GMAT Problem Solving Discussions

sharkon · January 2, 2008, 10:00am

Q.The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4Pi/3 ,what is the length of line segment RU?

A.4/3

B.8/3

C.3

D.4

E.6

Answer would be B => 8/3

(Length of arc RTU ) /(Length of semicircular ARC)
= (Length of RU) / (Length of Diameter)

ie (4/3pi) / 4PI = RU/8

=> RU = 8/3

nitya34 · January 2, 2008, 4:43pm

Thanks for this wonderful thread!!

the_boss · January 3, 2008, 6:18pm

ok This is a tough one for me :-
A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. what is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?

Let's call the probability evens P(S) --- The probability for Harry to be chosen as the secretary and P(T)---- the probability for Harry to be chosen as the Treasurer.

P(S) or P(T) = ????????? I would really appreciate it if you provide an explaination not only the answer. I already have the answer but it is not too convincing. I have been working with discrete independent problems. I am not sure what kind of a problem is this one.

Thanks guys in advanced and keep the good work.

dumbjoe · January 3, 2008, 6:37pm

Total permutations = 10p3
favorable = 2c1 x 9p2

Fav/Total = 0.2

Here just combinations wont do as relative order is also important, the total possible permutations are simple to figure out, for favourable cases the 2 possible can be chosen in 2c1 ways and then the same case of possible permutations from remaining 9 people.

dumbjoe · January 4, 2008, 11:45am

Here are more details as you asked for :)

To determine the probability, you need two things. first, the total possibilities and second, the possibilities you are interested in. Now, here, the total cases would be when you consider not only selection of a group of three but their relative order as well, the association of person with the post, that is.

This is 10c3 x 3! or simply 10p3.

Now for the possible cases, since they are perfectly symmetric we can just start with i possibility and multiply by 2c1, a selection between either of two cases. The case is when the guy is The treasurer, then out of the other 9 people two more are taken to form a team and each team differs when a person holds a different responsibility. So like earlier 9p2, and since two ways we are interested a factor of 2c1 giving 2c1 x 9p2

PS - rude of me, but even if you have a flawed answer/ expression in probability or P&C;, to figure the reasoning behind that expression is rather easy

maverick.jd · January 4, 2008, 1:49pm

Answer would be B => 8/3

(Length of arc RTU ) /(Length of semicircular ARC)
= (Length of RU) / (Length of Diameter)

ie (4/3pi) / 4PI = RU/8

=> RU = 8/3

Dudes, the answer is 4, not 8/3....

the_boss · January 4, 2008, 2:04pm

Total permutations = 10p3
favorable = 2c1 x 9p2

Fav/Total = 0.2

Dude I still don't know what is 10P3, 2c1, or 9P2. how do u calculate it?

ajayreddy · January 4, 2008, 4:34pm

Total permutations = 10p3
favorable = 2c1 x 9p2

Fav/Total = 0.2

Dude I still don't know what is 10P3, 2c1, or 9P2. how do u calculate it?

see, if it is a permutation, eg. 10P3, then u can calculate it as

p = 10!/(10-3)! = 10!/7!

and if it is a combination, eg. 10C3, then u can calculate it as

c = (10x9x

/3!

eg. 12C4

c = (12x11x10x9)/4!

for combination, while writing the numerator, start wid the first number and write 'n' decreasing consecutive numbers where n is the second number and in the denominator, write the factorial of the second number..

a few more ex.

6C4
this can also be written as 6c(6-4) = 6C2 = (6x5)/2!

for combination, NcD is the same as Nc(N-D)

eg.
8C5 = 8C3 = (8x7x6)/3!

hope u understood....

peak_25579392 · January 6, 2008, 11:52am

Pls help me with following questions:

1)If x and y are positive, is x^3 > y
(1)square root of x >y
(2)x > y

2)What is the value of integer k?
(1)k + 3 > 0
(2) k^4
3)If the units digit of the three-digit positive integer "k" is non-zero, what is the tens digit of "k"?
(1)The tens digit of k + 9 is 3
(2)The tens digit of k + 4 is 2

Two problems are in the attachment.

ajayreddy · January 10, 2008, 4:16pm

Pls help me with following questions:

1)If x and y are positive, is x^3 > y
(1)square root of x >y
(2)x > y

2)What is the value of integer k?
(1)k + 3 > 0
(2) k^4
3)If the units digit of the three-digit positive integer "k" is non-zero, what is the tens digit of "k"?
(1)The tens digit of k + 9 is 3
(2)The tens digit of k + 4 is 2

Two problems are in the attachment.

Q.1
using st.1 alone,
let x=4, y=1....sqrt(x)>y....and x^3>y in all cases for x,y>0
hence, st.1 alone is sufficient

using st.2 alone,

x = 2, y = 1....x^3>y for all cases x,y>0
so st.2 alone is also sufficient...
hence, answer is C...

Q.2
st.1 is not sufficient alone
using st.2,
k^4the only value of k which satisfies condition 2 is 0...(since k is an integer)
so answer is B...

Q.3
using st.1 alone,
since units digit is non zero, the min. value it can hve is 1 and max value is 9...so in any case, for the tens digit of k+9 to be 3, the original ten's digit has to be 2 in all cases, eg. 121, 129, 221, 224, 228 etc...

Q.22
neither st. alone is sufficient to solve the problem,
using both st. alone, u can find the supplementary angles of w and z which are 85 and 55 resp..
in the quad, the supplementary angles of x,y,w,z form a quadrilateral...and their sum = 360
hence, sum of supplementary angles of x and y = 360-55-85 = 220
now,
x+y+supplementary x + supplementary y = 360
hence, x+y = 140
thus, answer is C....

