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At Cambridge Junior School, there are 90 students who represent x% of

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At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:10
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Weekly Quant Quiz Question - 3



At Cambridge Junior School, there are 90 students who represent x% of total boys at the school. If the total no of boys at the school make up 40% of the total students x. Find the value of x.
a) 100
b) 120
c) 150
d) 200
e) Can not be determined.
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C
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:17
Please find my solution in attached image, IMO Option C is correct.
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:19
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Let total boys be B.

x% of B = 90

40% of x = B

x/b *100 = 90; 40/100 *x = b which leads to no where.

Answer E - cannot be determined.
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:14
x% of B = 90

40% of Total Student = B(Total no. Of Boys)

While substutuing the valve , Total No. Of students = 150
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:16
90 = x/100 * (40/100)x---->solving this gives u 150
C is answer
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:18
90=\(\frac{xb}{100}\) and b=\([fraction]{40x}{100}[/fraction]\)
therefore 90= {40x^2}/10000
so x=150
C
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:18
90=(x/100)(40/100)x ==>x=150 Ans C
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:26
Total boys =T
So based on the question stem,90=(x/100)*T
and Based on 2nd stem: T=0.4x

On solving 2 equations, taking positive root for x,answer is 150 I.e C

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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:34
90=X% * b
900=bx
B=40%*x
Substituting we get x=150
Answer-C
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 10:35
E.



The number of boys is represent the number for xpercent of total boys at cambridge university it's not represent the number of total boys, we had to now the value of xpercent to know the total boys at that school. And the question how much is the total students, and we can't determine the total numbers of the students if we can't determine the number of total boys at that school.

size=80]Posted from my mobile device[/size]

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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 11:02
x% of boys = 90
boys= (90/x)*100 ... (1)

40% of x = boys ... (2)

(90/x)*100 = 40% * x
x^2 = (90*100*100)/40
x= 150 (avoid negative root)
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 11:34
Quote:
At Cambridge Junior School, there are 90 students who represent x% of total boys at the school. If the total no of boys at the school make up 40% of the total students x. Find the value of x.
a) 100
b) 120
c) 150
d) 200
e) Can not be determined.


OA:C

\(90 = \frac{x}{100}*\)Total boys ...(1)

Total boys \(= \frac{40}{100}*Total \quad Students = \frac{40}{100}*x\) ....(2)

Putting value of Total boys from (2) into (1), we get

\(90=\frac{x}{100}* \frac{40}{100}*x\)

\(x^2=\frac{90}{40}*100^2\)

\(x= \frac{3}{2}*100=150\)
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 11:54
Let total boys be y.

90 = (x/100) * y
xy = 9000

y = (40/100)*x

Thus, x* x*(40/100) = 9000

On simplication, we get,

4*x*x = 90000

Taking square root on both sides,

2x = 300
x = 150

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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 14:55
Let b be the number of boys

90 = (x/100)*B

B=(40/100)*x

90=(x/100)*(40/100)*x

x=150


Therefore C
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   29 Sep 2018, 22:12
90 students at the school represent x% of #boys

#boys are 40% of total students.

#total students not known as 90 is not given to be THE #students in the school.

so, #boys cannot be determined.
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink] New post   23 Sep 2023, 13:23
My problem with having 150 as the answer is that it does not make any sense. They are telling you that 90 Is "some" percentage of the boys, and that the total percentage of the boys is 40% of the students, meaning that the 40% is equal or greater that 90. With that alone you can tell that the 100% is going to be more that 150. At minimum, the total amount of students would be 225, which happens when you take de 40% of boys as 90 and solve like this:

40/100 * x = 90
x = 225

But then again, that would be the minimum, so the answer should be "E" in my opinion.
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Re: At Cambridge Junior School, there are 90 students who represent x% of [#permalink]
23 Sep 2023, 13:23
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