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The number of students enrolled at school X this year is 7 percent

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The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 12 Nov 2014, 09:54
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A
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D
E

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Tough and Tricky questions: Percents.



The number of students enrolled at school \(X\) this year is 7 percent more than it was last year. The number of students enrolled at school \(Y\) this year is 3 percent more than it was last year. If school \(X\) grew by 40 more students than school \(Y\) did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school \(Y\) last year?


A. 480
B. 1600
C. 1920
D. 2080
E. 2400

Kudos for a correct solution.

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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 12 Nov 2014, 11:26
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I started with answer choice C and worked backwards and used some ballparking. If school Y had 1920 students last year, 3% increase would be slightly more than 57. X would have had 2080 students and a 7% increase would be around 145 students. The difference in increases is much too large so we should aim for a larger Y population in the answer choices.

I went to answer E next, knowing that if this was correct, I am good to go, but if not, D must be the answer.

With answer E, school Y had 2400 students and a 3% increase is 72. X would have had 1600 students. 7% of 1600 is 112.

112-72 = 40 :)

Answer choice E!
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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 12 Nov 2014, 11:40
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1
Bunuel wrote:

Tough and Tricky questions: Percents.



The number of students enrolled at school \(X\) this year is 7 percent more than it was last year. The number of students enrolled at school \(Y\) this year is 3 percent more than it was last year. If school \(X\) grew by 40 more students than school \(Y\) did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school \(Y\) last year?


A. 480
B. 1600
C. 1920
D. 2080
E. 2400

Kudos for a correct solution.



Given Info:
No. of students enrolled in school X is= 7% more than previous year's strength= 7X/100
No. of students enrolled in school Y is= 3% more than previous year's strength= 3Y/100

Given that "THIS YEAR" school X have 40 students more than school Y. So the increase in strength can be written as

7X/100= 40 + 3Y/100

7X= 4000 + 3Y....................(1)

And total students on previous year are X + Y=4000......................(2)

Equating & Solving we get, Y=2400

ANS is E
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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 12 Nov 2014, 11:58
1
2
Let us assume, number of student enrolled at school X last year is x
number of student enrolled at school Y last year is y.

this year enrollment at school X increases by 7% i.e. 7x/100
this year enrollment at school Y increases by 3% i.e. 3y/100

As per question stem, school X grew by 40 more students than school Y did
this means 7x/100 = 40+ 3y/100 --- equation(1)

last year total student at school was 4000
i.e. x+y = 4000 --- equation(2)

Equate Equation (1) & (2), y will be 2400

Answer: E

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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 12 Nov 2014, 20:26
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1
......................... School X ................ School Y ................... Total

Last Yr ................. 4000-a ..................... a ............................ 4000 (Assumed "a" as number of students in last yr)


Difference ......... \((4000-a) * \frac{7}{100}\) ................. \(a * \frac{3}{100}\) ..............
(Growth)

Given that "Growth" of School X is 40 more than growth of School Y

Setting up the equation

\(\frac{3a}{100} + 40 = \frac{7}{100} * (4000-a)\)

\(10a = 7 * 4000 - 4000\)

a = 2400

Answer = E
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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 13 Nov 2014, 09:20
Bunuel wrote:

Tough and Tricky questions: Percents.



The number of students enrolled at school \(X\) this year is 7 percent more than it was last year. The number of students enrolled at school \(Y\) this year is 3 percent more than it was last year. If school \(X\) grew by 40 more students than school \(Y\) did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school \(Y\) last year?


A. 480
B. 1600
C. 1920
D. 2080
E. 2400

Kudos for a correct solution.


Official Solution:

The number of students enrolled at school \(X\) this year is 7 percent more than it was last year. The number of students enrolled at school \(Y\) this year is 3 percent more than it was last year. If school \(X\) grew by 40 more students than school \(Y\) did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school \(Y\) last year?

A. 480
B. 1600
C. 1920
D. 2080
E. 2400

We must determine the number of students enrolled at school \(Y\) last year.

We can set up two equations to describe this situation.

First: last year, the number of students enrolled at school \(X\) (which we will call \(x\)) and the number of students enrolled at school \(Y\) (which we will call \(y\)) together were equal to 4000. So \(x + y = 4000\).

Second: the number of additional students at school \(X\) this year (equal to 7 percent of last year's student body of \(x\), or \(0.07x\)) is 40 more than the number of additional students at school \(Y\) this year (equal to 3 percent of last year's student body of \(y\), or \(0.03y\)). Therefore, \(0.07x - 0.03y = 40\).

Now we use substitution to solve for \(y\). Rearrange the first equation to express \(x\) in terms of \(y\): \(x = 4000 - y\). Then, substitute for \(x\) in the second equation: \(0.07(4000 - y) - 0.03y = 40\).

