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02 Oct 2019, 10:49
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
60% (02:52) correct
40%
(03:29)
wrong
based on 20
sessions
History
Date
Time
Result
Not Attempted Yet
Trucks of three different sizes - small, medium and large - are used to transport cargo to a remote village. Four large trucks carry as much cargo as do seven small trucks. Three medium trucks carry the same amount of cargo as do two large trucks and one small truck. Fifteen large, seven medium and fourteen small trucks each made thirty-six journeys to transport supplies. In order to transport the same amount of supplies, how many journeys would twelve large, fourteen medium and twenty-one small trucks need to make?
(A) 25
(B) 29
(C) 32
(D) 49
(E) 68
(A) 25
(B) 29
(C) 32
(D) 49
(E) 68
Archived Topic
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02 Oct 2019, 14:08
Kudos
Bookmarks
Trucks of three different sizes - small, medium and large - are used to transport cargo to a remote village. Four large trucks carry as much cargo as do seven small trucks. Three medium trucks carry the same amount of cargo as do two large trucks and one small truck. Fifteen large, seven medium and fourteen small trucks each made thirty-six journeys to transport supplies. In order to transport the same amount of supplies, how many journeys would twelve large, fourteen medium and twenty-one small trucks need to make?
(A) 25
(B) 29
(C) 32
(D) 49
(E) 68
Step 1: define the variables by themselves
Let L = 1 Large Truck
Let M = 1 Medium Truck
Let S = 1 Small Truck
Step 2: Define all variables in terms of one variable. Use the ratios to do so.
4 large trucks = 7 small trucks.
4L = 7S
4/7 L = 1S
S=4/7L
Now, define M in terms of L
Three medium trucks = two large trucks + one small truck
3M=2L+1S
We know 1S= 4/7 L, So rewrite the equation as:
3M= 2L + 4/7L
therefore, M= ((2+(4/7))/3)L
Step 4: Solve for the number of trips from the 2nd group of trucks.
We are told that 36 trips from 15 large, 7 medium and 14 small trucks is equal to x number of trips from 12 large, 14 medium and 21 small trucks. Therefore,
36(15L+7M+14S)=X(12L+14M+21S)
convert all variables into terms of L using values from step 2:
36(15L+7*(((2+(4/7))/3)L + 14*(4/7)L)=X(12L +14*(((2+(4/7))/3)L+21*(4/7)L
Distribute within to get equivalent number of large trucks for 1 trip for each group:
36((15L+6L+8L))=X((12L+12L+12L))
Multiply:
1044L=X*36L
Divide:
(1044L)/(36L)=X
29=X
it would take 29 trips from group two (right side) to carry the same amount of cargo as group one (right side)
Ans=B
(A) 25
(B) 29
(C) 32
(D) 49
(E) 68
Step 1: define the variables by themselves
Let L = 1 Large Truck
Let M = 1 Medium Truck
Let S = 1 Small Truck
Step 2: Define all variables in terms of one variable. Use the ratios to do so.
4 large trucks = 7 small trucks.
4L = 7S
4/7 L = 1S
S=4/7L
Now, define M in terms of L
Three medium trucks = two large trucks + one small truck
3M=2L+1S
We know 1S= 4/7 L, So rewrite the equation as:
3M= 2L + 4/7L
therefore, M= ((2+(4/7))/3)L
Step 4: Solve for the number of trips from the 2nd group of trucks.
We are told that 36 trips from 15 large, 7 medium and 14 small trucks is equal to x number of trips from 12 large, 14 medium and 21 small trucks. Therefore,
36(15L+7M+14S)=X(12L+14M+21S)
convert all variables into terms of L using values from step 2:
36(15L+7*(((2+(4/7))/3)L + 14*(4/7)L)=X(12L +14*(((2+(4/7))/3)L+21*(4/7)L
Distribute within to get equivalent number of large trucks for 1 trip for each group:
36((15L+6L+8L))=X((12L+12L+12L))
Multiply:
1044L=X*36L
Divide:
(1044L)/(36L)=X
29=X
it would take 29 trips from group two (right side) to carry the same amount of cargo as group one (right side)
Ans=B
02 Oct 2019, 19:10
Kudos
Bookmarks
Given-
1) 4L=7S
2) 3M=2L+S=3.5S+S=4.5S
3M=4.5S or 2M=3S
From 1 and 2
12L=14M=21S
36(15L+7M+14S)= n*(12L+14M+21S)
36(15L+6L+8L)= n*(12L+12L+12L)
36*29L=n*36L
n=29
1) 4L=7S
2) 3M=2L+S=3.5S+S=4.5S
3M=4.5S or 2M=3S
From 1 and 2
12L=14M=21S
36(15L+7M+14S)= n*(12L+14M+21S)
36(15L+6L+8L)= n*(12L+12L+12L)
36*29L=n*36L
n=29
Hovkial
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
