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krakow
11-16-2004, 04:20 PM
X is the set of all fractions in the form a-10/a+10,
where a is a positive integer less than 25.

Column A

The product of all the fractions that are in X

Column B

1/25

thebullfighter
11-16-2004, 06:24 PM
X is the set of all fractions in the form a-10/a+10,
where a is a positive integer less than 25.

Column A

The product of all the fractions that are in X

Column B

1/25
for a frm 1->9, fractions formed are all negative. for a=11->all are positive.

Hence, their Product will be Negative. (as 9 fractions with '-'/minus sign.)
So, Column A is Negative.
& Column B is Positive.

Hence, B>A

panther_vip
11-16-2004, 06:48 PM
for a frm 1->9, fractions formed are all negative. for a=11->all are positive.

Hence, their Product will be Negative. (as 9 fractions with '-'/minus sign.)
So, Column A is Negative.
& Column B is Positive.

Hence, B>A
As 'a' is a positive integer less than 25.Then one of the values of 'a' must be 10. The one of the fractions will be 0.which in turn makes the product 0. Thus B>A.

thebullfighter
11-16-2004, 07:02 PM
As 'a' is a positive integer less than 25.Then one of the values of 'a' must be 10. The one of the fractions will be 0.which in turn makes the product 0. Thus B>A.
And all these years i thought '0' was an INTEGER, and not a Fraction.;) (integers & fractions, Two Diff. caterories of Rational Numbers. where Rational numbners are defined as any number that can be expressed in th form p/q, where qis not= 0)

& somehow, i will keep believin in the same.

HTH

Bull.http://us.i1.yimg.com/us.yimg.com/i/mesg/tsmileys2/37.gif

awhig
11-16-2004, 07:08 PM
for a frm 1->9, fractions formed are all negative. for a=11->all are positive.

Hence, their Product will be Negative. (as 9 fractions with '-'/minus sign.)
So, Column A is Negative.
& Column B is Positive.

Hence, B>A
Column A will be 0. You are forgetting the case of a = 10.That is (10-10)/20 = 0

Thus A < B

thebullfighter
11-16-2004, 07:11 PM
Column A will be 0. You are forgetting the case of a = 10.That is (10-10)/20 = 0

Thus A < Bit's Not 0.

please refer to post #4

__________________________________________________ _____________

X is the set of all fractions in the form a-10/a+10,
where a is a positive integer less than 25.

Column A

The product of all the fractions that are in X

Column B

1/25

krakow
11-16-2004, 08:55 PM
what about p = 0, and q = 1

p/q = ?

:whistle:

thebullfighter
11-16-2004, 09:06 PM
what about p = 0, and q = 1

p/q = ?

:whistle:
p/q= 0 (<- is an integer, nt Fraction)
in th same way as 5/1 is an integer.

integers are Rational numbers. Rational numbers expressed in th form of p/q & Two Diff. types of Rational numbers are Integers & Fractions.

Where, Integers are: (....-2,-1), (1,2,3....) & '0'
and others are Fractions.

danielman
11-17-2004, 04:39 PM
p/q= 0 (<- is an integer, nt Fraction)
in th same way as 5/1 is an integer.

integers are Rational numbers. Rational numbers expressed in th form of p/q & Two Diff. types of Rational numbers are Integers & Fractions.

Where, Integers are: (....-2,-1), (1,2,3....) & '0'
and others are Fractions.

Hi Bullfighter,

What you say has sense but sounded weird to me, so I decided to investigate. In "Math Review for practicing to take the GRE general Test" the ETS' staff states:

"A fraction is a number of the form a/b, where a and b are integers and b <>0. The a is called the numerator of the fraction, and b is called the denominator."

and that's the only definition they give. So, as far as ETS concerns, it seems that fractions are just rational numbers. Barron's seems to agree. Moreover, they expresely say it:

"A fraction with 1 as the denominator is the same as the whole number that is its numerator"

thebullfighter
11-17-2004, 09:18 PM
well then!! what can i say. But i ws just laying down th actual Basics(Facts).
I too have seen Weird logics with people & even ETS. But this 1 goes off th limit. Fractions & Integers are actually Two Different categories OF Rational Numbers.

ie. Rational numbers expressed in th form of p/q & Two Diff. types of Rational numbers are Integers & Fractions.

