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Retired Moderator V
Joined: 27 Oct 2017
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At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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1 00:00

Difficulty:   45% (medium)

Question Stats: 65% (02:13) correct 35% (01:47) wrong based on 70 sessions

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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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GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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Please find my solution in attached image, IMO Option C is correct.
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File comment: Q3 Q3_sep29.jpeg [ 143.49 KiB | Viewed 935 times ]

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Intern  B
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Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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x% of B = 90

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

While substutuing the valve , Total No. Of students = 150
Senior Manager  P
Joined: 24 Jun 2012
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Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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90 = x/100 * (40/100)x---->solving this gives u 150
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Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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90=$$\frac{xb}{100}$$ and b=$$[fraction]{40x}{100}[/fraction]$$
therefore 90= {40x^2}/10000
so x=150
C
RC Moderator V
Joined: 24 Aug 2016
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GMAT 1: 540 Q49 V16 GMAT 2: 680 Q49 V33 Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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90=(x/100)(40/100)x ==>x=150 Ans C
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Manager  B
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GMAT 1: 670 Q50 V31 Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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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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Intern  B
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Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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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]

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90=X% * b
900=bx
B=40%*x
Substituting we get x=150
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Intern  Joined: 10 Dec 2017
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Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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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]

Posted from my mobile device
Intern  B
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Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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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)
Senior Manager  V
Joined: 22 Feb 2018
Posts: 415
Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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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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Intern  B
Joined: 18 Oct 2017
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Location: India
Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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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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Senior Manager  P
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Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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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
Intern  B
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GMAT 1: 700 Q44 V44 GPA: 3.54
Re: At Cambridge Junior School, there are 90 students who represent x% of  [#permalink]

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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. Re: At Cambridge Junior School, there are 90 students who represent x% of   [#permalink] 29 Sep 2018, 22:12
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# At Cambridge Junior School, there are 90 students who represent x% of  