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Bunuel
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One-fifth of the students at a nursery school are 4 years old or older 17 Aug 2018, 12:07
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A
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73% (02:04) correct 27% (02:17) wrong based on 450 sessions

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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
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A
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One-fifth of the students at a nursery school are 4 years old or older 17 Aug 2018, 12:18
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Total number of students =x;
students >= 4 = x/5;
students less than 3 =16;
hence x/5 + 16 =40;
thus x = 120.
Sol : A
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One-fifth of the students at a nursery school are 4 years old or older 20 Aug 2018, 11:18
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Bunuel
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
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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
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One-fifth of the students at a nursery school are 4 years old or older 04 Mar 2023, 04:50
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There is some iota of confusion here :

40 students are not between 3 years old and 4 years old

That implies that 40 students are distributed as follow :

S1 <= 3 years old
S2 >= 4 Years old

In the premise we have the info :

No. of students less than 3 years = 16

How can we say S1 = 16. What about the students who are exactly 3 years old.
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One-fifth of the students at a nursery school are 4 years old or older 25 Mar 2023, 21:04
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abhishekmayank
There is some iota of confusion here :

40 students are not between 3 years old and 4 years old

That implies that 40 students are distributed as follow :

S1 <= 3 years old
S2 >= 4 Years old

In the premise we have the info :

No. of students less than 3 years = 16

How can we say S1 = 16. What about the students who are exactly 3 years old.
Show more

I have same doubt. What about 3 years old students? If we will consider them seprately there will be one more unknown and then making cases there can be two answers for total students 70 or 60.
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One-fifth of the students at a nursery school are 4 years old or older 06 Feb 2026, 10:40
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Deconstructing the Question
Split students into 3 age groups:
- Under 3 years old = 16
- Between 3 and 4 years old = (unknown)
- 4 years old or older = (Older)

Given:
1) Older is \(\frac{1}{5}\) of the total \(T\).
2) \(\text{Under3}=16\).
3) 40 students are NOT between 3 and 4, meaning:
\(\text{Under3} + \text{Older} = 40\)

Step-by-step
From "not between 3 and 4":
\(16 + \text{Older} = 40\)
So:
\(\text{Older}=24\)

But Older is one-fifth of the total:
\(24=\frac{1}{5}T\)

Solve:
\(T=24\cdot 5=120\)

Answer: 120
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