Where, Integers are: (....-2,-1), (1,2,3....) & '0'
and others are Fractions.

http://dictionary.reference.com/search?q=integers&r=67
http://dictionary.reference.com/search?q=fractions&r=67

http://www.tpub.com/math1/5.htm
"The emphasis in previous chapters of this course has been on integers (whole numbers). In this chapter, we turn our attention to numbers which are not integers. The simplest type of number other than an integer is a COMMON FRACTION. Common fractions and integer8 together comprise a set of numbers called the RATIONAL NUMBERS; this set is a subset of the set of real numbers."

(but im sure there will be Many counter links too. as rarely any1 gets th logic.)

this 1 is fimiliar to another concept(basic/Fact/Can not be changed) sometimes messed up by many.

For the following Qs, slove for x.
Q1. x^2 = 16
Q2. x = sqrt16

These two Qs are not the same. Q1. OA is 4,-4 & Q2. OA is Only 4.

yaps i know many of u thought so, but because i posted em' together & while trying to make a point which leaves a hint. otherwise, believe me.. i hav seen a many with th same answers for both. ie 4, -4.

I hope u all got th idea.

But i'll advice (if th thingi about ETS is true) to follow the other approach itself. ie 0 (or even 1,2,3,4,...) are also Fractions. (:crazy: )

Just trying to help.

regards.
Bull

nikitaR
12-10-2004, 03:43 AM
well then!! what can i say. But i ws just laying down th actual Basics(Facts).
I too have seen Weird logics with people & even ETS. But this 1 goes off th limit. Fractions & Integers are actually Two Different categories OF Rational Numbers.

ie. Rational numbers expressed in th form of p/q & Two Diff. types of Rational numbers are Integers & Fractions.

Where, Integers are: (....-2,-1), (1,2,3....) & '0'
and others are Fractions.

http://dictionary.reference.com/search?q=integers&r=67
http://dictionary.reference.com/search?q=fractions&r=67

http://www.tpub.com/math1/5.htm
"The emphasis in previous chapters of this course has been on integers (whole numbers). In this chapter, we turn our attention to numbers which are not integers. The simplest type of number other than an integer is a COMMON FRACTION. Common fractions and integer8 together comprise a set of numbers called the RATIONAL NUMBERS; this set is a subset of the set of real numbers."

(but im sure there will be Many counter links too. as rarely any1 gets th logic.)

this 1 is fimiliar to another concept(basic/Fact/Can not be changed) sometimes messed up by many.

For the following Qs, slove for x.
Q1. x^2 = 16
Q2. x = sqrt16

SPOILER: These two Qs are not the same. Q1. OA is 4,-4 & Q2. OA is Only 4.

yaps i know many of u thought so, but because i posted em' together & while trying to make a point which leaves a hint. otherwise, believe me.. i hav seen a many with th same answers for both. ie 4, -4.

I hope u all got th idea.

But i'll advice (if th thingi about ETS is true) to follow the other approach itself. ie 0 (or even 1,2,3,4,...) are also Fractions. (:crazy: )

Just trying to help.

Isn't it just faster to admit you were wrong? :D

thebullfighter
12-10-2004, 11:20 AM
i never wanted to bring this thing here,
but just for the records (so all of the people here on gmat are wrong and all of the people giving gre are right?? nice going every1(th 1's who say that 0,1,-1 etc are FRACTIONS). btw, the Q in the below link is a Real-test-ETS Q, and it makes NO sense if we take 0, 1, -1, ... 27 etc as FRACTIONS.)