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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 12:33
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For Lemon flavored: There are 42 non-lemon candies (24 strawberry + 18 orange). After picking these 42, the next candy must be lemon flavored, so Sarah needs to pick 43 candies to ensure getting at least one lemon flavored.

For Strawberry flavored: There are 36 non-strawberry candies (18 lemon + 18 orange). After picking these 36, the next candy must be strawberry flavored, so Sarah needs to pick 37 candies to ensure getting at least one strawberry flavored.
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 12:40
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There are total 60 candies: 24 strawberry flavored, 18 lemon flavored, and 18 orange flavored
The minimum number of candies to be selected for the following =

i) Lemon Flavored = Strawberry flavored + Orange flavored + 1 lemon flavored = 24 + 18 + 1 = 43

ii) Strawberry Flavored = Orange + Lemon + 1 Strawberry = 18 + 18 + 1 = 37

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A candy jar contains 60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored. Sarah randomly picks candies from the jar.

Select for Lemon flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy, and select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 12:55
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Lemon flavored: 37
Strawberry flavored: 43
The Candy Jar Challenge 🍬

Sarah’s task is to ensure she picks at least one candy of each flavor. To guarantee a lemon-flavored candy, she could pick all 18 strawberry and 18 orange candies first, leaving only lemon candies. So, she needs to pick 37 candies (18 strawberry + 18 orange + 1 lemon). For strawberry, after picking all 18 lemon and 18 orange candies, she would still need to pick 43 to ensure at least one strawberry. It’s like guaranteeing a treasure by picking through the whole map—determined, but precise!
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 13:13
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To determine the minimum number of candies Sarah must pick to ensure she gets at least one lemon-flavored candy and at least one strawberry-flavored candy.

The total candies in the jar are 60:
  • 24 strawberry candies
  • 18 lemon candies
  • 18 orange candies

If Sarah wants to ensure she picks at least one specific flavor, she must consider the worst-case scenario where she picks candies of all other flavors first.

Ensuring at least one lemon-flavoured candy -

  1. Worst case: Sarah picks all the candies that are not lemon flavored first:
    • Total candies that are not lemon flavored = 24 (strawberry) + 18 (orange) = 42 candies.
  2. To ensure she gets at least one lemon-flavored candy, she must pick one more candy after the 42 non-lemon candies.
    The minimum number of candies to ensure at least one lemon-flavored candy = 42 + 1 = 43.

Ensuring at least one strawberry flavoured candy -


  1. Worst case: Sarah picks all the candies that are not strawberry flavored first:
    • Total candies that are not strawberry flavored = 18 (lemon) + 18 (orange) = 36 candies.
  2. To ensure she gets at least one strawberry-flavored candy, she must pick one more candy after the 36 non-strawberry candies.

The minimum number of candies to ensure at least one strawberry-flavored candy = 36 + 1 = 37.
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A candy jar contains 60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored. Sarah randomly picks candies from the jar.

Select for Lemon flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy, and select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 13:45
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This is a Max/Min Problem.

To insure picking one flavor we need to take the extreme case in each situation.

60 Total
S L O
24 18 18

In order to get at lease 1 Lemon. The extreme case is picking all the S and then all the O.
now, the next pick must be a Lemon. so: 24+18+1 = 43

In order to get at lease 1 Strawberry. The extreme case is picking all the L and then all the O.
now, the next pick must be a Strawberry. so: 18+18+1 = 37
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 14:53
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The number of lemon candies is 43 and the number for strawberry is 37.

Because, if you pick 24strawberry and 18 orange = 42, the next candy would definitely be lemon which would be 43 minimum candies to get a lemon candy.

Similarly, for getting a strawberry candy 18 orange +18 lemon = 36 and the next pick will definitely be a strawberry candy so 37.
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 15:42
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A candy jar contains 60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored. Sarah randomly picks candies from the jar.

Select for Lemon flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy, and select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. Make only two selections, one in each column.
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To get atleast one lemon flavored candy, assume that Sarah has to complete picking the entirety of both Strawberry and Orange flavored candies.

So, 18 + 24 = 42. Now since there is only type of candies left, the 43rd candy should most definitely be a Lemon flavored candy.

Similarly, to get atleast one strawberry flavored candy, assume that Sarah has to complete picking the entirety of both Lemon and Orange flavored candies.

So, 18 + 18 = 36. Now, the 37th candy should most definitely be a Strawberry flavored candy.

S=37, L=43
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 15:47
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In total, there are 60 candy.
s = 24
l = 18
o = 18

To ensure getting one lemon flavored candy, we must first get rid of all the other candys.
We have to pick 42 candy first to get rid of all the other candy And then pick one more time to ensure having a lemon picked flavor in our hand. 42 + 1 = 43
--> 43

Same procedure. Pick 36 candy and one more to ensure having a strawberry flavor in our hand. 36 + 1 = 37
--> 37

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A candy jar contains 60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored. Sarah randomly picks candies from the jar.

