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In Cliff’s impressive rock collection, there are half as many igneous

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Bunuel
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In Cliff’s impressive rock collection, there are half as many igneous [#permalink] New post   29 Feb 2016, 10:35
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In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?

A. 30
B. 45
C. 60
D. 90
E. 135
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OptimusPrepJanielle
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Re: In Cliff’s impressive rock collection, there are half as many igneous [#permalink] New post   01 Mar 2016, 22:26
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Bunuel wrote:
In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?

A. 30
B. 45
C. 60
D. 90
E. 135


Assume total sedimentary rocks to be 2x
Total igneous rocks = x

Shiny igneous rocks = 2x/3
Matte igneous rocks = x/3

Shiny sedimentary rocks = 2x/5

Given 2x/3 = 30
x = 45

Total rocks = igneous + sedimentary = x + 2x = 3*45 = 135
Option E
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Re: In Cliff’s impressive rock collection, there are half as many igneous [#permalink] New post   01 Mar 2016, 23:56
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Bunuel wrote:
In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?

A. 30
B. 45
C. 60
D. 90
E. 135



We can start with the known quantity and then go on to find the others.

Shiny igneous ricks are 30. These are (2/3) of total igneous rocks.
(2/3)*Total igneous rocks = 30
Total igneous rocks = 30 * (3/2) = 45

Total sedimentary rocks = 2*Total igneous rocks = 2*45 = 90

Total number of rocks = 45 + 90 = 135

Answer (E)
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Re: In Cliff’s impressive rock collection, there are half as many igneous [#permalink] New post   10 May 2017, 20:02
Let sedimentary rocks = x
So igneous rocks = x/2

Shiny igneous = x/2 * 2/3 = x/3
We are given that shiny igneous rocks are 30
So x/3 = 30; thus x=90
Implying that sedimentary rocks are 90, igneous rocks are 90/2 =45.
So total = 135

option E
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Re: In Cliff’s impressive rock collection, there are half as many igneous [#permalink] New post   15 May 2017, 17:33
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Bunuel wrote:
In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 2/3 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?

A. 30
B. 45
C. 60
D. 90
E. 135



We can let the number of igneous rocks = x.

Since 2/3 of the igneous rocks are shiny and since we know that there are 30 shiny igneous rocks, we have:

(2/3)x = 30

2x = 90

x = 45

Since Cliff has half as many igneous rocks as he has sedimentary rocks, he has 90 sedimentary rocks. Thus, in total there are 45 + 90 = 135 rocks.

(Note that the information that 1/5 of the sedimentary rocks were shiny is not necessary for the solution.)

Answer: E
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Re: In Cliff’s impressive rock collection, there are half as many igneous [#permalink] New post   21 Jan 2021, 19:47
Let g be igneous rocks
Let s be sedimentary

g = s/2 Igneous rocks
s = g x 2 Sedimentary rocks

2/3g = 30 ---> g = 45 igneous rocks

45 = s/2 ---> s = 90 sedimentary rocks

Total = 90 + 45 = 135
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Re: In Cliffs impressive rock collection, there are half as many igneous [#permalink] New post   08 May 2023, 04:01
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Re: In Cliffs impressive rock collection, there are half as many igneous [#permalink]
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