During the first two weeks of January, the total rainfall

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

During the first two weeks of January, the total rainfall

by Gmat_mission » Sat Apr 14, 2018 3:13 am

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During the first two weeks of January, the total rainfall in Springdale was 15 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January?

A. 5 inches
B. 6 inches
C. 9 inches
D. 10 inches
E. 12 inches

[spoiler]OA=C[/spoiler].

I got confused here. What is the equation that solves this PS question? I'd appreciate some help.

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Source: Beat The GMAT — Problem Solving | Sat Apr 14, 2018 3:13 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Sat Apr 14, 2018 5:44 am

Hi Gmat_mission.

Let's take a look at your question.

Let's call "x" the rainfall in the first week.

"the rainfall during the second week was 1.5 times the rainfall during the first week" implies that the rainfall during the rainfall during the second week was 1.5*x.

"During the first two weeks of January, the total rainfall in Springdale was 15 inches" this implies the following: $$x+1.5\cdot x=15\ \ \ \Rightarrow\ \ \ 2.5x=15\ \ \ \Rightarrow\ \ \ x\ =6.$$ Therefore, the rainfall during the first week was 6 inches and this implies that the rainfall during the second week was 1.5*6=9 inches.

Hence, the correct answer is C .

I hope this explanation may help you.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Apr 25, 2018 3:50 pm

Gmat_mission wrote:During the first two weeks of January, the total rainfall in Springdale was 15 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January?

A. 5 inches
B. 6 inches
C. 9 inches
D. 10 inches
E. 12 inches

We can let the rainfall in the first week = a and the rainfall in the second week = b and create the following two equations:

a + b = 15

and

b = 1.5a

Substituting, we have:

a + 1.5a = 15

2.5a = 15

a = 6

Thus, the rainfall in the second week was 15 - 6 = 9 inches.

Answer: C

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