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605-655 Level|   Math Related|               
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For Q2,
In the Ones classroom, Minimum Ratio Staff:Children = 1:4
Monday 13 Kids => 4 Staff Staff:Children=4:13 (greater than 0.25)
Tuesday 13 Kids => 4 Staff Staff:Children=4:13 (greater than 0.25)
Wednesday 11 Kids => 3 Staff Staff:Children=3:11 (greater than 0.25)
Thursday 12 Kids => 3 Staff Staff:Children=3:12 (equal to 0.25)
Friday 10 Kids => 3 Staff Staff:Children=3:10 (greater than 0.25)­

Least Ratio is on Thursday
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Gemmie in 3rd question, how did you take the lower ratio in case of combining Ones and Twos and Threes and FourFives ??
Gemmie
1. From the Saturday before Week 2 through the Friday of Week 2, exactly eight of the children in attendance at CCC had birthdays. Two children turned 1, one child turned 2, one child turned 3, and four children turned 4. All changes to classroom attendance from Week 2 to Week 3 were due to these birthdays.

For each of the following classrooms, select More staff if more classroom staff members were assigned to that classroom on the Monday of Week 3 than on the Monday of Week 2. Otherwise, select Same/fewer staff.


Monday of W2

- Age 2: 9 (<10) | Ratio 1:10 => Current staff are enough for 10

- Age 3: 15 (=13+3) | Ratio 1:13 => Current staff are enough for 26 (=2*13)

- Age 4-5: 12 (<13) | Ratio 1:13 => Current staff are enough for 13


Monday of W3

- Age 2: 9+1-1 = 9 (1 child turned 2 and 1 child turned 3) => Same/few staff

- Age 3: 15 + 1 - 4 = 12 (1 child turned 3 and 4 children turned 4) => Same/few staff


- Age 4 - 5: 12 + 4 = 16 (4 children turned 4) => More than 13 => More staff



2. In the Ones classroom in Week 2, for which one of the following days was the ratio of classroom staff to children least?
­
Ones: Min ratio: 1:4

The ratio is the least when exactly there is 1 teacher for every 4 children

=> The number of children on that day is divisble by 4

=> Thursday



3. Suppose that, in an effort to reduce staffing costs for the Friday of Week 2, the director of CCC had considered combining some classes for that day. For each of the following combinations, select Decrease if combining those classes would have decreased the number of classroom staff needed, provided that no other changes had occurred. Otherwise, select Increase/no change.

Infant, Ones:
- Infant: 9 children & Ratio: 1:4 => 3 teachers
- Ones: 10 children & Ratio: 1:4 => 3 teachers
- Combined: 9 + 10 = 19 => 5 teachers < 3 + 3
==> decrease

Ones, Twos
- Ones: 10 children & Ratio: 1:4 => 3 teachers
- Twos: 6 children & Ratio: 1:6 => 1 teacher
- Combined: 10 + 6 = 16 children & Ratio: 1:4 => 4 teachers = 3 + 1
=> Increase/no change

Threes, FourFives
- Threes: 12 chidren & Ratio: 1:10 => 2 teachers
- FoursFives: 8 children & Ratio: 1:13 => 1 teacher
- Combined: 12 + 8 = 20 children & Ratio: 1:10 => 2 teachers < 2 + 1
==> decrease­
­
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Tab 2 (Regulation): The minimum ratio for a particular classroom is determined by the age of the youngest child in the classroom.
So e.g. when combining Ones and Tw​​​​​​​os, we take the ratio applied to Ones
kanikaa9
Gemmie in 3rd question, how did you take the lower ratio in case of combining Ones and Twos and Threes and FourFives ??
Gemmie
1. From the Saturday before Week 2 through the Friday of Week 2, exactly eight of the children in attendance at CCC had birthdays. Two children turned 1, one child turned 2, one child turned 3, and four children turned 4. All changes to classroom attendance from Week 2 to Week 3 were due to these birthdays.

For each of the following classrooms, select More staff if more classroom staff members were assigned to that classroom on the Monday of Week 3 than on the Monday of Week 2. Otherwise, select Same/fewer staff.


