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# Which has the greatest value 1. 1/( 3 ^2 * 5 ^2) 2. 2 / ( 3

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Director
Joined: 24 Oct 2005
Posts: 554
Location: NYC
Which has the greatest value 1. 1/( 3 ^2 * 5 ^2) 2. 2 / ( 3  [#permalink]

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20 Jun 2007, 18:41
1
Which has the greatest value

1. 1/( 3 ^2 * 5 ^2)

2. 2 / ( 3 ^2 * 5 ^2)

3. 7/ (3^3 * 5 ^2)

4. 45/ (3^3 * 5^3)

5. 75/(3^4 * 5 ^5)

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Director
Joined: 26 Feb 2006
Posts: 854
Re: Which of t5 he following fraction has the greatest value  [#permalink]

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20 Jun 2007, 19:09
bewakoof wrote:
Which has the greatest value

1. 1/ (3^2 * 5^2)
2. 2 / (3^2 * 5^2)
3. 7/ (3^3 * 5^2)
4. 45/ (3^3 * 5^3)
5. 75/ (3^4 * 5^5)

make the denomenator equal to the highest denomenotor (3^4 x 5^5):

a = (3^2 x 5^3) / (3^4 x 5^5)
b = (2 x 3^2 x 5^3) / (3^4 x 5^5)
c = (7 x 3 x 5^3) / (3^4 x 5^5)
d = (3^3 x 5^3) /(3^4 x 5^5)
e = (3 x 5^2) / (3^4 * 5 ^5)

so the highest is D (3^3 x 5^3) /(3^4 x 5^5).
Director
Joined: 30 Nov 2006
Posts: 573
Location: Kuwait

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22 Jun 2007, 15:49
Simplifying choices C,D and E:

C. 7/ (3^3 * 5 ^2)
-----------------------
if the numerator is 6, then the value is 2/(3^2 * 5^2). So the value of option C is barely higher than the value of B

D. 45/ (3^3 * 5^3)
------------------------
= 3*3*5/(3^3*5^3) = 3/(3^2 * 5^2)

E. 75/(3^4 * 5 ^5)
------------------------
= 3*5*5/(3^4 * 5^5) = 1/(3^3 * 5^2), which is much smaller by a factor of at least 1/3 than all other choices.

VP
Joined: 08 Jun 2005
Posts: 1133

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22 Jun 2007, 20:53
I second (D)

Director
Joined: 12 Jun 2006
Posts: 516
Re: Which of t5 he following fraction has the greatest value  [#permalink]

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22 Jun 2007, 22:29
Himalayan wrote:
bewakoof wrote:
Which has the greatest value

1. 1/ (3^2 * 5^2)
2. 2 / (3^2 * 5^2)
3. 7/ (3^3 * 5^2)
4. 45/ (3^3 * 5^3)
5. 75/ (3^4 * 5^5)

make the denomenator equal to the highest denomenotor (3^4 x 5^5):

a = (3^2 x 5^3) / (3^4 x 5^5)
b = (2 x 3^2 x 5^3) / (3^4 x 5^5)
c = (7 x 3 x 5^3) / (3^4 x 5^5)
d = (3^3 x 5^3) /(3^4 x 5^5)
e = (3 x 5^2) / (3^4 * 5 ^5)

so the highest is D (3^3 x 5^3) /(3^4 x 5^5).

Himalayan,

Director
Joined: 26 Feb 2006
Posts: 854
Re: Which of t5 he following fraction has the greatest value  [#permalink]

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23 Jun 2007, 09:51
ggarr wrote:
Himalayan wrote:
bewakoof wrote:
Which has the greatest value

1. 1/ (3^2 * 5^2)
2. 2 / (3^2 * 5^2)
3. 7/ (3^3 * 5^2)
4. 45/ (3^3 * 5^3)
5. 75/ (3^4 * 5^5)

make the denomenator equal to the highest denomenotor (3^4 x 5^5):

a = (3^2 x 5^3) / (3^4 x 5^5)
b = (2 x 3^2 x 5^3) / (3^4 x 5^5)
c = (7 x 3 x 5^3) / (3^4 x 5^5)
d = (3^3 x 5^3) /(3^4 x 5^5)
e = (3 x 5^2) / (3^4 * 5 ^5)

so the highest is D (3^3 x 5^3) /(3^4 x 5^5).

Himalayan,

an example: which one is grater?

a. 3/10
b. 1/5
c. 4/15
d. 6/25
e. 7/30

We can make either neumerator or denomenator equal. lets make all of their denomenator equal:

Since the LCM of all denomenator is 150, so lets make each of the denomenetor equal to 150:

a. (3/10) (15/15) = 45/150
b. (1/5) (30/30) = 30/150
c. (4/15) (10/10) = 40/150
d. (6/25) (6/6) = 36/150
e. (7/30) (5/5) = 35/150

since all denomenators are equal, the fraction with the highest neumerator is the largeest. it is 45/150. So A.

Similarly we can make the each of the neumerators qual and the fraction with lowest denomenotor will have the largest value. the LCM of all neumerator is 84. lets make all neumerators equal to 84.

a. (3/10) (28/28) = 84/280
b. (1/5) (84/84) = 84/420
c. (4/15) (21/21) = 84/315
d. (6/25) (14/14) = 84/350
e. (7/30) (12/12) = 84/360

Since the smallest denomenator is 280 in A, the largest fraction is 84.280 in A.

HTH..

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This discussion does not meet community quality standards. It has been retired.

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Re: Which has the greatest value 1. 1/( 3 ^2 * 5 ^2) 2. 2 / ( 3  [#permalink]

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22 Jul 2018, 16:55
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Re: Which has the greatest value 1. 1/( 3 ^2 * 5 ^2) 2. 2 / ( 3 &nbs [#permalink] 22 Jul 2018, 16:55
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