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Four scientists collaborate on a research project for which they

by BTGModeratorVI » Wed Jan 06, 2021 8:17 am

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Four scientists collaborate on a research project for which they receive a prize that comes with a monetary award. They agree to divide the money into four shares in proportion to the time that each scientist spent on the project. If the shares are in the amounts a/2, a/3, a/4, and a/6, respectively, what is the value of a?

A. 1/3

B. 4/15

C. 4/5

D. 5/4

E. 3

Answer: C
Source: Veritas Prep
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Re: Four scientists collaborate on a research project for which they

by Brent@GMATPrepNow » Wed Jan 06, 2021 10:44 am
BTGModeratorVI wrote: ↑
Wed Jan 06, 2021 8:17 am
 Four scientists collaborate on a research project for which they receive a prize that comes with a monetary award. They agree to divide the money into four shares in proportion to the time that each scientist spent on the project. If the shares are in the amounts a/2, a/3, a/4, and a/6, respectively, what is the value of a?

A. 1/3

B. 4/15

C. 4/5

D. 5/4

E. 3

Answer: C
Source: Veritas Prep
KEY PROPERTY: The sum of all four shares must be 1.
So, we can write: a/2 + a/3 + a/4 + a/6 = 1
Find common denominators: 6a/12 + 4a/12 + 3a/12 + 2a/12 = 1
Simplify: 15a/12 = 1
Multiply both sides by 12 to get: 15a = 12
Divide both sides by 15 to get: a = 12/15 = 4/5

Answer: C

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Re: Four scientists collaborate on a research project for which they

by swerve » Wed Jan 06, 2021 2:57 pm
BTGModeratorVI wrote: ↑
Wed Jan 06, 2021 8:17 am
 Four scientists collaborate on a research project for which they receive a prize that comes with a monetary award. They agree to divide the money into four shares in proportion to the time that each scientist spent on the project. If the shares are in the amounts a/2, a/3, a/4, and a/6, respectively, what is the value of a?

A. 1/3

B. 4/15

C. 4/5

D. 5/4

E. 3

Answer: C
Source: Veritas Prep
Since the sum of the shares is \(1\), we have:

\(\dfrac{a}{2} + \dfrac{a}{3} + \dfrac{a}{4} + \dfrac{a}{6} = 1\)

\(\dfrac{6a}{12} + \dfrac{4a}{12} + \dfrac{3a}{12} + \dfrac{2a}{12} = 1\)

\(\dfrac{15a}{12} = 1\)

\(15a = 12\)

\(a = \dfrac{12}{15} = \dfrac{4}{5}\)
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Re: Four scientists collaborate on a research project for which they

by Scott@TargetTestPrep » Thu Jan 14, 2021 4:34 am
BTGModeratorVI wrote: ↑
Wed Jan 06, 2021 8:17 am
 Four scientists collaborate on a research project for which they receive a prize that comes with a monetary award. They agree to divide the money into four shares in proportion to the time that each scientist spent on the project. If the shares are in the amounts a/2, a/3, a/4, and a/6, respectively, what is the value of a?

A. 1/3

B. 4/15

C. 4/5

D. 5/4

E. 3

Answer: C
Solution:

Since the sum of the shares is 1, we have:

a/2 + a/3 + a/4 + a/6 = 1

Multiplying the equation by 12, we have:

6a + 4a + 3a + 2a = 12

15a = 12

a = 12/15 = 4/5

Answer: C

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