Distribute the 0.07 to get: \(0.07(4000) - 0.07y - 0.03y = 40\)

Simplify and combine like terms: \(280 - 40 = (0.07 + 0.03)y\), or \(240 = 0.1y\).

Multiply both sides by 10: \(2400 = y\).

Answer: E.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 25 Feb 2016, 05:26
Bunuel wrote:
Bunuel wrote:

Tough and Tricky questions: Percents.



The number of students enrolled at school \(X\) this year is 7 percent more than it was last year. The number of students enrolled at school \(Y\) this year is 3 percent more than it was last year. If school \(X\) grew by 40 more students than school \(Y\) did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school \(Y\) last year?


A. 480
B. 1600
C. 1920
D. 2080
E. 2400

Kudos for a correct solution.


Official Solution:

The number of students enrolled at school \(X\) this year is 7 percent more than it was last year. The number of students enrolled at school \(Y\) this year is 3 percent more than it was last year. If school \(X\) grew by 40 more students than school \(Y\) did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school \(Y\) last year?

A. 480
B. 1600
C. 1920
D. 2080
E. 2400

We must determine the number of students enrolled at school \(Y\) last year.

We can set up two equations to describe this situation.

First: last year, the number of students enrolled at school \(X\) (which we will call \(x\)) and the number of students enrolled at school \(Y\) (which we will call \(y\)) together were equal to 4000. So \(x + y = 4000\).

Second: the number of additional students at school \(X\) this year (equal to 7 percent of last year's student body of \(x\), or \(0.07x\)) is 40 more than the number of additional students at school \(Y\) this year (equal to 3 percent of last year's student body of \(y\), or \(0.03y\)). Therefore, \(0.07x - 0.03y = 40\).

Now we use substitution to solve for \(y\). Rearrange the first equation to express \(x\) in terms of \(y\): \(x = 4000 - y\). Then, substitute for \(x\) in the second equation: \(0.07(4000 - y) - 0.03y = 40\).

Distribute the 0.07 to get: \(0.07(4000) - 0.07y - 0.03y = 40\)

Simplify and combine like terms: \(280 - 40 = (0.07 + 0.03)y\), or \(240 = 0.1y\).

Multiply both sides by 10: \(2400 = y\).

Answer: E.


Hey - I'm just wondering why it isnt 1.07X and 1.03Y as the question states that its "7% more than last year"... same with Y
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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 18 Feb 2017, 10:36
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Since the problem states that:

" If school X grew by 40 more students than school Y did "

It talks about the individual growth and not the total number of students.
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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 18 Feb 2017, 22:17
Let x be the number of students in X and y in Y.

As per the question,

x +y = 4000 ... (1)
0.07x - 0.03y = 40
=> 7x - 3y = 4000 ... (2)

Solving equation 1 and 2:

y = 2400
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The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 24 Feb 2017, 11:21
why cant we say that 1.07X=1.03Y+40 ?

can you elaborate more?

is it because it talks about the growth of students?

How would the question have to be if we were to write 1.07X=1.03Y+40 ? "at the end of the year the school X had 40 students more than Y" ? or this would be the same as the stem?

These differences in language are so subtle..
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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 24 Feb 2017, 15:04
iliavko

Since the question stem says - 'If school X grew by 40 more students than school Y did' i.e. the number of additional students at school X this year (equal to 7 percent of last year's student body of x, or 0.07x) is 40 more than the number of additional students at school Y this year (equal to 3 percent of last year's student body of y, or 0.03y), hence .07x=.03y+40.

Hope this helps.
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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 24 Feb 2017, 15:38
Bunuel wrote:

Tough and Tricky questions: Percents.



The number of students enrolled at school \(X\) this year is 7 percent more than it was last year. The number of students enrolled at school \(Y\) this year is 3 percent more than it was last year. If school \(X\) grew by 40 more students than school \(Y\) did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school \(Y\) last year?


A. 480
B. 1600
C. 1920
D. 2080
E. 2400

Kudos for a correct solution.


let x and y=number of students at X and Y respectively last year
x=4000-y
.07(4000-y)-.03y=40
y=2400 students
E
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Re: The number of students enrolled at school X this year is 7 percent [#permalink]

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New post 18 Apr 2018, 09:21
Let the number of students last year be X and Y. This year the number of students will be 1.07X and 1.03Y.

We have 2 equations -

a) 0.07X=0.03Y+40
b) X+Y=4000

Solve the two and get the value of Y as 2400 or option E.
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Re: The number of students enrolled at school X this year is 7 percent   [#permalink] 18 Apr 2018, 09:21
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