What is x

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j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Sun Oct 26, 2014 4:09 am

90 students represent x percent of the boys at Jones elementary school. If the boys as Jones elementary make up 40% of the total population of x students. What is x.

A)125
B)150
C)225
D)250
E)500

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Source: Beat The GMAT — Problem Solving | Sun Oct 26, 2014 4:09 am

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 » Sun Oct 26, 2014 5:32 am

j_shreyans wrote:90 students represent x percent of the boys at Jones elementary school. If the boys as Jones elementary make up 40% of the total population of x students. What is x.

A)125
B)150
C)225
D)250
E)500

We can PLUG IN THE ANSWERS, which represent the value of x.

D: x=250
The boys as Jones elementary make up 40% of the total population of x students.
Thus, the total number of boys = 40% of the 250 students = (0.4)(250) = 100.
90 students represent x percent of the boys at Jones elementary school.
x% of the boys = 250% of the 100 boys = (2.5)(100) = 250.
Since only 90 students should represent x% of the boys, a SMALLER ANSWER CHOICE is needed.
Eliminate D and E.

B: x=150
The boys as Jones elementary make up 40% of the total population of x students.
Thus, the total number of boys = 40% of the 150 students = (0.4)(150) = 60.
90 students represent x percent of the boys at Jones elementary school.
x% of the boys = 150% of the 60 boys = (1.5)(60) = 90.
Success!

The correct answer is B.

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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 » Sun Oct 26, 2014 6:37 am

j_shreyans wrote:90 students represent x percent of the boys at Jones elementary school. If the boys as Jones elementary make up 40% of the total population of x students. What is x.

A)125
B)150
C)225
D)250
E)500

Here's an algebraic solution:

90 students represent x percent of the boys at Jones elementary school
Let B = the number of boys at the school
So, we can write: 90 = x% of B
In other words, 90 = (x/100)B

The boys at Jones elementary make up 40% of the total population of x students
We can write: B = 40% of x
In other words, B = (40/100)x
Simplify to get: B = (2/5)x

Now take 90 = (x/100)B and replace B with (2/5)x to get...
90 = (x/100)(2/5)x
Simplify: 90 = 2xÂ²/500
Multiply both sides by 500 to get: 45,000 = 2xÂ²
Divide both sides by 2 to get: 22,500 = xÂ²
Solve: x = 150

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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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 » Mon Oct 27, 2014 10:33 am

One last approach!

We know that

90 = x% of the boys

and that the boys = 40% of the total, or 40% of x,

so we have the equation

90 = x% of (40% of x)

or

90 = (x/100)(.4x)
90 = (.4xÂ²)/100
9000 = .4xÂ²
90000 = 4xÂ²
22500 = xÂ²
150 = x

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