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

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

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New post 20 Jun 2007, 19:41
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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Re: Which of t5 he following fraction has the greatest value  [#permalink]

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New post 20 Jun 2007, 20:09
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).
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New post 22 Jun 2007, 16:49
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.


ANSWER: D
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New post 22 Jun 2007, 21:53
I second (D)

:-D
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Re: Which of t5 he following fraction has the greatest value  [#permalink]

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New post 22 Jun 2007, 23:29
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,

please explain your solution a bit more.
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Re: Which of t5 he following fraction has the greatest value  [#permalink]

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New post 23 Jun 2007, 10:51
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,

please explain your solution a bit more.


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

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New post 22 Jul 2018, 17:55
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Re: Which has the greatest value 1. 1/( 3 ^2 * 5 ^2) 2. 2 / ( 3 &nbs [#permalink] 22 Jul 2018, 17:55
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