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GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Each student in a certain class is considered intermediate or strong,  [#permalink]

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Difficulty:   15% (low)

Question Stats: 81% (02:28) correct 19% (02:56) wrong based on 47 sessions

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GMATH practice exercise (Quant Class 6)

Each student in a certain class is considered intermediate or strong, but not both. The average of the grades of the strong students is 6.3 points, exactly two points above the average of the grades of the intermediate students. What is the percentage of strong students in this class, if the average of all students grades in this class is half point below the average of the grades of the strong students?

(A) 60%
(B) 65%
(C) 70%
(D) 75%
(E) 80%

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Joined: 19 Feb 2019
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Re: Each student in a certain class is considered intermediate or strong,  [#permalink]

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AV of strong students = 6.3
AV of intermediate students = 4.3 (given)
AV of all students = 5.8 (given)
Let number of strong students be s and number of intermediate ones be i.
(6.3s + 5.8i)/(s + i) = 5.8

Solving this gives s = 3i
So Answer = (3i/(3i+i))*100 = 75% = D

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GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Each student in a certain class is considered intermediate or strong,  [#permalink]

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fskilnik wrote:
GMATH practice exercise (Quant Class 6)

Each student in a certain class is considered intermediate or strong, but not both. The average of the grades of the strong students is 6.3 points, exactly two points above the average of the grades of the intermediate students. What is the percentage of strong students in this class, if the average of all students grades in this class is half point below the average of the grades of the strong students?

(A) 60%
(B) 65%
(C) 70%
(D) 75%
(E) 80% $$?\,\, = \,\,{{100} \over {100 + x}}$$

$$\left( {{\text{Alligation}}} \right)\,\,\,\,?\,\, = \,\,\frac{{100}}{{100 + x}}\,\, = \,\,\frac{{5.8 - 4.3}}{{6.3 - 4.3}}\,\, = \,\,\frac{{1.5}}{2}\,\, = \,\,\underleftrightarrow {\frac{1}{{10}}\left( {\frac{{15}}{2}} \right) = 0.75}\,\, = \,\,75\%$$

The correct answer is (D).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Location: India
Concentration: Sustainability, Marketing
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Each student in a certain class is considered intermediate or strong,  [#permalink]

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I = 4.3 and Strong = 6.3
avg of class = 6.3-0.5 ; 5.8
so we can say
x*43+6.3*y/x+y= 5.8
we get
3x=y

to find
y/x+y
so
3x/4x = 75 %
IMO D

fskilnik wrote:
fskilnik wrote:
GMATH practice exercise (Quant Class 6)

Each student in a certain class is considered intermediate or strong, but not both. The average of the grades of the strong students is 6.3 points, exactly two points above the average of the grades of the intermediate students. What is the percentage of strong students in this class, if the average of all students grades in this class is half point below the average of the grades of the strong students?

(A) 60%
(B) 65%
(C) 70%
(D) 75%
(E) 80% $$?\,\, = \,\,{{100} \over {100 + x}}$$

$$\left( {{\text{Alligation}}} \right)\,\,\,\,?\,\, = \,\,\frac{{100}}{{100 + x}}\,\, = \,\,\frac{{5.8 - 4.3}}{{6.3 - 4.3}}\,\, = \,\,\frac{{1.5}}{2}\,\, = \,\,\underleftrightarrow {\frac{1}{{10}}\left( {\frac{{15}}{2}} \right) = 0.75}\,\, = \,\,75\%$$

The correct answer is (D).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Originally posted by Archit3110 on 20 Feb 2019, 11:49.
Last edited by Archit3110 on 20 Feb 2019, 11:59, edited 1 time in total.
GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Each student in a certain class is considered intermediate or strong,  [#permalink]

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Archit3110 wrote:
fskilnik
how did you deduce value of 5.8?

Hi Archit3110 !

"... the average of all students grades in this class is half point below the average of the grades of the strong students"

Hence: 6.3 - 0.5 = 5.8

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net Re: Each student in a certain class is considered intermediate or strong,   [#permalink] 20 Feb 2019, 11:54
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