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Four staff members

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Four staff members

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For staff members at a certain company worked on a project. The amounts of time that the four 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?

80
96
160
192
240

Is there a faster approach?
Thanks

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Let the total number of hours that the four staff members worked on the project be T. It can then be written that:

2x + 3x + 5x + 6x = T
Note that if one of the four staff members worked on the project for 30 hours, x can take on the values x = 15 for the worker who worked for 2x hours, x = 10 for the worker who worked 3x hours, x = 6 for the worker who worked 5x hours and finally x = 5 for the worker who worked 6x hours.

When x = 15, T = 30 + 45 + 75 + 90 = 240
When x = 10, T = 20 + 30 + 50 + 60 = 160
We can stop here since we know that for x = 6 and x = 5, we'll get lower values of T than 160 and 240. Therefore, the only option that works is:

Choice D

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alex.gellatly wrote:
For staff members at a certain company worked on a project. The amounts of time that the four 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?

80
96
160
192
240

Is there a faster approach?
Thanks
Total hours worked is: 2x + 3x + 5x + 6x = 16x. So, if any of the answer choices is not a multiple of 16, choose that, but all are multiples of 16. So, we need to check each option:

If 6x worked for 30 hrs, then x is 5. And 16*5 = 80. Eliminate A
If 5x worked for 30 hrs, then x is 6. And 16*6 = 96. Eliminate B.

On the similar lines. 16*10 = 160 and 16*15=240. So, eliminate C and E.
D remains.

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I will (Learn. Recognize. Apply)

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alex.gellatly wrote:
For staff members at a certain company worked on a project. The amounts of time that the four 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?

80
96
160
192
240
Let the 4 workers be W, X, Y and Z.
W:X:Y:Z = 2:3:5:6.
Since the sum of the parts of the ratio = 2+3+5+6 = 16, the total amount of time must be a multiple of 16.
When a problem seems to require that all 5 answers be checked, the correct answer is likely to be D or E, with the result that the average test-taker will waste time checking A, B and C.
Since D and E are the greatest answer choices, try to MAXIMIZE the total amount of time.
W and X work for the least amounts of time.
Thus, the total amount of time will be MAXIMIZED if either W or X works for 30 hours.

If W works for 30 hours, the multiplier for the ratio is 15 -- since 15*2 = 30 -- with the result that the total amount of time = 15*16 = 240.
Eliminate E.

If X works for 30 hours, the multiplier for the ratio is 10 -- since 10*3 = 30 -- with the result that the total amount of time = 10*16 = 160.
Eliminate C.

If Y or Z works for 30 hours, the total amount of time will be LESS than 160.

The correct answer is D.

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alex.gellatly wrote:
For staff members at a certain company worked on a project. The amounts of time that the four 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?

80
96
160
192
240

Is there a faster approach?
Thanks
Solution:

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, where 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.

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jeff@targettestprep.com



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