GMAT Problem Solving Discussions

MBA
843
Alright this problem's been driving me nuts.

A fairly biased coin is tossed 6 times. What is the probability that it will fall as a head more than twice but less than 5 times?

a)3/4
b)3/8
c)7/8
d)1/4
e)3/5

dude, u hv either gotten the data wrong or the options wrong..cuz acc. to the given data, the answer must be

(6C3+6C4)/2^6 = 35/64 which is nt there in the options...kindly recheck it and let us knw!!
844

Could someone explain the correct answer to this question?

If x ??????>?>?>?>0 ,then ((x^2)^1/2 )/x = ? (square root of x squared/x)

a)-1
b)0
c)1
d)x
e)x/x

845

Of the 12 temporary employees in a certain company,4 will be hired as permanant employees.If 5 of the 12 temporary employees are women,how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?
a)22,
b)35,
c)56,
d)70,
e)105

846
Could someone explain the correct answer to this question?

If x
0 ,then ((x^2)^1/2 )/x = ? (square root of x squared/x)

a)-1
b)0
c)1
d)x
e)x|/x

hi rajkumar
i guess the answer to the question is e
when you take square of a no. and then take square root it can have either of the two values i mean +x or -x so it becomes |x as x
0 so divided by x becomes the option e

hope this helps
Sillyfool
847
hi rajkumar
i guess the answer to the question is e
when you take square of a no. and then take square root it can have either of the two values i mean +x or -x so it becomes x| as x 0 so divided by x becomes the option e

hope this helps
Sillyfool


yes...the ans is E...but statement in bold is incorrect...bcoz square of a no is always +ve and square root of it is only positive..i.e 25^1/2 is only +5 and not -5...

lets plug in..if x=-5. x^2=25 & 25^1/2=5
i.e /x is 5/-5 = -1 i.e x/x

if x=5, x^2=25 & 25^1/2=5
i.e /x is 5/5=1 i.e x/x

Hence |x/x satisfies for +ve n -ve nos...Ans E
848
Of the 12 temporary employees in a certain company,4 will be hired as permanant employees.If 5 of the 12 temporary employees are women,how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?
a)22,
b)35,
c)56,
d)70,
e)105


out of 12 employees, we have 5 women and 7 men.
we have to select 3 women out of 5 and 1 man out of 7
i.e total no of ways = 5C3 * 7C1 = 70
849
yes...the ans is E...but statement in bold is incorrect...bcoz square of a no is always +ve and square root of it is only positive..i.e 25^1/2 is only +5 and not -5...

lets plug in..if x=-5. x^2=25 & 25^1/2=5
i.e /x is 5/-5 = -1 i.e x|/x

if x=5, x^2=25 & 25^1/2=5
i.e /x is 5/5=1 i.e x/x

Hence |x/x satisfies for +ve n -ve nos...Ans E

bhavin, could u please explain the statement "bcoz square of a no is always +ve and square root of it is only positive..i.e 25^1/2 is only +5 and not -5..."?
Both 5 and -5 squared give us 25.

Why cant the root of a squared number be negative?
((25)^1/2) cant be -5?????


i think the answer to that question should be "+1 or -1" (which is not an option though 😞 )
if u take x = 5, u get 5/5 ie 1.
if u take x = -5, u get 5/-5 ie -1

Am i showing signs of stress already?
850
bhavin, could u please explain the statement "bcoz square of a no is always +ve and square root of it is only positive..i.e 25^1/2 is only +5 and not -5..."?
Both 5 and -5 squared give us 25.

Why cant the root of a squared number be negative?
((25)^1/2) cant be -5?????


i think the answer to that question should be "+1 or -1" (which is not an option though 😞 )
if u take x = 5, u can have +5/5 or -5/5
if u take x = -5, u can have +5/-5 or -5/-5

Am i showing signs of stress already?

Hmm as an afterthought, x/x also equals +1 or -1.And that's why E is the answer.

However root of a squared number can very well be positive or negative.So Bhavin's reasoning is still flawed.
851
r u sure dis r the ans options?
my ans works to be 35/64

heads more than 2 n less than 5 implies 2 poss:
1) 3 H & 3 T
OR
2) 4 H & 2 T

i.e (6C3 + 6C4)/2^6
=(20+15)/64
=35/64


It gives the same result to me. The correct answer posted could be wrong.

