third is a non even prime and the fourth and fifth are two random digits not used before in the number?
a)2520
b)3150
c)3360
d)6000
e)7500

I am back with Probability...

Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs?

A 1/5
B 2/5
C 3/5
D 4/5
E 3/8


Pasting my old post again :

Case 1 :
Consider 1st couple to sit together. (Hence they are considered as 1 unit) .
So, 1 unit and remaining 3 people i.e total 4 people can be arrange in 4! ways and the couple themselves can be arranged in 2! ways..
Total ways in which 1st couple sit together = 2!*4! ways..

Case 2 :
Consider 2nd couple to sit together:
Similar to above calculation,
Total ways in which 2nd couple sit together = 2!*4! ways..

Now, its like a venn diagram, where each of the above cases has 1 special case where both couples could be seated together and this special case has been included in each of the cases above , hence we need to subtract this special case once.

Special Case : (both couples together )
Now, when both couples are seated next to each other,
Total no of ways = 2!*2!*3! ( each couple considered as 1 unit , and 2! ways for each of the couple to be seated among themselves )

Total ways (atleast 1 couple seated next to each other) = case 1 + case 2 - special case

= 2!*4! + 2!*4! - 2!*2!*3!
=48+48-24
=72

and 5 people can be arranged in 5! Ways..

Hence , p(no couple together) = 1-p(atleast 1 couple together)
= 1 - 72/120
= 48/120
=2/5.....Ans
One more for more practice:
A number sequence has 100 elements. Any of its elements (except for the first and last element) is equal to the product of its neighbors. The product of the first 50 elements, just as the product of all the elements is 27. What is the sum of the first and the second element?
a. 244/3
b. 10
c. 12
d. 28/3
e.1


Not sure if anybody has solved it already ...
Good sum ..

we have 2 independent values ...rest all are dependent ...
Let 1st term be x and 2nd term = y

Series is as follows :

x
y
y/x
1/x
1/y
x/y
x
y
.
.
.
Hence....cyclicity is 6 ...every 7th term is same as 1st , 8th same as 2nd ans so on ....

So product of set of 6 nos is 1 ..
Product of first 50 nos is same as product of first 2 nos (6*8 + 2)
and product of all is same as product of first 4 terms (16*6 + 4)

Hence, 2 eqns are
xy =27 and y^2/x = 27 ....
Solving, we get x = 3 and y=9

Hence sum of first 2 terms is 12

Is this the OA ?