Monday of W2

- Age 2: 9 (<10) | Ratio 1:10 => Current staff are enough for 10

- Age 3: 15 (=13+3) | Ratio 1:13 => Current staff are enough for 26 (=2*13)

- Age 4-5: 12 (<13) | Ratio 1:13 => Current staff are enough for 13


Monday of W3

- Age 2: 9+1-1 = 9 (1 child turned 2 and 1 child turned 3) => Same/few staff

- Age 3: 15 + 1 - 4 = 12 (1 child turned 3 and 4 children turned 4) => Same/few staff


- Age 4 - 5: 12 + 4 = 16 (4 children turned 4) => More than 13 => More staff



2. In the Ones classroom in Week 2, for which one of the following days was the ratio of classroom staff to children least?
­
Ones: Min ratio: 1:4

The ratio is the least when exactly there is 1 teacher for every 4 children

=> The number of children on that day is divisble by 4

=> Thursday



3. Suppose that, in an effort to reduce staffing costs for the Friday of Week 2, the director of CCC had considered combining some classes for that day. For each of the following combinations, select Decrease if combining those classes would have decreased the number of classroom staff needed, provided that no other changes had occurred. Otherwise, select Increase/no change.

Infant, Ones:
- Infant: 9 children & Ratio: 1:4 => 3 teachers
- Ones: 10 children & Ratio: 1:4 => 3 teachers
- Combined: 9 + 10 = 19 => 5 teachers < 3 + 3
==> decrease

Ones, Twos
- Ones: 10 children & Ratio: 1:4 => 3 teachers
- Twos: 6 children & Ratio: 1:6 => 1 teacher
- Combined: 10 + 6 = 16 children & Ratio: 1:4 => 4 teachers = 3 + 1
=> Increase/no change

Threes, FourFives
- Threes: 12 chidren & Ratio: 1:10 => 2 teachers
- FoursFives: 8 children & Ratio: 1:13 => 1 teacher
- Combined: 12 + 8 = 20 children & Ratio: 1:10 => 2 teachers < 2 + 1
==> decrease­
­
­
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Question 3:



Suppose that, in an effort to reduce staffing costs for the Friday of Week 2, the director of CCC had considered combining some classes for that day. For each of the following combinations, select Decrease if combining those classes would have decreased the number of classroom staff needed, provided that no other changes had occurred. Otherwise, select Increase/no change.



We are asked to determine whether combining certain classrooms on Friday of Week 2 would reduce the number of staff required. To start, we calculate how many staff are needed when the classes remain separate.

  • Infant: 9 children, youngest less than 2, ratio 1/4, so 3 staff
  • Ones: 10 children, youngest less than 2, ratio 1/4, so 3 staff
  • Twos: 6 children, youngest 2, ratio 1/6, so 1 staff
  • Threes: 12 children, youngest 3, ratio 1/10, so 2 staff
  • FourFives: 8 children, youngest 4, ratio 1/13, so 1 staff

Now we are moving to evaluate the combined groups.

  • Infant and Ones:

19 children, youngest under 2, ratio 1/4, so 5 staff. Separately they required 6. This means a decrease.

  • Ones and Twos:

16 children, youngest age 1, ratio 1/4, so 4 staff. Separately they required 4. This means no change.

  • Threes and FourFives:

20 children, youngest age 3, ratio 1/10, so 2 staff. Separately they required 3. This means a decrease.
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Can someone explain why did we take the lower end of the Ratio in Q3 instead of the Higher end?
What I mean is, for Ones and Twos, the Ratio if combined when taking into account of Twos would be 1/6, rather than 1/4. I am not able to understand what is the assumption here, I read the question & answer well enough, Maybe?
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chattyyee
Can someone explain why did we take the lower end of the Ratio in Q3 instead of the Higher end?
What I mean is, for Ones and Twos, the Ratio if combined when taking into account of Twos would be 1/6, rather than 1/4. I am not able to understand what is the assumption here, I read the question & answer well enough, Maybe?
Because the regulation says the ratio is based on the age of the youngest child in the classroom. When Ones and Twos are combined, the youngest is 1 year old, so the ratio must be 1:4, not 1:6. That’s why the stricter (lower-end) ratio applies.

Check compete solution HERE.

Hope it helps.
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I still don't understand how to approach question #1 in spite of the additional "birthdays" info. give. Bunuel can you please help?
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DiveshR
I still don't understand how to approach question #1 in spite of the additional "birthdays" info. give. Bunuel can you please help?
DiveshR The birthday information adds a layer of complexity because children move between classrooms. Let me guide you through a systematic approach.

Key Insight: When children have birthdays, they move "up" to the next classroom, creating a cascade effect that changes enrollment numbers and potentially staffing requirements.

