In Dewey Elementary School, there are two second-grade

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

In Dewey Elementary School, there are two second-grade

by BTGmoderatorLU » Fri May 24, 2019 2:59 pm

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In Dewey Elementary School, there are two second-grade classes: class A has 35 students and class B has 45 students. If 40% of the students in class A walk to school, and 80% of the students in class B walk to school, what percent of all the students in the second-grade at Dewey Elementary walk to school?

A. 40%
B. 42.5%
C. 60%
D. 62.5%
E. 75%

The OA is D

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Source: Beat The GMAT — Problem Solving | Fri May 24, 2019 2:59 pm

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

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by ceilidh.erickson » Sat May 25, 2019 10:43 am

In Dewey Elementary School, there are two second-grade classes: class A has 35 students and class B has 45 students. If 40% of the students in class A walk to school, and 80% of the students in class B walk to school, what percent of all the students in the second-grade at Dewey Elementary walk to school?

In class A, 40% (or 2/5) of the 35 students walk to school:
$$\frac{2}{5}\left(35\right)=14$$

In class B, 80% (or 4/5) of the 45 students walk to school:
$$\frac{4}{5}\left(45\right)=36$$

The total number of 2nd graders walking to school:
14 + 36 = 50

The total number of students:
35 + 45 = 80

50 as a percent of 80:
50/80 = 0.625

The answer is D.

Last edited by ceilidh.erickson on Sat May 25, 2019 11:03 am, edited 1 time in total.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

by ceilidh.erickson » Sat May 25, 2019 10:56 am

Alternatively, you could treat this as a WEIGHTED AVERAGE problem.

If one class had 40% walk-to-schoolers and the other had 80%, the weighted average of both classes must be between 40 and 80. Eliminate A.

If we had an equal number of students in each class, we'd end up exactly halfway between 40 and 80: 60%. Since we have more students in class B, though, the average must be weighted toward 80% rather than 40%. That means the weighted average will be greater than 60. Eliminate B and C.

At this point, you could probably reason that since 45 is not that much greater than 35, the right answer shouldn't be that much greater than 60%. An answer of 75% would be very heavily weighted toward 80% - that's what we'd get if we had many times more students in class B than class A. So you should feel comfortable picking D as the only reasonable answer.

If you want to prove the answer mathematically (though I don't recommend that you take the time to do so on test day), you can do so as follows:

The ratio of 35 to 45 can be reduced to 7 to 9. So, we're looking for an answer that is 9/16 of the distance from 40 to 80:
$$\frac{9}{16}=\frac{x}{40}$$
$$\frac{9\cdot40}{16}=x$$
$$\frac{9\cdot5}{2}=x$$
$$\frac{45}{2}=x$$
$$22.5=x$$
$$40+22.5=62.5$$

Again, I definitely don't recommend doing this math! It's unnecessarily messy. It would be enough to realize that 9/16 is going to be just a little over the halfway point, so we want an answer that's just a little over 60%.

The answer is D.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pm; Thanked: 1443 times; Followed by:247 members

by ceilidh.erickson » Sat May 25, 2019 11:02 am

For more on estimating to find right answers on weighted average questions, see:
https://www.beatthegmat.com/mixture-pro ... tml#796297
https://www.beatthegmat.com/mgmat-5th-e ... tml#789804
https://www.manhattanprep.com/gmat/blog ... -pen-down/

And for more on using RATIOS to solve weighted averages:
https://www.beatthegmat.com/solution-x- ... tml#818927
https://www.beatthegmat.com/at-a-certai ... tml#825832

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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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 » Tue May 28, 2019 4:44 pm

BTGmoderatorLU wrote:Source: Magoosh

In Dewey Elementary School, there are two second-grade classes: class A has 35 students and class B has 45 students. If 40% of the students in class A walk to school, and 80% of the students in class B walk to school, what percent of all the students in the second-grade at Dewey Elementary walk to school?

A. 40%
B. 42.5%
C. 60%
D. 62.5%
E. 75%

The OA is D

(35 x 0.4 + 45 x 0.8)/(35 + 45) x 100 = 50/80 x 100 = 62.5 percent

Answer: D

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