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In a day care, 80% of the kids are American. 60% of the kids have sta

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Bunuel
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In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   03 Jul 2020, 03:56
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82% (02:24) correct 18% (02:28) wrong based on 186 sessions
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In a day care, 80% of the kids are American. 60% of the kids have started speaking. Of these, only 20% are under the age of 2 years. If the number of non-American kids at the day care is 40, what is the number of kids who can speak and are not under 2 years of age?

A. 24
B. 50
C. 96
D. 120
E. 160
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C
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rajatchopra1994
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Re: In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   03 Jul 2020, 04:35
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Explanation:
Let total Kids are = X
80% are American kids = 0.8X
Non -American Kids= 0.2X
non-American kids = 40 = 0.2X
x = 200.

60% speaks = 120
20% are under 2 years who speaks = 24
Speaks but not under 2 years = 120 - 24
= 96

IMO-C
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In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   03 Jul 2020, 04:41
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Bunuel wrote:
In a day care, 80% of the kids are American. 60% of the kids have started speaking. Of these, only 20% are under the age of 2 years. If the number of non-American kids at the day care is 40, what is the number of kids who can speak and are not under 2 years of age?

A. 24
B. 50
C. 96
D. 120
E. 160


Solution


    • Let us assume that there are x children in the day care.
      o So, number of American kids \( = x* \frac{4}{5} \)
      o And, the number of non-American kids \(= x- x* \frac{4}{5} = x* \frac{1}{5} = 40\)
         \( ⟹ x = 40*5 = 200\)
    • Now, the number of kids who has started speaking \(=200* \frac{3}{5} =120 \)
      o Out of these 120 kids, 20% are under the age of 2 years.
      o This means, Out of these 120 kids, \((100-20= 80)\)% are not under the age of 2 years.
         Thus, the number of kids who can speak and are not under 2 years of age \(= 120* \frac{4}{5} = 96\)
Thus, the correct answer is Option C.
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Re: In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   03 Jul 2020, 04:43
Non Americans at a day care centre = 40 which is 20% of all kids at day care centre

Total no. Of kids at the day care centre= 40*100/20 = 200

60% kids at the day care centre can speak = 200*0.6 = 120

Out of these 80% are 2 or above 2 years old.
120*0.8 = 96

Answer is C

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Re: In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   03 Jul 2020, 05:32
96 is the answer

Total kids are 5* 40 = 200

Out of 200 kids, 120 started speaking and 80 not

Again out of 120 Kids who started speaking 24 Kids are under 2 yrs and 96 Kids are not under 2 yrs

So 96 Kids started speaking but not under 2 yrs
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Re: In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   12 Aug 2020, 03:49
IMO C

Non Americans at a day care centre = 40 which is 20% of all kids at day care centre

Total number of kids = 40*100 / 20 = 200

60% kids at the day care centre can speak = 200*0.6 = 120

Out of these 80% are 2 or above 2 years old.

120*0.8 = 96

Answer C
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In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   12 Aug 2020, 03:59
Expert Reply
80% of the kids are American which means 20 % of the kids are non-American.

Given: non-American kids at the daycare is 40, hence 20 % of Total kids = 40.

=> Total kids = \(\frac{40*100}{20}\) = 200.

Hence, Total kids =200.

American kids = 80% of 200 = 160.
Non-American = 40.

60% of the kids have started speaking => 60% of 200 = \(\frac{60}{100}\)*200 = 120.

20% are under the age of 2 years that means 80% are above the age of 2 years

Therefore, the number of kids who can speak and are not under 2 years of age = 80% of 120

=> \(\frac{80}{100}\)*120 = 96

Answer C
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Re: In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   08 Sep 2020, 15:38
Can this be solved using a Venn diagram?
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Re: In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   19 Jan 2021, 02:48
fmcgee1 wrote:
Can this be solved using a Venn diagram?

Not a simple 3 set venn diagram.
Could make a 3d matrix chart...
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Re: In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   20 Jan 2021, 20:24
I figured it out in about 4.5 minutes because the three features took me for a loop. Does anyone know a more efficient way of solving these kinds of questions that don't involve a venn diagram? I'd rather not freeze when I run into something like this.

Part 1:
4/5x + 40 = x
x = 200 kids total

Part 2:
3/5(200) = 120 (started speaking)
1/5(120) = 24 (started speaking + under 2)
120 - 24 = 96 (started speaking + above 2)

Answer is C.
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Re: In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink] New post   22 Feb 2024, 02:43
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Re: In a day care, 80% of the kids are American. 60% of the kids have sta [#permalink]
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