Select for Lemon flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy, and select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 16:22
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For Sarah to ensure picking one lemon and strawberry sweets we are assuming the worst case scenario.
Under this scenario, Sarah picks first all the non-desired flavours first and then selects the desired one:

Minimum number of candies picked to ensure picking one lemon candy:

- Picking all strawberries = 24
- Picking all orange sweets = 18
- Picking the first lemon = 1
Sum = 24 + 18 + 1 = 43


For picking one strawberry:
- Picking all lemon flavour candies = 18
- Picking all orange flavour candies = 18
- Picking the first strawberry cadre = 1
Sum = 18*2 + 1 = 37
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 16:53
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Lemon flavored: the worst case is when you choose all straberry and orange candies before getting a lemon one. 24+18+1=43

Strawberry flavored: the worst case is when you choose all lemon and orange candies before getting a strawberry one. 18+18+1=37
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 17:20
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A candy jar contains 60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored. Sarah randomly picks candies from the jar.

Select for Lemon flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy, and select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. Make only two selections, one in each column.
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To guarantee getting a lemon flavored one, we have to examine the possibility that all non-lemon candies get chosen first. So that's 24 strawberries + 18 oranges = 42. The next candy will be the lemon one - that means the answer is 43 candies.

To guarantee getting a strawberry flavored one, we have to examine the possibility that all non-strawberry candies get chosen first. So that's 18 lemons + 18 oranges = 36. The next candy will be the strawberry one - that means the answer is 37 candies.
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 18:31
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Lemon flavored
If you have bad luck you could get all the other candies before getting a lemon candy:
S+O+1=43

Strawberry flavored
If you have bad luck you could get all the other candies before getting a strawberry candy:
L+O+1=37

Answers 43 and 37
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 18:36
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Lemon flavored = 43
Strawberry flavored = 37

To pick the minimum amount, we can assume every candy Sarah picks is the wrong kind until they get the right kind. For lemon flavored, we can assume Sarah picks all 24 strawberry and all 18 orange flavored candies before getting a lemon flavored candy, so she would need to pick at least 24 + 18 + 1 = 43 candies.

Likewise, for strawberry flavored, we can assume Sarah picks all 18 lemon and all 18 orange flavored candies before getting a strawberry flavored candy, so she would need to pick at least 18 + 18 + 1 = 37 candies.

This is similar to calculating P(at least one lemon) = 1 - P(no lemon), where P(no lemon) = P(all strawberry) + P(all orange); similarly, P(at least one strawberry) = 1 - P(no strawberry), where P(no strawberry) = P(all lemon) + P(all orange).
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A candy jar contains 60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored. Sarah randomly picks candies from the jar.

Select for Lemon flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy, and select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 19:24
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Out of 60 ->
24 - strawberry, 18 - lemon, 18 - orange
if minimum 1 strawberry is to picked up, make sure we have no other option but to take strawberry i.e if you have already collected lemon& orange, the next one u take will for sure be strawberry. Hence 18+18+1=37

similarly for Lemon - 18+24+1=-43
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 19:43
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A candy jar contains 60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored. Sarah randomly picks candies from the jar.

Select for Lemon flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy, and select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. Make only two selections, one in each column.
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To ensure Lemon flavored candy,
Lets assume, each candy we pick is of a flavor other than Lemon = Strawberry + Orange = 24 + 18 = 42
The next candy we pick will surely be lemon now, so total candies = 42 + 1 = 43

To ensure Strawberry flavored candy,
Lets assume, each candy we pick is of a flavor other than Strawberry = Lemon + Orange = 18 + 18 = 36
The next candy we pick will surely be strawberry now, so total candies = 36 + 1 = 37
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 20:30
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A candy jar contains 60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored. Sarah randomly picks candies from the jar.

Select for Lemon flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy, and select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. Make only two selections, one in each column.
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At least one lemon flavored candy
All strawberry flavored 24 + All orange flavored 18 + 1 lemon flavored = 43

At least one Strawberry flavored candy
All orange flavored 18 + All lemon flavored 18 + 1 strawberry flavored = 37
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 20:43
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A candy jar contains 60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored. Sarah randomly picks candies from the jar.

Select for Lemon flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy, and select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. Make only two selections, one in each column.
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The minimum number of candies for a particular type would be the sum of all rest of the candies plus 1, since we would have to pick up our own candy.
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 20:48
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Reasoning:
  • For Lemon (18 total):
    To guarantee at least one lemon candy, consider the worst case: Sarah picks all the candies that are not lemon first. That is all 24 strawberry plus all 18 orange, totaling 24 + 18 = 42. Even after picking 42 candies, she may have picked no lemon candies at all. Once she picks the 43rd candy, it must be lemon because no other kinds remain.
    Minimum number to ensure at least one lemon = 43
  • For Strawberry (24 total):
    To guarantee at least one strawberry candy, consider the worst case: Sarah picks all the non-strawberry candies first (that is the 18 lemon plus 18 orange) for a total of 36. After picking these 36 candies, she still might not have any strawberry. Once she picks the 37th candy, it must be strawberry because no other kinds remain.
    Minimum number to ensure at least one strawberry = 37
Answer:
  • Lemon flavored: 43
  • Strawberry flavored: 37
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 20:56
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Strawberry-24, lemon and orange - 18 each
Minimum number of candies to be selected to ensure a strawberry is picked - 18 (lemon) + 18 (orange) + 1 (strawberry) = 37

Minimum number of candies to be selected to ensure a lemon is picked = 24+18+1 =43
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12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 16 Dec 2024, 21:02
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To ensure at least 1 candy of a flavour is picked in a random selection, consider the worst case - you don’t pick that flavour unless it’s the only flavour left in the jar

=> you have to pick 24 strawberry and 18 orange before you pick a lemon = 24+18+1=43
=> you have to pick 18 lemon and 18 orange before you pick strawberry = 18+18+1=37
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