School X and School Y

Expert replies

j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Thu Sep 11, 2014 2:42 am

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

Guys ,

where i am wrong , pls correct me.

Let last year no. of students in school X be x and in school Y be y

x+y=4000 ----------(given in ques)

this year 7% more than the last year so = x(1+7/100) will be 1.07x this year students in school X

and in School Y = y(1+3/100) will be 1.03y this year students in school Y

According to the question :

1.07x=1.03y+40

So now we have two equation with two variables .

Pls help me out

Like this post

Source: Beat The GMAT — Problem Solving | Thu Sep 11, 2014 2:42 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Sep 11, 2014 3:05 am

j_shreyans wrote: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 can PLUG IN THE ANSWERS, which represent the number of students in school Y last year.
Since the enrollment in Y grows by 3% = 3/100, the correct answer choice must be a multiple of 100.
Eliminate A, C and D.
When the correct answer choice is plugged in, X's enrollment will grow by 40 more students than Y's.

Answer choice B: 1600
Increase in Y this year = 3% of 1600 = 48.
Since last year there were 4000 students between the 2 schools, X's enrollment last year = 4000-1600 = 2400.
Increase in X this year = 7% of 2400 = 168.
X's increase - Y's increase = 168-48 = 120.
Doesn't work.

The correct answer is E.

Answer choice E: 2400
Increase in Y this year = 3% of 2400 = 72.
Since last year there were 4000 students between the 2 schools, X's enrollment last year = 4000-2400 = 1600.
Increase in X this year = 7% of 1600 = 112.
X's increase - Y's increase = 112-72 = 40.
Success!

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

KlavdiaTeratai: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Sep 11, 2014 5:40 am

by KlavdiaTeratai » Thu Sep 11, 2014 7:53 am

Can you please solve it directly without plugging in the answer choices? I understand that on the test plugging in the answers for such questions would be the best option, however, I would like to see the best way to solve this problem directly for thorough understanding of the concepts tested in this question. I have tried different approaches of solving this problem directly, but there comes a point in the calculations where I have to round up, leading me to get the wrong answer. Thank you very much!

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Sep 11, 2014 8:09 am

j_shreyans wrote: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

Algebraic solution:

There were 4000 total enrolled students last year at both schools.
x + y = 4000.

School X (whose enrollment increased by 7%) grew by 40 more students than school Y (whose enrollment increased by 3%).
Since X's 7% increase is 40 more than Y's 3% increase, we get:
0.07x = 0.03y + 40
7x = 3y + 4000.

The first equation can be rephrased as follows:
x = 4000 - y
7x = 28000 - 7y.

Since 7x = 3y + 4000 and 7x = 28000 - 7y, the expressions in red are equal:
3y + 4000 = 28000 - 7y
10y = 24000
y = 2400.

The correct answer is E.

Like this post

j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Thu Sep 11, 2014 7:57 pm

Hi ,

Shouldn't be like below:

7% more than it was last year = x(1+7/100) =1.07x

3% more than it was last year = y(1+3/100) = 1.03y

Pls help me on this.

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Sep 11, 2014 9:31 pm

Hi j_shreyans,

The math translations that you've done would represent the CURRENT number of students at School X and School Y.

The third sentence tells us that "School X GREW by 40 more students than School Y did", so we don't need the current number of students at the two schools - we need the GROWTH at School X and the GROWTH at School Y

GROWTH at School X = .07X

GROWTH at School Y = .03Y

School X grew by 40 more students than school Y did --> .07X = .03Y + 40

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Thu Sep 11, 2014 10:02 pm

ooohhhh Yes.

Thanks for correting me .

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review