Elementary Grades

[edvhou812]

Manhattan GMAT practice test question. I got the correct answer during test review, but it took me five minutes. Can an expert or top poster help me with a quick way to the answer? Thanks.


At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/5 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?

12 greater
17 fewer
28 fewer
36 fewer
44 fewer

[cans]

ratio:16:1 ,total=510. thus 30 teachers and 480 students.
kindergarten-> 1/5 = 96 and remainder=4/5
5+6 -> (1/3)(4/5)=4/15
1+2 -> 1/4
let 3=4=x.
(1/5 + 1/4 + 4/15) 480 + 2x = 480 -> 2x = 480*17/60 -> x = 68.
Thus 96-68 = 28 fewer

[gmatboost]

A few tips on how to do the required calculations faster, if you decided to calculate the numbers in each grade or set of grades:

1/5 of 480
Instead of multiplying by 1/5 (dividing by 5) you should always multiply by 2/10, because it is much faster. 480/10 = 48. 48 * 2 = 96.
See more: https://blog.gmatboost.com/2011/08/02/mu ... e-quickly/

480 - 96
Instead of subtracting 96, subtract 100 and add back 4: 480 - 100 = 380. 380 + 4 = 384.

1/3 of 384:
Split 384 into 300 + 60 + 24
Take 1/3 of each: 100 + 20 + 8 = 128

1/4 of 480 = 120 should be no problem

Now to get 3rd + 4th
480 - 120 = 360
360 - 96 = 360 - 100 + 4 = 264
264 - 128 = 264 - 130 + 2 = 134 + 2 = 136.
3rd grade = 136/2 = (120 + 16)/2 = 60 + 8 = 68

96 - 68 = 96 - 70 + 2 = 26 + 2 = 28