Every junior at Central High School studies exactly one language: 75

Question

Every junior at Central High School studies exactly one language: 75 percent of the juniors study Gaelic, one-sixth of the juniors study Spanish, and the other 7 juniors study Tagalog. How many juniors are there at Central High School?

A. 80
B. 82
C. 84
D. 86
E. 88

A. 80
B. 82
C. 84
D. 86
E. 88

yashikaaggarwal · Answer

Let Total be 100 X
Only Gaelic Language Speaker = 75% of 100X = 75X
Only Spanish Language Speaker = 16.66% of 100X = 16.6X
Only Tagalog Language Speaker = 100-75-16.66 = 8.33X = 7
X = 7/8.33
Therefore,
100X = 100*7/8.33
100X =84.03

Since the closest total value is 84

Answer is C

ravigupta2912 · Answer

I don't think that venn diagram is accurate since the Q stem says "exactly 1 language". Therefore the circles shouldn't intersect, ideally speaking.

I solved it as under:-

Let total be x
75% = 3/4x = G
1/6x = S

7 is the remaining who study Tagalong OR x - 3/4x - 1/6x = 7
=> 2/24x = 7
=> x = 84

IanStewart · Answer

If 1/6 of the juniors study Spanish, then the number of juniors must be divisible by 6, and thus by 3. The only answer choice divisible by 3 is C, 84, so that must be right.

priyankas19 · Answer

HI
i solved it by initially cancelling out the options with the help of the options i.e the answer choice have to be divided by the by 6 and 4 since 75% is 3/4 so i started with option C "84" since students cant be in decimal so i got the answer like that easily.
3/4*84-one subject
1/6*84-one subject
rest 7-other subjects so total 84 students.
and only one option is divisible by 6 & 4 then also i solved it just to make sure.

when we solve problems where fractions are given the common multiple of denominator will work and be easily solved.

Kinshook · Answer

Given: Every junior at Central High School studies exactly one language: 75 percent of the juniors study Gaelic, one-sixth of the juniors study Spanish, and the other 7 juniors study Tagalog. 
Asked: How many juniors are there at Central High School?

Let the juniors at Central High School be x.

(100%-(75% + 1/6))x = 7
(25% - 1/6)x = 7
(1/4 - 1/6)x =7
x/12 = 7
x = 12*7 = 84

IMO C

Abhishek009 · Answer

Let total no of students be 12

Gaelic = 9
Spanish = 2
Tagalog = 1

So, 1 represents 7 , Thus, 12 represents 84 , Answer must be (C)

Every junior at Central High School studies exactly one language: 75

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Every junior at Central High School studies exactly one language: 75

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards