GMAT Problem Solving Discussions

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there are 5 possible locations for first 4.

if the first 4 goes at location
1, the second 4 can go at 5 different locations, number of ways = 5
2, the second 4 can go at 4 different locations, number of ways = 4
3, the second 4 can go at 3 different locations, number of ways = 3
4, the second 4 can go at 2 different locations, number of ways = 2
5, the second 4 can go at 1 different location, number of ways = 1

Total number of different 6 digit numbers = 5+4+3+2+1 = 15

Option D

Good question BTW .....

Can you explain the bold part?I believe only 4 locations are available for the next four.
here with the three points its became equilateral triangle

so ans is 25sqrt3/4


but spherical ball so i think ans is less than 25sqrt3/4 (i am not sure")


Answer should be D, since body formed by tying 3 nails is not a 2 dimensional figure. equilateral triangle will be a projection of this body, so area has to be greater than 25 (sqrt 3)/4
vikas.mogle Says
Answer should be D, since body formed by tying 3 nails is not a 2 dimensional figure. equilateral triangle will be a projection of this body, so area has to be greater than 25 (sqrt 3)/4


I do not quite understand. How can a three dimesional equilateral triangle have greater area than that of two dimensional eq. triangle?
ramviswa Says
I do not quite understand. How can a three dimesional equilateral triangle have greater area than that of two dimensional eq. triangle?


I think I was wrong. area should be same as that of equilateral triangle.

consider that you cut an equilateral triangle from a paper and paste it on a sphere, area still remains same.
I think I was wrong. area should be same as that of equilateral triangle.

consider that you cut an equilateral triangle from a paper and paste it on a sphere, area still remains same.


D is the answer given and that is the reason I asked for your explanation. Your explanation matches some what with the answer explanation for this question. Here is the explanation given:

Take a piece of paper in the shape of an equilateral triangle and side 5cm and try to stick it in the spherical surface and try to cover the curved area marked by the strings completely. We will observe that the paper gets "ripped off" in between. This shows that we are trying to fit less area in larger surface. Hence, the (curved) area covered by the strings is more than the plain are of the figure formed by the same strings, which is in accordance with the equilateral triangle.
vikas130678 Says
Can you explain the bold part?I believe only 4 locations are available for the next four.


Sorry for the delayed reply .. I'm not a regular here...

_2_0_0_2_

suppose you put first 4 at position 1

_4_2_0_0_2_

now the second 4 can actually go at six possible locations, but we'll consider only 5, because when both are together, its the same number

442002 (44 and 44 are same numbers)
424002
420402
420042
420024

hope that helps
Answer is 5C2 which is 5!/(5-2)! 2! = 5!/3! 2! = 10.

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1st 4 can be placed at any of the 5 positions. Once 1st 4 is placed, the 2nd 4 can be placed at any of the remaining 4 positions. So total number of ways 2 4's can be placed here is 5*4. Since both the number are 4 so positions have duplicate and the correct answer is 5*4/2 = 20/2 = 10.


no sir, your solution is wrong .... its not that simple a problem.... to prove my point .. here are 15 different numbers...

442002
244002
204402
200442
200244
424002
240402
204042
200424
420402
240042
204024
420042
240024
420024
D is the answer given and that is the reason I asked for your explanation. Your explanation matches some what with the answer explanation for this question. Here is the explanation given:

Take a piece of paper in the shape of an equilateral triangle and side 5cm and try to stick it in the spherical surface and try to cover the curved area marked by the strings completely. We will observe that the paper gets "ripped off" in between. This shows that we are trying to fit less area in larger surface. Hence, the (curved) area covered by the strings is more than the plain are of the figure formed by the same strings, which is in accordance with the equilateral triangle.


in that case the answer should be "e) greater than or equal to 25(root 3)/4"

becuase no where the size of spherical ball is mentioned... so if i take a large ball ... say earth ... and make a 5 cm triangle ... what will be the area 😃

not a "good" gmat question ...
Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then
put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the
sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is
numbered 5 ?

pls expln
Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then
put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the
sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is
numbered 5 ?

pls expln


combinations for sum 8 = (2,6) (6,2) (3,5) (5,3) (4,4).

Probability = 2/5

If X/X|
X>1

X>-1

X
X = 1

|X^2 > 1

if x/x|
X>1

x>-1

x
x = 1

x^2 > 1


e. |x^2 > 1

never mind...this isn't valid for negative values.
vikas.mogle^2 > 1


nope !!! thats not right

xx>0, |x>1

-1or x>1

That doesnt help, does it ?:drinking:

If X/X|
X>1

X>-1

X
X = 1

|X^2 > 1


my take choice A.
though a better choice would be x=(-1,0)u(1,infinity)
my take choice A.
though a better choice would be x=(-1,0)u(1,infinity)


the answer is B... you were close... all the values of X are in set (-1,0) U (1, infinite) and for all these values ... X > -1 will always be true...

if we select A, then we are leaving negative values of X..

Remember, the question is not asking all the possible values of X .. the question is "which of the following must be true for all X" ...

Only option B will always be true for all X
the answer is B... you were close... all the values of X are in set (-1,0) U (1, infinite) and for all these values ... X > -1 will always be true...

if we select A, then we are leaving negative values of X..

Remember, the question is not asking all the possible values of X .. the question is "which of the following must be true for all X" ...

Only option B will always be true for all X



Do you want to say that X will belongs to the said group that's y it should be>-1?
I believe that X>-1 will be considered as the domain and this has to be true for positive fractional value less than 1 too, which is definately not the case.
Do you want to say that X will belongs to the said group that's y it should be>-1?
I believe that X>-1 will be considered as the domain and this has to be true for positive fractional value less than 1 too, which is definately not the case.


we dont have to find the domain for X ... we just need to find a condition that will be true for all X... our x is defined in first line....

Let me give you an example ..
x is a member of set S =
which of the following must be true for all x
A. x >= 4
B. x >= -4

this is similar to the our original question... and the answer should be B

hope that helps

A contractor estimated that his 10-men crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, after 5 days of rain, on the 61-st day, he hired 6 more people to finish the project early. If the job was done in 100 days, on how many days after day 60 was it raining?

4
5
6
7
8

A contractor estimated that his 10-men crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, after 5 days of rain, on the 61-st day, he hired 6 more people to finish the project early. If the job was done in 100 days, on how many days after day 60 was it raining?

4
5
6
7
8


answer is 5.6 days.
so my take is 6 days