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A school has 60 students. Each student studies either Cantonese or Fre

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A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 16 Jul 2015, 01:19
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A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

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A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 16 Jul 2015, 03:25
Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.


NF + NC = 0 (as each student learns either cantonese or french)

Text in black: given values
Text in red: calculated values

From statement 1, we can see x/4 +x= 60 . Thus this statement is sufficient

From statement 2, we see that 2x-36=60. Thus this statement is sufficient as well. Thus both statements are sufficient and hence D is the correct answer.
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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 16 Jul 2015, 05:45
Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.


Solution -

From the given information, C + F = 60.

Stmt1 - The number of students who study French is 4 times the number of the students who study Cantonese. --> F = 4C.
Substitute F = 4C in C + F = 60 --> C + (4C) = 60 --> 5C = 60 --> C = 12 and F = 48. Sufficient.

Stmt2 - The number of students who study Cantonese is 36 fewer than the number who study French. --> C = F – 36.
Again, substitute C in the original equation C + F = 60 --> (F – 36) + F = 60 --> 2F – 36 = 60 --> F = 48. Sufficient.

ANS D.
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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 16 Jul 2015, 10:37
Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.


This question doesn't need to be solved by double matrix or Venn diagram because two of the catagories are already known as zero

Students who don't study either of the Cantonese and French = 0
Students who study Both Cantonese and French = 0

i.e. only categories are

Students studying Cantonese (C)
Students studying French (F)
and F + C = 60

Question : Students studying French = ?

Statement 1: The number of students who study French is 4 times the number of the students who study Cantonese

i.e. F = 4*C and F+C = 60
i.e. C = 12 and F = 48
SUFICIENT

Statement 2: The number of students who study Cantonese is 36 fewer than the number who study French.

C = F-36 and F+C = 60
i.e. C = 12 and F = 48
SUFICIENT

Answer: Option D
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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 17 Jul 2015, 07:21
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A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

c = Cantonese f= French => c + f =60

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
f=4c => c=4/f This can be plugged into the value for c in c+f=60 to solve for f. Sufficient.

(2) The number of students who study Cantonese is 36 fewer than the number who study French.
c=f - 36 This can be plugged into the value for c in c + f = 60 to solve for f. Sufficient.

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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 17 Jul 2015, 09:13
Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.


Because each student must take a language, and no student can take both, this makes the question easier.
1. 4x + x = 60
5x=60
x=12

There are 48 French students. Sufficient.

2. (x-36) + x = 60
2x=96
x=48
Again, there are 48 French students. Sufficient.

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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 17 Jul 2015, 15:54
Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.



Given : F + C = 60---- Eq 1

St 1: F = 4C => Can be solved with eq 1. Sufficient

St 2: C = F-36 => Can be solved with eq 1. Sufficient.

Hence Option D
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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 18 Jul 2015, 07:03
Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.


Statement 1:The number of students who study French is 4 times the number of the students who study Cantonese.
C+4C=60. Find the value of C and F. Sufficient.
Statement 2:The number of students who study Cantonese is 36 fewer than the number who study French
F+F-36=60. Sufficient
Answer D
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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 19 Jul 2015, 05:23
1
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Given : Each student studies either Cantonese or French, but not both
C + F = 60 -- Equation 1

Statement 1: F = 4c - Sufficient to solve equation 1

Statement 2: C = F - 36 --
So F-36 + F = 60 -- Sufficient to solve equation 1

Hence Option D
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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 19 Jul 2015, 08:01
(1): f = 4c. f+c = 60. so, 4c+c = 60, therefore c = 12, f = 48. Sufficient.

(2): f - c = 36. f+c = 60. Solving we get f = 48, c = 12. Sufficient.

Ans (D).
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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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New post 19 Jul 2015, 14:01
Bunuel wrote:
A school has 60 students. Each student studies either Cantonese or French, but not both. How many students study French?

(1) The number of students who study French is 4 times the number of the students who study Cantonese.
(2) The number of students who study Cantonese is 36 fewer than the number who study French.

Kudos for a correct solution.


800score Official Solution:

Use C to represent the number of students studying Cantonese and F to represent the number of students studying French. The given information tells us that the number of students adds up to 60, or C + F = 60.

Statement (1) gives us another equation: F = 4C. Now we can substitute F with 4C in the original equation:
C + F = 60
C + (4C) = 60
5C = 60
C = 60/5 = 12.

Since we are told that 4C = F, we know that:
F = 12 × 4 = 48.

Therefore, Statement (1) is sufficient.

Statement (2) tells us that F – 36 = C. Again, we can substitute this into the original equation:
C + F = 60.
(F – 36) + F = 60
2F – 36 = 60
2F = 96
F = 48.

Since, either statement alone is sufficient to solve for F, the correct answer is choice (D).
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Re: A school has 60 students. Each student studies either Cantonese or Fre  [#permalink]

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Re: A school has 60 students. Each student studies either Cantonese or Fre   [#permalink] 22 Dec 2018, 16:35
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