GMAT Problem Solving Discussions

[ajayreddy]

Originally Posted by cyndrella

please answer this...my doubt...should consecutive numbers always be considered from lower to higher or the other way round is also possible?

it can be either way round..since they have mentioned as 4 to be the last number and not the greatest number, u can hv the series frm -1 to 4 or from 4 to 9.... considering both the options, the answer is C

[ajayreddy]

Originally Posted by sharkon

Ajay is there a way where we can use permutations and combinations to reach this result.

yes sharkon...but i wanted to explain the sum in a much simpler way to others thts why i have used this raw method..

[sharkon]

Originally Posted by ajayreddy

yes sharkon...but i wanted to explain the sum in a much simpler way to others thts why i have used this raw method..

Ajay can u plz explain it using perm & coms .

[cyndrella]

try this one...

Flower shop: 2 tulips, 2 roses, 2 daisies, and 2 lillies. If 2 (two) are sold at random, what is the prob that both flowers are not tulips?

1/8
1/7
1/2
7/8

27/28

[ajayreddy]

Originally Posted by cyndrella

try this one...

Flower shop: 2 tulips, 2 roses, 2 daisies, and 2 lillies. If 2 (two) are sold at random, what is the prob that both flowers are not tulips?

1/8
1/7
1/2
7/8

27/28

probability that both flowers are not tulips = 1- probability that both flowers are tulips
= 1 - 2C2/8C2
= 1 - 1/28
= 27/28

[ajayreddy]

Originally Posted by sharkon

Ajay can u plz explain it using perm & coms .

i dont knw if such a method exists...and even if it did, i m sure this method is easier to remember than some complex formula..

[Sriram_Avadhani]

Originally Posted by perseverant

if x^2 + 5y = 49, is y an integer?
(1) 1 < x < 4
(2) x^2 is an integer.

EXPLANATION:
You can rearrange the equation to read

5y = 49 - x^2, or y = (49-x^2)/5. y will be an integer if 49-x^2 is a multiple of 5.
Statement 1 tells you that x is greater than 1, but less than 4. so 1 < x^2 < 16. so 49-x^2 could be a multiple of 5, say if x^2=2, or may not be a multiple of 5, say if x^2=1. Eliminate (1) and (4).
Statement 2 tells you that x^2 is an integer, which means 49-x^2 is an integer, but does not tell you if it is a multiple of 5. Eliminate answer (2).
combining the statements gives you that x^2 is an integer between 1 and 16. This still does not help, since 49-x^2 could be a multiple of 5, say x^2=2, or may not be a multiple of 5, say if x^2=1.

I think explanation is a little bit complicated.
With choice a x can be 2 or 3 or any non integer numer.ex 1.3 ,2.5, 3.8 ....So this does not lead to anything.
choice b x2 is an integer means x is also an integer. this also does not lead to any conclusion
combining both x is 2 or 3. measn x2 is 4 or 9
means 5y = 49-4=45 or 49-9=40. in either case y is an integer. so anwer is C

[cyndrella]

Originally Posted by ajayreddy

probability that both flowers are not tulips = 1- probability that both flowers are tulips
= 1 - 2C2/8C2
= 1 - 1/28
= 27/28

but you din consider the case when one flower may be a tulip and the other some else?

[Sriram_Avadhani]

Originally Posted by Sriram_Avadhani

I think explanation is a little bit complicated.
With choice a x can be 2 or 3 or any non integer numer.ex 1.3 ,2.5, 3.8 ....So this does not lead to anything.
choice b x2 is an integer means x is also an integer. this also does not lead to any conclusion
combining both x is 2 or 3. measn x2 is 4 or 9
means 5y = 49-4=45 or 49-9=40. in either case y is an integer. so anwer is C

this has an assumption that x is an rational number. If x can be an irrational number like Root7 etc... This explanaition does not hold good. In that case Answer is E

[dumbJoe]

Originally Posted by cyndrella

but you din consider the case when one flower may be a tulip and the other some else?

since the flowers must come from the rest 6, we only need to consider that case
6c2, total possibilities being 8c2. here for all practical purposes we can take them to be distinct, because while calculating probability we are counting the cases altogether........but i dont see the answer 6c2/8c2 ie 15/28