Q.25
x1 = 3

x2 = 2(3)-1 = 5
x3 = 9
x4 = 17

now, x3-x2 = 4 = 2^2
x4-x3 = 8 = 2^3

hence, x20-x19 = 2^19
answer is A...

one suggestion,
u wud get better and earlier responses if u post the DS questions in its respective thread....

maverick.jd · January 15, 2008, 4:40pm

1.For any integer n greater than 1,n! denoted the product of all the integers from 1 to n,

inclusive.How many prime numbers are there between 6!+2 and 6!+6,inclusive ?
a.none
b.one
c.two
d.three
e.four

2.the cost of manufacturing a certain product can be estimated by the formula
c=0.03 rs(t*t),
where r and s are the amounts,in hours.If r is increased by 50 percent, s is

increased by 20 percent and t is decreased by 30 percent, by approximately what percent will

the estimated cost of manufacturing the product change
a.40 % increase
b.12 % increase
c.4% % increase
d.12 % decrease
e.24 % decrease

ajayreddy · January 15, 2008, 5:01pm

1.For any integer n greater than 1,n! denoted the product of all the integers from 1 to n,

inclusive.How many prime numbers are there between 6!+2 and 6!+6,inclusive ?
a.none
b.one
c.two
d.three
e.four

2.the cost of manufacturing a certain product can be estimated by the formula
c=0.03 rs(t*t),
where r and s are the amounts,in hours.If r is increased by 50 percent, s is

increased by 20 percent and t is decreased by 30 percent, by approximately what percent will

the estimated cost of manufacturing the product change
a.40 % increase
b.12 % increase
c.4% % increase
d.12 % decrease
e.24 % decrease

Q.1
see, 6! = 6x5x4x3x2x1 = 720
so u need to find no. of prime numbers between 722 and 726 which is equal to ZERO....

q.2
r is increased by 50%...hence, new value of r = 1.5r similarly, new s = 1.2s, new t = 0.7t
c1 = .03rs(t*t)*(
1.5*1.2*0.7*0.7) which is approx equal to 0.9
so this means that the new value is 0.1 or 10% less than the old value...hence, the closest answer is D...

maverick.jd · January 15, 2008, 5:04pm

hmmm, simple answers, but m carrying out silly mistakes..:-(

Q.1
see, 6! = 6x5x4x3x2x1 = 720
so u need to find no. of prime numbers between 722 and 726 which is equal to ZERO....

q.2
r is increased by 50%...hence, new value of r = 1.5r similarly, new s = 1.2s, new t = 0.7t
c1 = .03rs(t*t)*(
1.5*1.2*0.7*0.7) which is approx equal to 0.9
so this means that the new value is 0.1 or 10% less than the old value...hence, the closest answer is D...

paki · January 16, 2008, 9:26pm

I'm starting to do math exercises...
"A student took 6 courses last year and received an average grade of 100. The year before, the student took 5 courses and received an average grade of 90. To the nearest tenth of a point, what was the student's average grade for the entire two year period?
A. 79
B. 89
C. 95
D. 95.5
E. 97.2

Can somebody explain why is 95.5? Tks!

vicky.verma · January 16, 2008, 10:08pm

I'm starting to do math exercises...
"A student took 6 courses last year and received an average grade of 100. The year before, the student took 5 courses and received an average grade of 90. To the nearest tenth of a point, what was the student's average grade for the entire two year period?
A. 79
B. 89
C. 95
D. 95.5
E. 97.2

Can somebody explain why is 95.5? Tks!

6 courses...average of 100...gives total score of 600
5 courses...average of 90...gives total score of 450

Total score : 450+600 --> in 11 courses

1050/11 -> 95.5

-Viv

paki · January 17, 2008, 12:04am

TKS:smilecol:

crazykat · January 18, 2008, 6:24am

A problem..
there are 9 balls...one out of which is different..(lighter or heavier)
have to find out in 3 measurements..which one is tht....

plzz help

vicky.verma · January 18, 2008, 7:05am

A problem..
there are 9 balls...one out of which is different..(lighter or heavier)
have to find out in 3 measurements..which one is tht....

plzz help

Incase you know if the ball is lighter or heavier this can be done in 3 steps. I'll take the case where u have to find the lighter ball :

Make 3 packs...3 balls each...

1. Compare the weights of any 2 packs. Incase they are equal choose the 3rd pack and go to step 3.
2. Incase the above are not equal, pick the lighter pack.
3. Compare the balls from this pack 2 at a time. This will take 2 tries.

Incase it is not known if the ball is lighter or heavier it will take more tries.

vicky.verma · January 18, 2008, 7:13am

Q.The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is 4Pi/3 ,what is the length of line segment RU?

A.4/3

B.8/3

C.3

D.4

E.6

Here you go :

Let the length of line segment RU : x
Length of arc : 4Pi/3 => Angle made at the center is 60 degrees.

cos 60 = (r^2 + r^2 - x^2)/(2.r.r)

which gives x as 4

rockeeze · January 21, 2008, 2:56pm

hi ajay
in the following prob.
1)If x and y are positive, is x^3 > y
(1)square root of x >y
(2)x > y
Q.1
using st.1 alone,
let x=4, y=1....sqrt(x)>y....and x^3>y in all cases for x,y>0
hence, st.1 alone is sufficient
i differ from ur ans
coz, x is only a positive number so sq rt of x can be 0.2
and clearly x^3 is even smaller
in tht case we wud be unable to gt an answer
i feel this ques cannot be ans evn by using both the statements
do comment
regards
rock