At the beginning of the year, the ratio of juniors to seniors in high

Question

At the beginning of the year, the ratio of juniors to seniors in high school X was 3 to 4. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 4 to 5, how many seniors were there in high school X at the beginning of the year?

A. 80
B. 90
C. 100
D. 110
E. 120

Suppose, initially the ratio was: 3x/4x
Due to transfer, it stands: 3x-10/4x-20 = 4/5
upon calculation: x = 30
the seniors were: 4*30 = 120

Answer: E

A. 80 
B. 90 
C. 100 
D. 110 
E. 120

PareshGmat · Accepted Answer

Juniors .............. Seniors

3x ........................... 4x (Initially)

After transfers

3x-10 .................. 4x-20

Given that new ratio  = \frac{3x-10}{4x-20} = \frac{4}{5}

x = 30

Seniors initially = 120

Answer = E

iamevitaerc · Answer

Step1: J/S=3/4 => J=3/4(S)
Step 2: (J+10)/(S+20)=4/5
Step 3: substitute Value of J from step1 in step 2 to get s
s=120 (E)

manpreetsingh86 · Answer

let the total number of juniors and seniors at the beginning of the year be 3x and 4x respectively.

now 10 juniors and 20 seniors are transferred to another school. thus no. of juniors and seniors students left in the school X are 3x-10 and 4x-20 respectively. the ratio of these juniors and seniors students = 4/5
thus we have (3x-10)/(4x-20) = 4/5
15x-50= 16x-80
x=30

thus total no. of seniors at the beginning of the year =4(30)= 120

LighthousePrep · Answer

Here's how I did it:

j  = juniors at beginning of year
 s  = seniors at beginning of year

Part 1)  \frac{j}{s}  =  \frac{3}{4}

Part 2)  \frac{(j-10)}{(s-20)} = \frac{4}{5}

Reframe Part 1 in terms of j:
 j  =  \frac{3}{4}s  =  .75s

Substitute j in part 2:

\frac{(j-10)}{(s-20)} = \frac{4}{5}

=  \frac{(.75s-10)}{(s-20)} = \frac{4}{5}

Now, solve for s, and you get your answer.

keats · Answer

I am not sure as to why you added 10, and 20 instead of subtracting it  iamevitaerc

Senthil7 · Answer

Beginning of Year J/S = 3/4 => J = (3/4)S

After transfer : (J-10)/(S-20) = 4/5
= 5J-50 = 4S - 80 => Substitute from the first equation
= (1/4)S = 30
=> S = 120 hence choice D

GMAT01 · Answer

For these ratio questions I would assume it would not matter which method(two methods listed below) you use for any question throughout the GMAT correct?

Just like this question for example you can use3X/4X = J/S > 3X - 10/4X- 20 = 4/5 to start off the equation and solve as opposed to J/S = 3/4 > J - 10 / S - 20 = 4/5

ydmuley · Answer

At the beginning of the year, the ratio of juniors to seniors in high school X was 3 to 4. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 4 to 5, how many seniors were there in high school X at the beginning of the year?

A. 80
B. 90
C. 100
D. 110
E. 120

Suppose, initially the ratio was: 3x/4x
Due to transfer, it stands: 3x-10/4x-20 = 4/5
upon calculation: x = 30
the seniors were: 4*30 = 120

Answer: E

No. Of Juniors = 3x

No. Of Seniors = 4x

New No. Of Juniors = 3x - 10

New No. Of Seniors = 4x - 20

All the above points we have written based on the given information on ratios.

3x - 10/4x - 20 = 4/5

5(3x - 10) = 4(4x - 20)

15x - 50 = 16x - 80

x = 30

No. Of Seniors at the beginning = 4x = 4 * 30 = 120

Hence, the Answer is E

Posted from my mobile device

Abhishek009 · Answer

Originally -

\frac{Juniors}{Seniors} = \frac{3x}{4x}

\frac{3x - 10}{4x - 20} = \frac{4}{5}

15x - 50 = 16x - 80

x = 30

So, The total number of seniors in high school is  4*30 = 120

Thus, the correct answer must be (E) 120

ZahidPavel · Answer

At the beginning of the year, the ratio of juniors to seniors in high school X was 3 to 4. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 4 to 5, how many seniors were there in high school X at the beginning of the year?

A. 80
B. 90
C. 100
D. 110
E. 120

Suppose, initially the ratio was: 3x/4x
Due to transfer, it stands: 3x-10/4x-20 = 4/5
upon calculation: x = 30
the seniors were: 4*30 = 120

Answer: E

A. 80 
B. 90 
C. 100 
D. 110 
E. 120

Suppose, initially the ratio was: 3x/4x
Due to transfer, it stands: 3x-10/4x-20 = 4/5
upon calculation: x = 30
 the seniors were: 4*30 = 120

Answer: E

anushrisarda0501 · Answer

There is a time-saving trick to do such questions:
look at the numbers in the ratios (here the numbers are 3,4 and 5)
now analyze the answer choices and see which number is a multiple of all 3 numbers in the ratio.
option E satisfies the condition, so it is the correct choice.

Disclaimer: I don't know if this is a legit trick but I tried this trick on a few similar questions and it worked for me.
please correct me if I'm wrong.

Thx in advance!

bumpbot · Answer

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At the beginning of the year, the ratio of juniors to seniors in high

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