+ = 20/64 + 15/64= 35/64
852
Of the 12 temporary employees in a certain company,4 will be hired as permanant employees.If 5 of the 12 temporary employees are women,how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?
a)22,
b)35,
c)56,
d)70,
e)105


We have 4 places, 3 of which for women and 1 for men.

{ [5x4x3x7 /4! x (4!/ 3!)) . = 70. Asnwer d)
853
Hmm as an afterthought, x/x also equals +1 or -1.And that's why E is the answer.

However root of a squared number can very well be positive or negative.So Bhavin's reasoning is still flawed.



no dude...there is no flaw in the reasoning.
root of a positive integer can never be negative, though square of a negative number is positive...

so root of a positive number is only positive...and root of a negative no is imaginary or complex...

and u get ans as 1 when x is 5 and -1 when x= -5
and not +/- 1 when x is 5 and -5....

sign is taken care by x in denominator..hence the answer is E....and not bcoz it can be 1 and -1 simultaneously...
854
We have 4 places, 3 of which for women and 1 for men.

{ [5x4x3x7 /4! x (4!/ 3!)) . = 70. Asnwer d)

hi Paki,

70 is the correct answer to the question.
I understand the soln 5C3 x 7C1 = 70
I do not understand how you get 4! into your soln.

Thanks,
Raj
855
hi rajkumar
i guess the answer to the question is e
when you take square of a no. and then take square root it can have either of the two values i mean +x or -x so it becomes x| as x
0 so divided by x becomes the option e

hope this helps
Sillyfool

hi sf,


Thanks again for the soln. choice E is the correct answer.
Does x also mean +x and -x?
Because I never thought of it that way.I was thinking |x means only the absolute
value.

Raj
856
Of the 12 temporary employees in a certain company,4 will be hired as permanant employees.If 5 of the 12 temporary employees are women,how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?
a)22,
b)35,
c)56,
d)70,
e)105

hi rajkumar i will try to post it in a simpler way
look there are 4 employyes to be selected and
we can choose 3 women out of 5 in 5c3 ways and 1 man out of 7 in 7c1 ways
so the result becomes

5c3 * 7c1 that is
5!/(3! * 2!) * 7!/(6! * 1!) = 70

hope this helps
Sillyfool
857
hi sf,


Thanks again for the soln. choice E is the correct answer.
Does x| also mean +x and -x?
Because I never thought of it that way.I was thinking x means only the absolute
value.

Raj

well rajkumar x| is -x for x0

In general while solving problems we take the value of |x = x

hope this helps
Sillyfool

P.S. One request that i have is my name is Sillyfool i like to be called that way no sf please
858
hi Paki,

70 is the correct answer to the question.
I understand the soln 5C3 x 7C1 = 70
I do not understand how you get 4! into your soln.

Thanks,
Raj


5x4x3x7 dividided 4! (because the order is not important), and multiplied by 4! (number of permutations), and divided by 3! (number of repetitions of women).
Let me know if you have any more questions.
859
Of the 12 temporary employees in a certain company,4 will be hired as permanant employees.If 5 of the 12 temporary employees are women,how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?
a)22,
b)35,
c)56,
d)70,
e)105

the answer is very simple, i mean no need to complicate the things
here it goes......
select 3 women out of 5 in 5C3 ways
and select 1 man out of 7 in 7C1 ways
so ANSWER = 5C3 x 7C1 = 70 ways :new_smile-l:
860
Can Someone plz help me with this?
A group of 8 man r to b chosen from 12 men for rowing out of which 3 men can row on one side only & 2 can row on the other side only. Find the numbr of ways of arranging the crew with 4 members on each side.
40320
30240
60480
10080
20640
PS: the answer given is 60480 :banghead:
but can someone plz give proper explaination.:confused:
861

Where did you obtain that "kind" of exercise?
Also one answer choice is missing.

862
Where did you obtain that "kind" of exercise?
Also one answer choice is missing.

hey kindly mention the post u r referring !!
in case it was the one above........ i've added the 5th option.... i dint bother to add it earlier as i only wanted the explanation