Mo2men 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 Y.
Since the increase in Y = 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, a 7% increase in X will be 40 more than a 3% increase in Y.

B: Y=1600, implying that X = 4000-1600 = 2400
7% of X = (7/100)(2400) = 168.
3% of Y = (3/100)(1600) = 48.
Difference = 168-48 = 120.
Here, the difference is too great.
Eliminate B.

The correct answer is E.

Algebraic solution:

A 7% increase in X is 40 more than a 3% increase in Y:
(7/100)(X) = (3/100)Y + 40
7X = 3Y + 4000

There are 4000 students in total:
X + Y = 4000
X = 4000-Y

Substituting X=4000-Y into 7X = 3Y + 4000, we get:
7(4000-Y) = 3Y + 4000
28000 - 7Y = 3Y + 4000
24000 = 10Y
Y = 2400.

GMATGuruNY wrote:

Algebraic solution:

A 7% increase in X is 40 more than a 3% increase in Y:
(7/100)=(3/100)+40
7X = 3Y + 4000

Thank Mitch but I have big confusion.
Why did not you put it as (1.7/100)=(1.3/100)+40. What is the trigger words that makes you formulate it as above in your answer

Why did not you put it as (1.07)X=(1.03)Y+40. What is the trigger words that makes you formulate it as above in your answer

The equation in red represents the following:
After X increased by 7% and Y increased by 3%, the RESULTING NUMBER OF STUDENTS IN X was 40 more than the RESULTING NUMBER OF STUDENTS IN Y.

But the prompt states the following:
School X grew by 40 more students than School Y [grew].
The word in brackets is omitted, but its presence is implied.

The blue portions compare the GROWTH IN X to the GROWTH IN Y.
Since X grew by 7%, the growth in X = (7/100)X.
Since Y grew by 3%, the growth in Y = (3/100)Y.
Since X's increase is equal to 40 more than Y's increase, we get:
(7/100)X = (3/100)Y + 40.

[email protected] wrote:Hi Mo2men,

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

Hi Rich,

Your explanation is enlightening. A 'word' can really make difference.