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beater: Master | Next Rank: 500 Posts; Posts: 301; Joined: Tue Apr 22, 2008 6:07 am; Thanked: 2 times

by beater » Wed Sep 17, 2008 12:07 pm

Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
A. 80
B. 96
C. 160
D. 192
E. 240

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Source: Beat The GMAT — Problem Solving | Wed Sep 17, 2008 12:07 pm

bourne159: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Tue Mar 11, 2008 6:30 am; Thanked: 6 times

by bourne159 » Wed Sep 17, 2008 1:18 pm

Answer is D.

You just substitute 30 for each of the four cases. For each case get the factor by which you need to multiply the rest of the ratios.

Case 1: A:B:C:D = 2:3:5:6
Assume A = 30 , the value you need to multiply 2 to get to 30 is 15.
Now multiply 15 with each of the ratio values to preserve the ratios.
Here it will be 30(2*15): 45(3 * 15) : 75 (5 * 15) : 90 (6 *15)

The addition will give you 30 + 45 + 75 + 90 = 240

Similarly you will get 80, 96 and 160.

The only value you don't get is 192.

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ddm: Master | Next Rank: 500 Posts; Posts: 162; Joined: Mon Jul 28, 2008 8:33 pm; Location: San Jose,CA; Thanked: 1 times

by ddm » Wed Sep 17, 2008 3:22 pm

Is there a faster method to solve this problem?

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

by parallel_chase » Wed Sep 17, 2008 4:04 pm

ddm wrote:Is there a faster method to solve this problem?

Well there is one

2:3:5:6

2+3+5+6 = 16

80/16 = 5, 5*6 = 30. Eliminate.

96/16 = 6, 6*5 = 30. Eliminate.

160/16 = 10, 3*10 = 30. Eliminate.

240/16 = 15, 15*2 = 30. Eliminate.

192/16 = 12, 12*2 = 24, 12*3 = 36, 12*5= 60, 12*6 = 72.

We dont get a single value 30, therefore this is the answer.

Hope this helps.

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niraj_a: Legendary Member; Posts: 708; Joined: Sun Jun 01, 2008 4:59 amFollowed by: 1 member; Location: USA; Thanked: 13 times

by niraj_a » Wed Sep 17, 2008 6:29 pm

parallel

that is somewhat close to what i did.

i laid out each fraction first,

2/16 (i.e. 1/8), 3/16, 5/16, 6/16 (i.e. 3/8)

then i worked with each answer choice and eliminated those which resulted in a fraction that i didn't have in the list above.

for e.g. 30/240 = 1/8 - so eliminate this answer choice

and so on.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Sep 17, 2008 6:42 pm

Little different approach(but close to others though)

30 can be wither 2x,3x,5x,6x

Case 1: 2x= 30 x=15

2x = 30
3x = 45
5x = 75
6x = 90

240

Case 2: 3x= 30
Case3: 5x=30
Case4: 6x=30

The only value you wont get is 192.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Sep 17, 2008 6:44 pm

I think parallel chase's solution would be slighlty faster than the others though since we dont spend that extra time to check if we get to the total in 4 of the 5 cases

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