X % of boys at Jones elementary

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doclkk: Master | Next Rank: 500 Posts; Posts: 180; Joined: Tue Apr 07, 2009 3:46 pmFollowed by: 2 members; Thanked: 5 times

by doclkk » Fri Sep 04, 2009 7:41 pm

90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

125
150
225
250
500

(B)

The MGMAT explanation doesn't make sense to me. I guess I'm not understanding their method.

Can someone simplify this question for me and do this question both by picking answer choices and algebra?

Thanks =)

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Source: Beat The GMAT — Problem Solving | Fri Sep 04, 2009 7:41 pm

capnx: Master | Next Rank: 500 Posts; Posts: 268; Joined: Sat Aug 15, 2009 9:22 amFollowed by: 1 member; Thanked: 19 times; GMAT Score:700

by capnx » Fri Sep 04, 2009 9:33 pm

took sometime to understand the question. I did the pick number way, then saw how the algebra worked, lol.

so pick a mid number, x=225
90 of boys = 225% --> 90/b = 2.25
so b = 90/2.25, b = 40

boys make up 40% of total population X
so b/x = 40% --> 40/225 = 17%, NO

so not C. 17% is too low, to increase it, X has to be smaller. Try B

x = 150
90/b = 150, b = 60
60/150 = 40%, YES

Algebraically (from back solving)

90/boys = x%
boys/x (total population) = 40%
x can be solved

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PAB2706: Master | Next Rank: 500 Posts; Posts: 260; Joined: Sun Oct 12, 2008 8:10 pm; Thanked: 4 times

by PAB2706 » Fri Sep 04, 2009 9:46 pm

the best way to approach such problem is go the way it says....

90=x/100 of boys --------1

boys = 40/100 of x---------2

Put 2 in 1 we get

90=x/100 * 40/100 * x

solve this.. u get 22500=x^2

thus x=150

HTH

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: X % of boys at Jones elementary

by Scott@TargetTestPrep » Sun Mar 15, 2020 3:51 am

doclkk wrote: ↑
Fri Sep 04, 2009 7:41 pm
90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

125
150
225
250
500

(B)

The MGMAT explanation doesn't make sense to me. I guess I'm not understanding their method.

Can someone simplify this question for me and do this question both by picking answer choices and algebra?

Thanks =)

Let the number of boys = b. We can create the equation:

90 = b * x/100

and

b = 0.4x

Substituting 0.4x for b in the first equation, we have:

90 = 0.4x * x/100

9000 = 0.4x^2

22500 = x^2

150 = x

Answer: B

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