GMAT Problem Solving Discussions

MBA
1510
A die is rolled 4 times. What is the probability of not getting two even numbers on any two consecutive rolls?

(A) 0.25
(B) 0.4
(C) 0.5
(D) 0.75
(E) 0.8

(C) 0.5
What is not allowed is EEOO, OEEO, OOEE, & EEOE, EOEE, & EEEO, OEEE, & EEEE
Total combinations for this is = 3^4 * 8
Probability = ( 6^4 - 3^4 *8 ) / 6^4
= 1/2
What is OA?
1511

Dan and Ran are among 6 runners of a certain triathlon race. If there can be no tie, how many possible results are there where Ran is positioned higher than Dan?

(A) 15
(B) 36
(C) 180
(D) 360
(E) 720

1512
85 people at a certain college study atleast one of the three languages: english, german and swedish. 30 students study english and one more language. 21 students study german and one more language. 27 students study swedish and one more language. If only one person studies all three languages, how many students study both swedish and german but not english?

(A) 9
(B) 12
(C) 18
(D) 21
(E) 27

EG + ES = 30
EG + GS = 21
ES + GS = 27
Solving GS = 9
Answer (A)
What is OA
1513
Dan and Ran are among 6 runners of a certain triathlon race. If there can be no tie, how many possible results are there where Ran is positioned higher than Dan?

(A) 15
(B) 36
(C) 180
(D) 360
(E) 720

Each race can end in 6! results
Total kinds of results possible = 6! * 3.
In exactly half of them Dan will rank higher than Ran, vice versa in other half.
Hence, answer = (6! * 3) / 2 = 180
Answer = (C)
What is OA ?
1514

OA is (D) - 360.

Can someone plz help?

Each race can end in 6! results
Total kinds of results possible = 6! * 3.
In exactly half of them Dan will rank higher than Ran, vice versa in other half.
Hence, answer = (6! * 3) / 2 = 180
Answer = (C)
What is OA ?
1515

Yup. your right..OA is (A). Thanks

EG + ES = 30
EG + GS = 21
ES + GS = 27
Solving GS = 9
Answer (A)
What is OA
1516
OA is (D) - 360.

Can someone plz help?

it will be n!/2 ie 6!/2 = 360
1517
OA is (D) - 360.

Can someone plz help?


My 2 Cents ----
Consider the grid - as the positions.... The question is for the number of possibilites where Ran is positioned higher than Dan.

Dan is at 6th position-> there are 5(for Ran) * 4!(the other guys) = 5 * 4!
Dan is at 5th position-> there are 4(for Ran) * 4!(the other guys) = 4 * 4!
Dan is at 4th position-> there are 3(for Ran) * 4!(the other guys) = 3 * 4!
Dan is at 3th position-> there are 2(for Ran) * 4!(the other guys) = 2 * 4!
Dan is at 2th position-> there are 1(for Ran) * 4!(the other guys) = 1 * 4!

So totaling gives - 4! (5+4+3+2+1) = 24*15 = 360 and D it is!!. We need to remember that Ran should always be ahead of Dan but the other 4 ppl can be anywhere.

Hope this helps!!!
1518

Q. If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

Can Some One Solve and Explain this to me?
Well, I have solved it to an extent and then got stuck as it seems like the question is contradictory. Let me explain!

odd - odd = even
even - even = even.........(1)
odd - even = odd
even - odd = odd

odd/even = fraction or decimal
even/odd = even........................(2)
even/even = odd or even.............(3)
odd/odd= odd

Since both result in an even no. the options are (1) & (3).
So a and b are both even no.s.
The answer given for the Problem is option D, but i am not satisfied with it.....since (2+2)/2 = 2 and its not odd.
Can some one please help me , i am lost!!!!!!

jishnu 😃

1519
Q. If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

Can Some One Solve and Explain this to me?
Well, I have solved it to an extent and then got stuck as it seems like the question is contradictory. Let me explain!

odd - odd = even
even - even = even.........(1)
odd - even = odd
even - odd = odd

odd/even = fraction or decimal
even/odd = even........................(2)
even/even = odd or even.............(3)
odd/odd= odd

Since both result in an even no. the options are (1) & (3).
So a and b are both even no.s.
The answer given for the Problem is option D, but i am not satisfied with it.....since (2+2)/2 = 2 and its not odd.
Can some one please help me , i am lost!!!!!!

jishnu :)

Ans is D

For both a-b and a/b to be an even integer, both a and b have to be even
Also, since a/b is an even int, a>b and a is a multiple of b

(a+2)/2 always give an odd integer whereas (b+2)/2 will always be alwas be even.

