GMAT Problem Solving Discussions

MBA
3301
Eighty percent of the lights at Hotel California are switched on at 8 p.m. one evening. However, forty percent of the lights that are supposed to be switched off are actually switched on, and ten percent of the lights that are supposed to be switched on are actually switched off. What percent of the lights that are switched on are supposed to be switched off?

A22(2/9)%

B16(2/3)%

C11(1/9)%

D10%

E5%

Is the ans for the above q option d)10%.Here is how I worked it out

Total no.of lights = 100

Suppose to be: switched ON = 80 and switched OFF = 20.

Real condition : ON = 72 + 8
OFF = 12 + 8

So the actual percentage is 8/80 * 100 = 10%

Let x%= Ideally ON
y%= ideally OFF

x+y = 100 ....(1)

Now, Ideal Vs Actual
Actual ON = 0.9x + 0.4y

So, 0.9x + 0.4y = 80 ...(2)

Solve, simultaneously,
x = 80 ; y = 20

Now, from these 80, 0.4y i.e 0.4*20 = 8 shd have been OFF

Hence, Ans = 8/80 = 10 %

Ans D


bhavin, deepak u both got it right.

OA - D

btw, anotehr way to do this could be by using a 2x2 matrix..
3302
Good one!!

Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.

Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?

A. 8/33
B. 62/165
C. 17/33
D. 103/165
E. 25/33

Prob that there is no pair :

1st card = random selection, no prob involved
2nd card = shd not be the corr card, hence 10/11
3rd card = shd not be the corr prev 2 cards, hence 8/10
4th card = shd not be the corr prev 3 cards, hence 6/9

Prob ( no pair) = 1 * 10/11 * 8/10 * 6/9 = 16/33

Hence, p(atleast 1 pair) = 1 - 16/33 = 17/33 ..Ans C


Right again.. :)

OA - C
3303
The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?

A3

B14

C30

D42

E70


Bhavin, Deepak, nemo1.. u all got it right..

OA - D
3304

Q. In the xy plane each point on the circle K has non negative coordinates and the center of k is the point (4,7). what is the maximum possible area of k ?
a. 4pi
b. 9pi
c. 16pi
d. 28 pi
e. 49 pi

Please explain !! thanks !

3305
Q. In the xy plane each point on the circle K has non negative coordinates and the center of k is the point (4,7). what is the maximum possible area of k ?
a. 4pi
b. 9pi
c. 16pi
d. 28 pi
e. 49 pi

Please explain !! thanks !


For non negative co-ordinates entire circle must lie in 1st quadrant, and at at max the +ve X or Y axis could be tangent to the circle,

So if centre is (4,7) ...when radius is 4, Y axis is tangent to the circle...so thats the max ..hence max area is 16pi ..

Option C
3306
Q. In the xy plane each point on the circle K has non negative coordinates and the center of k is the point (4,7). what is the maximum possible area of k ?
a. 4pi
b. 9pi
c. 16pi
d. 28 pi
e. 49 pi

Please explain !! thanks !


The circle must lie n the first quadrant.So distance frm center to X-axis gives the radius of the circle.

so radius = 4.Area = 16pi.

My take is option C
3307
Q. In the xy plane each point on the circle K has non negative coordinates and the center of k is the point (4,7). what is the maximum possible area of k ?
a. 4pi
b. 9pi
c. 16pi
d. 28 pi
e. 49 pi

Please explain !! thanks !


Max radius can be 4 - that is the max length it can expand to towards the y axis, as none of the points in the circle are negative!!
hence area - 16pi

IMO C

OA?
3308
Try this one :

What is the tens digit of 7^202?

Ans : 4 ....

Cyclicity is 4 ...
for 7^4n and 7^(4n+1) ...tens digit is 0
for 7^(4n+2) and 7^(4n+3) ....tens digit is 4 ...


bhavin,

can u explain the part in bold a lil more...

thanks!!


Hey Nisha,
Lets observe the pattern for last 2 digits :

7^1 = 07
7^2 = 49
7^3 = 43
7^4 = 01
7^5 = 07
7^6 = 49

Hence, we observe that for tens digits 0,4,4,0 is tha pattern with a cyclicity of 4 ...

Hence,
for 7^4n and 7^(4n+1) ...tens digit is 0
for 7^(4n+2) and 7^(4n+3) ....tens digit is 4

Hope this helps
3309

Car B begins moving at 2 mph around a circular track with a radius of 10 miles. Ten hours later, Car A leaves from the same point in the opposite direction, traveling at 3 mph. For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?

A. 4pi 1.6

B. 4pi + 8.4

C. 4pi + 10.4

D. 2pi 1.6

E. 2pi 0.8

3310
Car B begins moving at 2 mph around a circular track with a radius of 10 miles. Ten hours later, Car A leaves from the same point in the opposite direction, traveling at 3 mph. For how many hours will Car B have been traveling when car A has passed and moved 12 miles beyond Car B?

A. 4pi - 1.6

B. 4pi + 8.4

C. 4pi + 10.4

D. 2pi - 1.6

E. 2pi - 0.8


Ans B
Total circular distance = 20pi
Distance covered by B in 10 hrs = 20 miles

Hence, Total relative distance in same time frame = (20pi - 20 + 12)
Relative speed = 5 mph

time = (20pi-20+12)/5
= 4pi - 1.6

Total time = 4pi - 1.6 +10 = 4pi + 8.4
Ans B
3311

If x>y^2>z^4, Which of the following could be true ?

