12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60 : Two-part Analysis (TPA)

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16 Dec 2024, 09:25

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To ensure atleast 1 lemon:
She must pick out all the rest:
18+24 candies = 42 candies + 1 more (which will be lemon)
> so 43 candies to ensure atleast 1 lemon

To ensure atleast 1 strawberry:
She must pick out all the rest: 18+18 + 1 more (which will be strawberry) = 37 candies
> so 37 candies to ensure atleast 1 strawberry

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16 Dec 2024, 09:30

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24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored

To ensure getting specific flavour, we need to count other flavor plus one candy.

Minimum to get lemon flavour
= strawberry + orange + 1
= 24 + 18 + 1
= 43

Minimum to get strawberry flavour
= orange + lemon + 1
= 18 + 18 + 1
= 37

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16 Dec 2024, 09:36

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To ensure getting at least one lemon flavoured candy she has to pick exactly the sum of all the other types of candy, so that only lemon flavoured candy remain in the jar, and then pick another candy:

1st column (lemon fl.): 24 (All strawberry) + 18 (All orange) + 1 = 43

Same thing for strawberry flavoured:

2nd column (strawberry fl.) 18 + 18 + 1 = 37

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16 Dec 2024, 09:43

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Lemon Flavoured: 43 (24+18+1)
Strawberry Flavoured: 37 (18+18+1)

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16 Dec 2024, 09:43

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Lemon Flavoured: 43 (24+18+1)
Strawberry Flavoured: 37 (18+18+1)

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16 Dec 2024, 09:48

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For lemon flavour, it is 43
For strawberry flavour, it is 37

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16 Dec 2024, 09:49

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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
= 24(Strawberry) + 18(Orange) + 1(Lemon)

Select for Strawberry flavored the minimum number of candies Sarah must pick from the jar to ensure getting at least one strawberry flavored candy. = 18(Lemon) + 18(Orange) + 1(Strawberry)

Lemon flavored	Strawberry flavored
24+18+1=43	18+18+1=37

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16 Dec 2024, 09:50

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Selecting all lemon & orange flavored candies would turn out to be 36 in number which won't be sufficient for us to select at least 1 strawberry but after selecting 37 items we can ensure at least one strawberry for sure

Similarly in the case for lemons if we select all strawberries & oranges we will have 42 items which won't be sufficient to select at least one lemon but after selecting 43 items we can ensure a lemon for sure

Hence for strawberries answer is 37 & for lemons it is 43

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16 Dec 2024, 09:52

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To definetly get lemon flavour candy suppose sarah pick 1st candy and it will be strawberry flavour and similarly she can get min 24 strawberry flavour candy and similarly she can pick min 18 orange flavour candy.
so to pick atleast 1 lemon flavour candy she needs to pick atleast 24(strawberry)+18(orange)=42 candy from jar , and 43rd candy she will pick will obviously be lemon flavour candy.
so she needs to pick 43 candy from jar to get atleast 1 lemon candy.

similarly is case for strawberry candy. she need to pick before 18(lemon)+18(orange) =36 . and 37th candy will be strawberry

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16 Dec 2024, 10:01

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Answer is 42 - Lemon and 36 - Strawberry. There is a 70 percent chance of not picking a lemon and a 60 percent chance of not picking a strawberry flavoured candy. 70 percent of 60 is 42, and 60 percent of 60 is 36.

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16 Dec 2024, 10:05

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Think about worst case scenario. Because we have to ensure that she gets the required candy.

Lemon : what if she picked all Strawberry candies and orange candies first =24+18=42 candies then i can be sure that the next candies she picks is lemon. So 42+1=43

Strawberry: what if she picked all Lemon candies and orange candies first =18+18=36 candies then i can be sure that the next candies she picks is strawberry. So 36+1=37

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16 Dec 2024, 10:06

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these are the right choices

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16 Dec 2024, 10:06

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To solve the problem, we determine the minimum number of candies Sarah must pick to guarantee getting at least one lemon candy and at least one strawberry candy. Here's the reasoning:
[hr]
Lemon-Flavored:

There are 24 strawberry-flavored, 18 lemon-flavored, and 18 orange-flavored candies.
The worst-case scenario for not picking a lemon candy is that Sarah picks all the non-lemon candies first.
The total number of non-lemon candies is 24 (strawberry) + 18 (orange) = 42.

Thus, if Sarah picks 42 candies, she could avoid all lemon candies. To guarantee at least one lemon candy, she must pick one more candy, which makes 42+1=43
Minimum candies to ensure at least one lemon-flavored candy: 43.
[hr]
Strawberry-Flavored:

Similarly, the worst-case scenario for not picking a strawberry candy is that Sarah picks all the non-strawberry candies first.
The total number of non-strawberry candies is 18 (lemon) + 18 (orange) = 36.

Thus, if Sarah picks 36 candies, she could avoid all strawberry candies. To guarantee at least one strawberry candy, she must pick one more candy, which makes 36+1=37.
Minimum candies to ensure at least one strawberry-flavored candy: 37.
[hr]
Selections:

Lemon flavored: 43
Strawberry flavored: 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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16 Dec 2024, 10:10

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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.

We try not to get a lemon flavored one as long as possible = 18 O + 24 S = 42. Until the 43rd, we must get a lemon one --> 43
We try not to get a strawberry flavored one as long as possible = 18 O + 18 L = 36. Until the 37th, we must get a lemon one --> 37

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16 Dec 2024, 10:16

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To ensure Sarah gets a particular candy, we must consider the worst-case scenario,

1. For Lemon flavor - let's say Sarah picked 18 orange and 24 strawberry first, then 18 + 24 + 1 = 43rd candy would be Lemon

2. For Strawberry flavor - let's say Sarah picked 18 orange and 18 lemon first, then 18 + 18 + 1 = 37th candy would be Strawberry

Answer 43 and 37

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16 Dec 2024, 10:20

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For the Lemon Flavored

Consider the Worst-Case scenario, he chooses all Strawberry candies first (24), then all Orange Flavored Candies (18), and after selecting all of those he got the 3rd one (that is Lemon Flavored) = 24+18+1(Lemon) = 43

For the Strawberry Candies

Consider the Worst-Case scenario, he chooses all Lemon candies first(18), then all Orange Flavored Candies(18), and after selecting all of those he got the 3rd one (that is Strawberry Flavored) = 18+18+1(Lemon) = 37

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16 Dec 2024, 10:23

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Total candies - 60

Strawberry flavored - 24
Lemon flavored - 18
Orange flavored - 18

Minimum candies required to get a lemon flavored candy is the worst case scenario where you pick up all strawberry and orange flavored 42 candies (24 + 18) and the last candy you pick is the lemon flavored which requires 43 selections.

Similarly, minimum candies required to get a strawberry flavored candy is the worst case scenario where you pick up all lemon and orange flavored 36candies (18 + 18) and the last candy you pick is the strawberry flavored which requires 37 selections.