PS - Word Translation Sets

Statement:
If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art

Meaning:
who take ever core class except art = students who take chemisty and biology together
therefore number of freshmen who take only Art is 3 times students who take chemisty and biology together

Solution:

A + AB + AC + ABC + B + BC + C = 100

B = 17
C = 10
AC + AB = 20
ABC = 5

A + 20 + 5 + 17 + BC + 10 = 100
A + BC + 52 = 100
A + BC = 48

From above A = 3BC
A + BC = 48
3BC + BC = 4BC = 48
BC = 12
A = 36

Freshmen who take art =
A + AB + AC + ABC
36 + 20 + 5 = 61
Ans = E

Should the bolded portion say "Art is 3 times the number of freshmen who takes every core class except ART"

Every core class except Art = shouldn't it mean all the remaining except Art
But ur explanation says about "students who take chemisty and biology together" Please explain???

theCEO wrote:Statement:
If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art

Meaning:
who take ever core class except art = students who take chemisty and biology together
therefore number of freshmen who take only Art is 3 times students who take chemisty and biology together

Solution:

A + AB + AC + ABC + B + BC + C = 100

B = 17
C = 10
AC + AB = 20
ABC = 5

A + 20 + 5 + 17 + BC + 10 = 100
A + BC + 52 = 100
A + BC = 48

From above A = 3BC
A + BC = 48
3BC + BC = 4BC = 48
BC = 12
A = 36

Freshmen who take art =
A + AB + AC + ABC
36 + 20 + 5 = 61
Ans = E

karthikpandian19 wrote:There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?

PS: I had confusion while translating the bolded portion into equation


(A) 25

(B) 32

(C) 36

(D) 48

(E) 61

We can plug in the answers, which represent the total number of art students.

5 take all three classes, and 20 take art and exactly one of the other two core classes.
ABC + (AB + AC) = 5+20 = 25.

The remaining art students take ONLY art.
The answer choices represent the TOTAL number of art students, implying the following options for the number of students who ONLY art:
25-25 = 0

32-25 = 7

36-25 = 11

48-25 = 23

61-25 = 36.

Since the number of students who take only art is 3 TIMES another value in the problem, the number of students who take only art must be a multiple of 3.
Only answer choice E is viable.

The correct answer is E.

karthikpandian19 wrote:Should the bolded portion say "Art is 3 times the number of freshmen who takes every core class except ART"

Every core class except Art = shouldn't it mean all the remaining except Art
But ur explanation says about "students who take chemisty and biology together" Please explain???

theCEO wrote:Statement:
If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art

Meaning:
who take ever core class except art = students who take chemisty and biology together
therefore number of freshmen who take only Art is 3 times students who take chemisty and biology together

Solution:

A + AB + AC + ABC + B + BC + C = 100

B = 17
C = 10
AC + AB = 20
ABC = 5

A + 20 + 5 + 17 + BC + 10 = 100
A + BC + 52 = 100
A + BC = 48

From above A = 3BC
A + BC = 48
3BC + BC = 4BC = 48
BC = 12
A = 36

Freshmen who take art =
A + AB + AC + ABC
36 + 20 + 5 = 61
Ans = E

Should the bolded portion say "Art is 3 times the number of freshmen who takes every core class except ART?
Yes, it is perfect to say so. If the question had stated this information in an other way, it would have been easy

Lets look at the following sentence:
the number of freshmen who take every core class:
this means the number of students who take every core class at the same time
so this would be 5 students according to the example


Lets look at the following sentence:
the number of freshmen who take every core class except Art:
there are 3 core classes - art, biology and chemistry
all the classes except art = biology and chemistry together.

Let me know if this helps.

GMATGuruNY wrote:

karthikpandian19 wrote:There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?

PS: I had confusion while translating the bolded portion into equation


(A) 25

(B) 32

(C) 36

(D) 48

(E) 61

We can plug in the answers, which represent the total number of art students.

5 take all three classes, and 20 take art and exactly one of the other two core classes.
ABC + (AB + AC) = 5+20 = 25.

The remaining art students take ONLY art.
The answer choices represent the TOTAL number of art students, implying the following options for the number of students who ONLY art:
25-25 = 0

32-25 = 7

36-25 = 11

48-25 = 23

61-25 = 36.

Since the number of students who take only art is 3 TIMES another value in the problem, the number of students who take only art must be a multiple of 3.
Only answer choice E is viable.

The correct answer is E.

GMATGuruNY

What happens if the choices had more than one number that were mulitiples of three. How would you solve the problem?

theCEO wrote:

GMATGuruNY wrote:

karthikpandian19 wrote:There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?

PS: I had confusion while translating the bolded portion into equation


(A) 25

(B) 32

(C) 36

(D) 48

(E) 61

We can plug in the answers, which represent the total number of art students.

5 take all three classes, and 20 take art and exactly one of the other two core classes.
ABC + (AB + AC) = 5+20 = 25.

The remaining art students take ONLY art.
The answer choices represent the TOTAL number of art students, implying the following options for the number of students who ONLY art:
25-25 = 0

32-25 = 7

36-25 = 11

48-25 = 23

61-25 = 36.

Since the number of students who take only art is 3 TIMES another value in the problem, the number of students who take only art must be a multiple of 3.
Only answer choice E is viable.

The correct answer is E.

GMATGuruNY

What happens if the choices had more than one number that were mulitiples of three. How would you solve the problem?

One formula for triple-overlapping groups is as follows:

T = Only A + Only B + Only C + AB + AC + BC + ABC

The problem give values for every grouping in the formula but Only A and BC.
Thus:
Only A + BC = 100 - (17+10+5+20) = 48.
Further, it is stated that Only A : BC = 3:1.

Let's say answer choices C, D and E offered the following values for the total number of art students, with the result that Only A must be one of the values in red:

C) 43-25 = 18

D) 49-25 = 24

E) 61-25 = 36

Answer choice C:
If Only A = 18, then BC = 6, for a total of 18+6 = 24.
Since the problem dictates that Only A + BC = 48 -- double the result here -- the correct answer must be E, which doubles the value of Only A to 36.

The correct answer is E.