I. x > y > z
II. z > y > x
III. x > z > y

a. I only
b. I and II only
c. I and III only
d. II and III only
e. I,II and III

^ = power

3312
If x>y^2>z^4, Which of the following could be true ?

I. x > y > z
II. z > y > x
III. x > z > y

a. I only
b. I and II only
c. I and III only
d. II and III only
e. I,II and III

^ = power

hi,
if we take z=1 and y=2, then x>4
which makes it I. x > y > z
if we take z=-1 and y=-2 then also x>4
which makes it III. x > z > y

so in my opinion, it will be c. I and III only
hope it is correct...
3313
Ans B
Total circular distance = 20pi
Distance covered by B in 10 hrs = 20 miles

Hence, Total relative distance in same time frame = (20pi - 20 + 12)
Relative speed = 5 mph

time = (20pi-20+12)/5
= 4pi - 1.6

Total time = 4pi - 1.6 +10 = 4pi + 8.4
Ans B


Bhavin,
Thanks for the solution. It is simple and effective approach.
But, when I worked on this problem, my thought did not take me towards using relative speed. So I was wondering what is wrong with my approach.

Please be patient and evaluate for my sake:

B traveled for 10 hrs before A was brought into picture.
From that point,
Let us say A and B meet at a point on the circle.
Distance traveled by B is : x ; So time taken by B is : x/2
Distance traveled by A is : 20pi -x ; so time taken by A is: (20pi -x) /2

Equating these two and solving for x we get x = 8pi
So, B traveled 8pi and A traveled 12pi.

From this point, let y be the distance that B travels, until the point when A travels some distance so that they both are 12 miles apart.
Let t be the time of travel for the above.
Based on the rates:
For B: (8pi + y) / t = 2
For A: (12pi + 12 - y)/t = 3
Solving we get y = 24/5, so t = 2.4

So,
time taken by B would be time taken for it to cover 8pi distance + t
8pi distance takes 4pi hours for B to cover.
So 4pi + t = 4pi + 2.4
Overall time for B therefore is: 4pi + 2.4 + original 10, 4pi + 12.4

Obviously I went wrong somewhere. Where ?
Can you pour in your thoughts please !!
3314
If x>y^2>z^4, Which of the following could be true ?

I. x > y > z
II. z > y > x
III. x > z > y

a. I only
b. I and II only
c. I and III only
d. II and III only
e. I,II and III

^ = power

IMO: E (I, II, and III )
first case: x = 20, y = 2, z = 1
20 > y^2 (4) > z^4 (1)
and x > y > z

second case: z = 1/2, y = 1/3, x = 1/4
x (1/4) > y^2 (1/9) > z^4 (1/16)
and z > y > x

third case: x = 1, y = 1/3, z = 1/2
x (1) > y^2 (1/9) > z^4 (1/16)
and x > z > y
3315
Ans B
Total circular distance = 20pi
Distance covered by B in 10 hrs = 20 miles

Hence, Total relative distance in same time frame = (20pi - 20 + 12)
Relative speed = 5 mph

time = (20pi-20+12)/5
= 4pi - 1.6

Total time = 4pi - 1.6 +10 = 4pi + 8.4
Ans B

Bhavin,
Thanks for the solution. It is simple and effective approach.
But, when I worked on this problem, my thought did not take me towards using relative speed. So I was wondering what is wrong with my approach.

Please be patient and evaluate for my sake:

B traveled for 10 hrs before A was brought into picture.
From that point,
Let us say A and B meet at a point on the circle.
Distance traveled by B is : x ; So time taken by B is : x/2
Distance traveled by A is : 20pi -x ; so time taken by A is: (20pi -x) /2

Equating these two and solving for x we get x = 8pi
So, B traveled 8pi and A traveled 12pi.

From this point, let y be the distance that B travels, until the point when A travels some distance so that they both are 12 miles apart.
Let t be the time of travel for the above.
Based on the rates:
For B: (8pi + y) / t = 2
For A: (12pi + 12 - y)/t = 3
Solving we get y = 24/5, so t = 2.4

So,
time taken by B would be time taken for it to cover 8pi distance + t
8pi distance takes 4pi hours for B to cover.
So 4pi + t = 4pi + 2.4
Overall time for B therefore is: 4pi + 2.4 + original 10, 4pi + 12.4

Obviously I went wrong somewhere. Where ?
Can you pour in your thoughts please !!

Bhavin, ur answer's right!!! great approach.. Thanks! :cheerio:

Vikram, you made one silly mistake..

If Distance travelled by B -> x
Distance travelled by A -> 20pi - 20 - x (If B travels x and A travel y miles, then x+y = 20pi - 20, So, y = 20pi-20 - x )

which means -> x = 8pi-8
t = 4pi - 4

to travel one portion of the 12 miles, B takes -> 2.4

total time -> 10+4pi-4+2.4 ~ 4pi + 8.4

i'd used a similiar approach in the test but screwed up at some place too and got it wrong..
HTH ... 😉
3316

x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

A)x = w

B)x > w

C)x/y is an integer

D)w/z is an integer

E)x/z is an integer

Pls explain ur approach

3317

A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

A)1/14

B)1/7

C)2/7

D)3/7

E)1/2

Pls explain ur approach!

3318
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

A) 1/14

B) 1/7

C) 2/7

D) 3/7

E) 1/2

ans : D) 3/7
3319
x is the sum of y consecutive integers. w is the sum of z consecutive integers. If y = 2z, and y and z are both positive integers, then each of the following could be true EXCEPT

A) x = w

B) x > w

C) x/y is an integer

D) w/z is an integer

E) x/z is an integer



My answer is A
3320
darkhorse_09 Says
ans : D) 3/7



My answer is A


can u pls share ur approach...