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schelljo: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Tue Apr 07, 2015 12:52 pm

by schelljo » Tue Jun 23, 2015 4:56 pm

Among the 1,600 students at Hamilton High School, 45% take science courses. If 5/12 of the students taking science courses are taking physics, how many students at Hamilton High School are taking physics?

a.300
b.360
c.400
d.600
e.720

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Source: Beat The GMAT — Problem Solving | Tue Jun 23, 2015 4:56 pm

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by Brent@GMATPrepNow » Tue Jun 23, 2015 5:26 pm

schelljo wrote:Among the 1,600 students at Hamilton High School, 45% take science courses. If 5/12 of the students taking science courses are taking physics, how many students at Hamilton High School are taking physics?

a.300
b.360
c.400
d.600
e.720

Among the 1,600 students at Hamilton High School, 45% take science courses.
45% of 1600 = (0.45)(1600)
= (9/20)(1600)
= 720
So, 720 students are taking science courses

If 5/12 of the students taking science courses are taking physics
So, number of physics students = 5/12 of 720
= (5/12)(720)
= [spoiler]300 = A[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Tue Jun 23, 2015 5:32 pm

Hi schelljo,

This question is ultimately just about multiplication, but you can approach the math steps in a couple of different ways (depending on the 'format' that you want to put the numbers in):

Total Students: 1600

45% of those students take science courses....you can write this in a few different ways...

(.45)(1600) =
(45/100)(1600) =

or you can use the '10% trick'....

10% of 1600 = 160
45% = (4.5)(160)

However you want to do the math, you'll end up with....

720 students take science courses.

Next, we're told that 5/12 of THOSE students are taking physics....again, you can choose how you want to organize this information....

(5/12)(720) = 300 taking physics

You could also get to this answer with some estimation. Since 5/12 is LESS than 1/2, we're looking for an answer that is LESS than HALF of 720. There's only one answer that fits...

Final Answer: A

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jun 23, 2015 5:44 pm

schelljo wrote:Among the 1,600 students at Hamilton High School, 45% take science courses. If 5/12 of the students taking science courses are taking physics, how many students at Hamilton High School are taking physics?

a.300
b.360
c.400
d.600
e.720

Percentage who take science = 45% = 45/100 = 9/20.

Since the number of physics students is equal to 5/12 of the 9/20 who take science, we get:
(5/12)(9/20)(1600)

= (1/4)(3/4)(1600)

= (3/16)(1600)

= 300.

The correct answer is A.

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Tue Jun 23, 2015 5:46 pm

You could opt for an algebraic approach as well:

Students taking science = x
Students taking physics = y

We know that x = .45*1600 = 720. We also (sort of) know that (5/12) * x = y, so (5/12) * 720 = y and y = 300.

The problem here is that there might be students taking ONLY physics, so the prompt seems sloppy.

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schelljo: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Tue Apr 07, 2015 12:52 pm

by schelljo » Tue Jun 23, 2015 7:17 pm

Thanks everyone for their responses. Can you tell me where my approach is wrong. So I made a table as below:

Science Not Science
Physics 300 unknown unknown (FIND)
Not Physics 420 unknown unknown
720 880 Total=1600

45% of 1600 = 720
5/12 of 720 = 300

I guess I read this as where Science and Physics were two different classes, not a category and subcategory. Did I totally misread this or is the wording in the question a bit off here?

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Tue Jun 23, 2015 7:20 pm

schelljo wrote:Thanks everyone for their responses. Can you tell me where my approach is wrong. So I made a table as below:

Science Not Science
Physics 300 unknown unknown (FIND)
Not Physics 420 unknown unknown
720 880 Total=1600

45% of 1600 = 720
5/12 of 720 = 300

I guess I read this as where Science and Physics were two different classes, not a category and subcategory. Did I totally misread this or is the wording in the question a bit off here?

Your table is a little tough for me to follow, but you've got the right idea.

In theory, we have four groups:

Science only = w
Physics only = x
Both = y
Neither = z

That should give us

w + x + y + z = 1600
(w + y) = .45*1600 = 720
(5/12) * (w + y) = y, or (5/12) * 720 = 300

That tells us y = 300, so 300 students take BOTH classes ... but we still don't know x.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jan 10, 2018 12:03 pm

schelljo wrote:Among the 1,600 students at Hamilton High School, 45% take science courses. If 5/12 of the students taking science courses are taking physics, how many students at Hamilton High School are taking physics?

a.300
b.360
c.400
d.600
e.720

Among the 1,600 students at Hamilton High School, 45% take science courses.
45% of 1600 = (0.45)(1600)
= (9/20)(1600)
= 720
So, 720 students are taking science courses

If 5/12 of the students taking science courses are taking physics
So, number of physics students = 5/12 of 720
= (5/12)(720)
= 300
= A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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