Hence OA is D
1520

Thank You srikanth267 you rock!
Great ! Great !

1521

Q. During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the trip?

A. (180-x)/2
B. (x+60)/4
C. (300-x)/5
D. 600/(115-x)
E. 12000/(x+200)

Please help me !
srikanth267 save me!

1522
Q. If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

Can Some One Solve and Explain this to me?
Well, I have solved it to an extent and then got stuck as it seems like the question is contradictory. Let me explain!

odd - odd = even
even - even = even.........(1)
odd - even = odd
even - odd = odd

odd/even = fraction or decimal
even/odd = even........................(2)
even/even = odd or even.............(3)
odd/odd= odd

Since both result in an even no. the options are (1) & (3).
So a and b are both even no.s.
The answer given for the Problem is option D, but i am not satisfied with it.....since (2+2)/2 = 2 and its not odd.
Can some one please help me , i am lost!!!!!!

jishnu :)


your reasoning is correct --
odd - odd = even
even - even = even.........(1)
odd - even = odd
even - odd = odd

odd/even = fraction or decimal
even/odd = even........................(2)
even/even = odd or even.............(3)
odd/odd= odd

This implies both must be even...

lets take a=20, b = 2.

a/2 = 10 - even
b/2 = 1 - odd
(a+b)/2 = 11 - odd
(a+2)/2 = 11 - odd
(b+2)/2 = 2 - even

lets take a = 16, b = 4
a/2 = 8 -even
b/2= 2 - even
(a+b)/2 = 10 - even
(a+2)/2 = 9 - odd
(b+2)/2 = 3 - odd

In both the above example only D is odd... hence the answer. There is another way to solve this...
from the above we can say a & b are even and a = (even no.) * b.
All even numbers can be written in the form of 2 *(some integer) and an odd integer as 2 *(some integer) + 1
so a = 2b (conidering the least even integer)
b = 2n
also a = 4n
now our choices:
1. (a/2) = 2n --> even
2. (b/2) = n (can be either even or odd)
3. (a+b)/2 = 3n (Can be either even or odd)
4. (a+2)/2 = 2n+1 ---> Must be Odd.
5. (b+2)/2 = n+1 (Can be either even or odd).

Hope this Helps
1523
Q. During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the trip?

A. (180-x)/2
B. (x+60)/4
C. (300-x)/5
D. 600/(115-x)
E. 12000/(x+200)

Please help me !
srikanth267 save me!


Consider the total distance to be 's' -->

Total time = +

So Total time, T = 40 * s + (s*x/5) / (60 * 40)

Avg. time = total distance/ total time
= s / T
= 12000/ (x+200)
Ans E - Hope this helps
1524
Hi, Please solve the following. Even though I know the answer still unable to solve.

The function f is defined for each positive three-digit integer n by f(n) = 2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 80
Ans - D
1525
Hi, Please solve the following. Even though I know the answer still unable to solve.
The function f is defined for each positive three-digit integer n by f(n) = 2x3y5z , where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), them m-v=?
(A) 8
(B) 9
(C) 18
(D) 20
(E) 80
Ans - D


Can you tell what f(n) is ... for example:

f(234) - is 4920?? or 4 * 9 * 20?? or something else...
1526

Sorry unable to write properly. f(n) is not 2x3y5z. here X is power of 2, Y power of 3, and Z power of 5. I hope it's clear now.

1527
Simmy Says
Sorry unable to write properly. f(n) is not 2x3y5z. here X is power of 2, Y power of 3, and Z power of 5. I hope it's clear now.


well in that case D seems correct
f(n) = 2^x 3^y 5^z

f(m) = 9 * f(v) = 9 * (2^x 3^y 5^z) = 2^x 3^(y+2) 5^z

so m = x y+2 z and v = x y z - -the only diff is in tenth place.. hence it must be 20 and D is the answer.
1528

Thanks, got it now. had got it till f(m) = 9 * f(v) = 9 * (2^x 3^y 5^z) = 2^x 3^(y+2) 5^z but then got confused when doing m-v. God save me from these confusions. Thanks a lot.

1529
Simmy Says
Thanks, got it now. had got it till f(m) = 9 * f(v) = 9 * (2^x 3^y 5^z) = 2^x 3^(y+2) 5^z but then got confused when doing m-v. God save me from these confusions. Thanks a lot.


Happens all the times....

glad to be of help and you can actually thank me my clicking the 'Thank' button rather than send a message too :-).

All the Best...