Step 1: Map the Birthday Movements
Track where each child moves:
  • \(2\) children turned \(1\): Move from Infant → Ones
  • \(1\) child turned \(2\): Moves from Ones → Twos
  • \(1\) child turned \(3\): Moves from Twos → Threes
  • \(4\) children turned \(4\): Move from Threes → FourFives

Step 2: Calculate Week 3 Monday Enrollment
Starting with Week 2 Monday numbers, apply the birthday changes:

Twos classroom:
Week 2: \(10\) children
Changes: \(+1\) (from Ones) \(-1\) (to Threes) = \(10\) children

Threes classroom:
Week 2: \(15\) children
Changes: \(+1\) (from Twos) \(-4\) (to FourFives) = \(12\) children

FourFives classroom:
Week 2: \(12\) children
Changes: \(+4\) (from Threes) = \(16\) children

Step 3: Calculate Required Staff
Use the minimum ratios and round UP to nearest whole number:

Twos: \(10\) children ÷ \(6\) (ratio \(1:6\)) = \(1.67\) → 2 staff (both weeks)
Threes: \(12\) children ÷ \(10\) (ratio \(1:10\)) = \(1.2\) → 2 staff (same as Week 2)
FourFives: \(16\) children ÷ \(13\) (ratio \(1:13\)) = \(1.23\) → 2 staff (Week 2 had only 1)

What Went Wrong in Your Approach:
You likely struggled with tracking the "chain reaction" of movements. The key is to treat birthdays as transfers: every child leaving one classroom enters another.

Answer:
  • Twos: Same/fewer staff
  • Threes: Same/fewer staff
  • FourFives: More staff
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As per the line The roster of children attending CCC—as well as the days of the week each child attended—was unchanged from Week 1 through Week 3.

There should be no change in roster right? Also, Q1 does not specify IF from the saturday.....
Bunuel




Suppose that, in an effort to reduce staffing costs for the Friday of Week 2, the director of CCC had considered combining some classes for that day. For each of the following combinations, select Decrease if combining those classes would have decreased the number of classroom staff needed, provided that no other changes had occurred. Otherwise, select Increase/no change.



We are asked to determine whether combining certain classrooms on Friday of Week 2 would reduce the number of staff required. To start, we calculate how many staff are needed when the classes remain separate.

  • Infant: 9 children, youngest less than 2, ratio 1/4, so 3 staff
  • Ones: 10 children, youngest less than 2, ratio 1/4, so 3 staff
  • Twos: 6 children, youngest 2, ratio 1/6, so 1 staff
  • Threes: 12 children, youngest 3, ratio 1/10, so 2 staff
  • FourFives: 8 children, youngest 4, ratio 1/13, so 1 staff

Now we are moving to evaluate the combined groups.

  • Infant and Ones:

19 children, youngest under 2, ratio 1/4, so 5 staff. Separately they required 6. This means a decrease.

  • Ones and Twos:

16 children, youngest age 1, ratio 1/4, so 4 staff. Separately they required 4. This means no change.

  • Threes and FourFives:

20 children, youngest age 3, ratio 1/10, so 2 staff. Separately they required 3. This means a decrease.
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werty_123
As per the line The roster of children attending CCC—as well as the days of the week each child attended—was unchanged from Week 1 through Week 3.

There should be no change in roster right? Also, Q1 does not specify IF from the saturday.....


"The roster of children attending CCC—as well as the days of the week each child attended—was unchanged from Week 1 through Week 3" means the same children kept coming to CCC during Weeks 1, 2, and 3, and each child came on the same days every week.

So, for example, if Emma came on Monday, Wednesday, and Friday in Week 1, she also came on Monday, Wednesday, and Friday in Weeks 2 and 3.

It does not mean their classroom or age group stayed the same, only that attendance patterns didn’t change.

So, that line doesn’t conflict with the birthdays. The birthdays simply change each child’s age, which can move them into a new classroom and affect staffing in Week 3. The roster line only means no child stopped coming or changed the days they attended.
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Can someone explain the q2 please
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Can someone explain the q2 please
Question 2:

In the Ones classroom in Week 2, for which one of the following days was the ratio of classroom staff to children least?



The Ones classroom follows the rule of 1 staff member for every 4 children.

Monday 13 children need 4 staff. Three staff cover 12 children (3*4=12), and one more staff is required for the remaining child.
Ratio = 4:13 ≈ 0.31

Tuesday 13 children again need 4 staff.
Ratio = 4:13 ≈ 0.31

Wednesday 11 children need 3 staff. Two staff cover 8 children (2*4=8), so one more is needed for the remaining 3.
Ratio = 3:11 ≈ 0.27

Thursday 12 children need 3 staff. Three staff cover exactly 12 children (3*4=12).
Ratio = 3:12 = 0.25

Friday 10 children need 3 staff. Two staff cover 8 children, leaving 2 more children, which requires one extra staff.
Ratio = 3:10 = 0.30

The least staff-to-child ratio was on Thursday.
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