GMAT Problem Solving Discussions

MBA
4106
Puys help me out in inequalities specially modulus...No clue how to approach the problem.any study material for it...and ya here is 1 question:-
1. X / X|
A. X > 1
B. X > -1
C. X D. X = 1
E.|X^2 > 1


Please explain the approach and solution?How to approach modulus inequality?


How about this question?
Modulus is killing me...pls help
4107
How about this question?
Modulus is killing me...pls help


is the answer A...
4108
kapur.arnav Says
is the answer A...


Yes answer is A) but the explanation is really poor in the doc..can u help me out for the approach.i have gone to inequalities question from CAT book but they are of quadratic equation...what is approach wen u first see a modulus inequality prob.?
pls help
4109
Yes answer is A) but the explanation is really poor in the doc..can u help me out for the approach.i have gone to inequalities question from CAT book but they are of quadratic equation...what is approach wen u first see a modulus inequality prob.?
pls help


This is a pretty straightforward question:

The q says that X / X|

You can see that any negative integer value for X will not suffice the inequality. Hence, X is positive but >1 as 1 doesn't satisy the inequality. Thus, the answer is A.

To approach any inequality modulus question you should know the following funda:

If |x -1. That is -1
Please throw more questions if you have further doubts. Thanks..
4110
1. Here is another 1
Is x+y| = 5?
1) x = 3
2) |y = 2

Please tell the approach. AND please give some inequality modulus study material if someone has. i need to practice as it play a major role in gmat.don't know how to approach.Suggestion are welcome.
4111
1. Here is another 1
Is x+y| = 5?
1) x = 3
2) |y = 2

Please tell the approach. AND please give some inequality modulus study material if someone has. i need to practice as it play a major role in gmat.don't know how to approach.Suggestion are welcome.



Here is huv I worked it out

statement 1) x = 3 or x = -3 ..Insuff
statement 2) y = 2 or y = -2...Insuff

Combining both we get , x = 3 , y = 2 mod (x+y) = 5 or

x = 3 , y = -2 mod (x+y) is not equal to 5

I will go with option E
4112
Heere is another 1
1. In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
OA
4113
Here is huv I worked it out

statement 1) x = 3 or x = -3 ..Insuff
statement 2) y = 2 or y = -2...Insuff

Combining both we get , x = 3 , y = 2 mod (x+y) = 5 or

x = 3 , y = -2 mod (x+y) is not equal to 5

I will go with option E

CORRECT

Pls tell the approach and some good study material to master modulud inequality?Help me out puys...
4114

Puys is this thread dead pr what?

4115
Heere is another 1
1. In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
OA



Factorise 88000

88000 - 2^6 * 11 * 5^3

So, no.of Red chips - 1
no .of green chips - 25
no .of purple chips - 8 ( since the value of purple lies b/w 5 & 11). So purple will have a value of 8. So no.of chips is 8.


Wats the OA?


-Deepak.
4116

Hi,

Fine. This was my way of thinking too.
But, I have a doubt.

Since,
88000 could also be written as 8 X 11 X 1000

Why can't the number of the chips be the following.

RED - 1 (11 points)
Green - 200 (1000 points)
Purple - 1 (8 points) ?????

@Anu: It'd be better, if there are options.


Factorise 88000

88000 - 2^6 * 11 * 5^3

So, no.of Red chips - 1
no .of green chips - 25
no .of purple chips - 8 ( since the value of purple lies b/w 5 & 11). So purple will have a value of 8. So no.of chips is 8.


Wats the OA?


-Deepak.
4117
Hi,

Fine. This was my way of thinking too.
But, I have a doubt.

Since,
88000 could also be written as 8 X 11 X 1000

Why can't the number of the chips be the following.

RED - 1 (11 points)
Green - 200 (1000 points)
Purple - 1 (8 points) ?????

@Anu: It'd be better, if there are options.


Well the OA is 2.
pls read the question carefully.
4118
Well the OA is 2.
pls read the question carefully.


Yeah got the solution now...Very good question.

88000 - 11 * 5^3 * 2^6

we have correctly identified the point value of purple as 8.So no.of purple marbles must be equal to the power of 8.

88000 = 11 * 5^3 * 8^2

So we have 1 RED , 3 GREEN Marbles, 2 PURPLE marbles

-Deepak.
4119

What is the value of x| ?
(1) x = -
(2) x^2 = 4
What is the approach.

4120
What is the value of x| ?
(1) x = x
(2) x^2 = 4
What is the approach.


1)x = -1 ,-2,-3....insuff
2) X^2 = 4 . x = +2 or -2 .So, |x = 2 ....suff..

I will go with option B

-Deepak.
4121
1)x = -1 ,-2,-3....insuff
2) X^2 = 4 . x = +2 or -2 .So, x = 2 ....suff..

I will go with option B

-Deepak.


Why in 1) x=-1,-2,-3...why only negative values why not positive values...pls tell the approach of these modulus and share any study material specifically for this...DS number properties any approach u can share...OG's DS last q's are pretty tough nut to crack..any hint.
4122
What is the value of x| ?
(1) x = x
(2) x^2 = 4
What is the approach.


Statement 1: X = -X,
hence X| = |-|X|| = |X = 1, 2, 3, 4, etc.. INSUFFICIENT.

Statement 2: X^2 = 4 = 2 ; SUFFICIENT.

Hence "B"
4123

Are all of the numbers in a certain list of 15 numbers
equal?
(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.

Pls explain the answer

4124
Are all of the numbers in a certain list of 15 numbers
equal?
(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.

Pls explain the answer

Stmt 1: The sum of the numbers is 60 does not tell us much.
Numbers could be 1,.....,1(14 times), 46.

Stmt 2: "ANY" is the keyword here.
Lets say the numbers are a1,a2,a3,....,a15.
this says that a1+a2+a3 = a2+a3+a4 = a3+a4+a1=a2+a4+a5...and so on.
By equating the mini equations:
a1+a2+a3 = a2+a3+a4 => a1=a4 ....(1)
similarly a2+a3+a4 = a3+a4+a1 => a2=a1...(2)....and so on....
we can get 105(Sorry...I don't have the time ) equations like these and prove that all the numbers are equal to each other....

Answer choice (B)
4125

The product of the units digit, the tens digit, and the
hundreds digit of the positive integer m is 96. What is
the units digit of m ?
(1) m is odd.
(2) The hundreds digit of m is 8.