Problem Solving

Hi All,

We're told that 1/5 of the students at a nursery school are 4 years old or older, 16 students have not yet reached their third birthday and a total of 40 students are NOT between 3 years old and 4 years old. We're asked for the total number of children in the nursery school. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

Since 1/5 of the students are 4 or older, we know that the TOTAL number of students MUST be a multiple of 5 (since you can't have a 'fraction' of a student). Thus, we can eliminate Answers B and E immediately.

Let's TEST Answer C: 70 students

IF..... there are 70 students
(1/5)(70) = 14 are 4 years old or older
and 16 are under 3 years old
These two groups represent the students who are NOT between 3 and 4 years old. However, this only totals 14+16 = 30 students; we're told that 40 students fit that description. Thus, 70 is TOO SMALL a number - and we need there to be MORE students. There's only one answer that fits...

Final Answer: A

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

BTGmoderatorLU wrote:Source: Princeton Review

One-fifth of the students at a nursery school are 4 years old or older. If 16 students have not yet reached their third birthday, and a total of 40 students are not between 3 years old and 4 years old, how many children are in the nursery school?

A. 120
B. 96
C. 70
D. 60
E. 24

Let's let x = the total number of students at the school. We know that 1/5 of the total number of students, or 0.2x, are 4 years old or older. Additionally, we are given that 16 students are less than age 3. The key piece of information is that a total of 40 students are NOT between ages 3 and 4, which means that:

0.2x + 16 = 40

2x + 160 = 400

2x = 240

x = 120

Answer: A