12 Days of Christmas GMAT Competition - Day 1: A candy jar contains 60

The only way to be sure to pick a certain candy is to pick all other candies plus 1.

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 = 43

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 = 37

We have to take the worst case scenarios

Minimum one lemon flavored =

Sarah picks all strawberry and all orange candies = 24 + 18 + 1 = 43

Minimum one strawberry flavored =

Sarah picks all lemon and all orange candies = 18 + 18 + 1 = 37

Column A = 43
Column B = 37

Sarah is picking candies randomly from a jar containing:
24 identical strawberry flavored candies,
18 identical lemon flavored candies, and
18 identical orange flavored candies.
She needs to ensure getting at least one candy of a specific flavor.

Lemon Flavored
We must account for the worst-case scenario where Sarah picks as many candies as possible without getting a candy of the desired flavor

There are 18 lemon flavored candies in total.
To ensure Sarah gets at least one lemon flavored candy, consider the worst-case scenario
Sarah picks all24 strawberry candies and all 18 orange candies first.
This accounts for 24+18=42
24+18=42 candies, none of which are lemon flavored.
Thus, on the
43rd candy, she is guaranteed to pick a lemon flavored candy.


Strawberry Flavored
There are 24 strawberry flavored candies in total.
To ensure Sarah gets at least one strawberry flavored candy, consider the worst-case scenario
Sarah picks all 18 lemon candies and all 18 orange candies first.
This accounts for 18+18=36 candies, none of which are strawberry flavored.
Thus, on the 37 th candy, she is guaranteed to pick a strawberry flavored candy.

60 candies: 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored.

To pick minimum number of candies in order to ensure Sarah picks at least 1 lemon flavored candy, worst possible scenario should be considered. In this scenario, Sarah will not pick lemon flavored candy until she has picked all the remaining candies. So 24 (strawberry) + 18 (orange) = 42. She has picked 42 candies, yet she has not picked a lemon flavored candy (worse possible scenario). Now she will pick 1 more candy, which has to be lemon flavored as only lemon flavored candies are left to be picked. So it makes the minimum count to 42 + 1 = 43 for lemon flavored candies.

Similarly for strawberry candies, minimum number would be 18 (lemon) + 18 (orange) = 36. Now she will pick 1 more candy, which has to be strawberry flavored as only strawberry flavored candies are left to be picked. So, 36 + 1 = 37.

This is pretty straightforward: to make sure we're getting a Lemon candy, we need to take out all the other candies (just in case we're terribly unlucky and we keep getting the wrong one every step of the way ).
So, \(S+O=24+18=42\)
Then, on the 43rd candy we'll surely get Lemon.

Same applies to Strawberry: \(L+O=18+18=36\)
And our luck should turn on the 37th.

The answers are: 43 for Lemon, 37 for Strawberry.

You need to pick at least 43 candies to get a lemon candy. Since there are 24 strawberries and 18 orange, picking 42 candies takes care of strawberries + orange.

Now, no matter which candy you pick, you will get one lemon for sure.

Similarly for strawberries

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.
Solution: Overall 60, Lemon 18, Strawberry 24.
At least 1 lemon: 60-18+1=43
At least 1 strawberry: 60-24+1=37

Lemon Flavored: Sarah must take all the Strawberry and Orange flavored candies, so that the next one she takes will be Lemon flavored one.

\(Strawberry+Orange=24+18=42\).

\(43rd\) candy will be surely Lemon

Strawberry Flavored: Sarah must take all the Lemon and Orange flavored candies, so that the next one she takes will be Strawberry flavored one.

\(Lemon + Orange=18+18=36\).

\(37th\) candy will be surely Strawberry

Answers:

E: 43
C: 37

Hi All,

According to me,

minimum number of candies Sarah must pick from the jar to ensure getting at least one lemon flavored candy = Total no of candies not lemon flavoured + 1

therefore total no of non lemon candies = 24+18=42

So now the next pick Sarah does will be surely a lemon candy that is why +1 was addded in the above equation.

Ans-> 42+1=47

Similarily if we find for strawberry flavoured candy --> 18+18+1 = 37

We have - 24 identical strawberry flavored, 18 identical lemon flavored, and 18 identical orange flavored.

For Lemon flavored - In the worst case, she could pick all 24 + 18 = 42 non-lemon candies first. The next candy (43rd) must be a lemon-flavored candy.
So to ensure getting at least one lemon flavored candy Sarah must pick a minimum of 43 Candies

For Strawberry flavored - In the worst case, she could pick all 18 + 18 = 36 non-strawberry candies first. The next candy (37th) must be a strawberry-flavored candy.
So to ensure getting at least one strawberry flavored candy Sarah must pick a minimum of 37 Candies

minimum is needed- so for lemon- 24+28+1= 42
for strawberry -18+18+1= 37

Total candies= 60
Strawberry candies = 24
Lemon candies = 18
Orange Candies = 18
Picking atleast 1 lemon candy = picked all strawberry candies + picked all orange candies + 1 lemon candy = 24+18+1=43

Picking atleast 1 strawberry candy = picking all lemon & orange candies + 1 strawberry candy
= 18+18+1=37

Answer: (43,37)

To ensure getting at leat one lemon flavored candy, all strawberry and orange flavored candies need to be gone. Since there are 24+18= 42 of them, after the 43rd pick it is ensured that Sarah got at least one lemon flavored candy. This does not mean that the 43rd pick will be lemon flavored but at last the 43rd pick will be lemon flavored in case she solely picked strawbery and orange flavored candies. Similiarly for the strawberry flavored candies. At last the 37th pick will be a strawberry flavored candy.

43rd.. 24+18 will be all other candies and the next one (43rd) has to be the desired candy, with similar logic we arrive at 37
ans> 43,37

To answer this question, we need to think about worst case scenarios.

In order to pick at least one lemon candy: It is possible that we can keep picking only other two flavors. So, to make sure at least one lemon candy is being picked we need to outnumber the strawberries and orange candies. There are 24 strawberry candies and 18 orange candies. So, we need to pick 24+18+1 = 43 candies to make sure that lemon flavor is being picked.

The same above reasoning also applies to pick at least one strawberry candy (we need to outnumber lemon and orange available). So, we need to pick 18+18+1 = 37 candies to make sure that Strawberry flavor is being picked.

1. Worst case Lemon Flavor candy is last so: 24 S + 18 O = 42 than 43 will be surely lemon flavor.
2. Strawberry: 18 L + 18 O = 36 than 37th will be surely strawberry.

Can simply use the p@c combination method to get to this one with a little bit of logical reasoning.