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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

Practice Questions Question: 56 Page: 159 Difficulty: 600

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

A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.

If 2x = 30 then 16x = 240; If 3x = 30 then 16x = 160; If 5x = 30 then 16x = 96; If 6x = 30 then 16x = 80;

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08 Oct 2012, 01:59

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Let the time taken is 2x, 3x , 5x & 6x Total time taken 16x Any one of 2x, 3x , 5x & 6x equals 30 . So 16x can take any of the below mentioned values - 30*16/2 , 30*16/3, 30*16/5 , 30*16/6 240 , 160, 96, 80 Answer D
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Re: Four staff members at a certain company worked on a project. [#permalink]

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08 Oct 2012, 02:31

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Let the time taken as 2x, 3x , 5x & 6x Total time taken 16x Any one of 2x, 3x , 5x & 6x equals 30 and x can be 15, 10, 6 and 5 respectively. Now for all values of X (15,10,6 & 5) 16x will be = 16*15 = 240 (E) = 16*10 = 160 (C) = 16*6 = 96 (B) = 16*5 =80 (A)

Hence Answer D
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09 Oct 2012, 20:57

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Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x. But we are told that one of these individual works is 30hrs. hence, possible scenarios, if (1)2x =30 => 16x = 240 (2) 3x =30 => 16x = 160 (3) 5x =30 => 16x = 96 (4) 6x =30 => 16x = 80 Hence Answer is D 192 which can not be any of these. Another alternate is to backsolve, for options A to E, Answer/16 should give us a multiplication factor (which is denoted by x in first solution). Since this multiplication factor should be present for individual work also, 30 should be divisible by this to give individual work ratio of any out of 2,3,5,6. eg. 80/16 =5 and 30/5 =6 or 240/16=15 and 30/15=2, but 192/16=12 and 30/12 =2.5 (not one of the ratios) This leaves us with choice D again.

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

Practice Questions Question: 56 Page: 159 Difficulty: 600

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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

A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.

If 2x = 30 then 16x = 240; If 3x = 30 then 16x = 160; If 5x = 30 then 16x = 96; If 6x = 30 then 16x = 80;

Only answer choices which is not obtained is 192.

Answer: D.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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11 Oct 2012, 13:41

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Hi Bunuel,

If we change this question to say that the ratios are still the same i.e 2, 3, 5 and 6 but the prompt says that the the sum of the hours worked by two of the workers is 121 and then we are asked to find the sum of total hours worked by all the workers. Would this be still a valid variation provided we restrict the number of hours in integers only?

If we change this question to say that the ratios are still the same i.e 2, 3, 5 and 6 but the prompt says that the the sum of the hours worked by two of the workers is 121 and then we are asked to find the sum of total hours worked by all the workers. Would this be still a valid variation provided we restrict the number of hours in integers only?

Thanks in advance.

Yes.

Given: A:B:C:D=2x:3x:5x:6x, for some positive integer x and the sum of the hours worked by two of the workers is 121.

Since the only sum which gives integer value for x is 5x+6x=121 --> x=11, then total time is 16x=16*11.

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12 Oct 2012, 00:23

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Given Ratios- 2:3:5:6 2x+3x+4x+5x=16x lets check one by one with ACs, and when we come to D; 16x=192 =>x=12 if you put x= 12 in any individual's value (2x,3x,5x,6x) 30 can not be acheived.

Answer : D
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25 Jun 2014, 20:36

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Re: Four staff members at a certain company worked on a project. [#permalink]

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10 Sep 2014, 20:47

Bunuel wrote:

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

Practice Questions Question: 56 Page: 159 Difficulty: 600

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01 Oct 2015, 20:56

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06 Feb 2017, 07:47

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Re: Four staff members at a certain company worked on a project. [#permalink]

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08 Feb 2017, 18:50

Bunuel wrote:

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

We are given that the amounts of time that the four members worked on the project were in the ratio 2 to 3 to 5 to 6. A straightforward approach is to create a ratio with x multipliers. The ratio becomes: 2x : 3x : 5x : 6x, in which 2x was person 1’s time, 3x was person 2’s time, 5x was person 3’s time, and 6x was person 4’s time.

From this information, we can determine that the total time worked by all the members is the sum of our ratios: 2x + 3x + 5x + 6x = 16x.

We are also given that one of the members worked for 30 hours. Thus, we can create 4 different equations to get 4 different possible x values.

Option 1) If Person 1 was the individual who worked 30 hours, then 2x = 30 and x = 15

Option 2) If Person 2 was the individual who worked 30 hours, then 3x = 30 and x = 10

Option 3) If Person 3 was the individual who worked 30 hours, then 5x = 30 and x = 6

Option 4) If Person 4 was the individual who worked 30 hours, then 6x = 30 and x = 5

The above results show the 4 different options for the total number of hours an individual staff member worked.

Now, remember that the entire group worked for 16x hours. We substitute each of the 4 possible values for x into this expression:

Option 1: 16x = (16)(15) = 240 hours

Option 2: 16x = (16)(10) = 160 hours

Option 3: 16x = (16)(6) = 96 hours

Option 4: 16x = (16)(5) = 80 hours

The only value that we did not get was 192 hours, so D is the correct answer.

Answer: D
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