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Bunuel
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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.
TO guarantee that a given option is chosen, one must assume the worst possible outcome, that the needed object is chosen last.

To guarantee that a lemon candy is selected, one must reach a point where no other selection is possible, which means that there is no possibility to select a candy other than lemon. Therefore, 24 for strawberry and 18 for orange must have been chosen so the next will definitely be lemon candy, therefore 42+1.

Apply the same line of reasoning to the strawberry candy and you get 18+18+1=37
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To be sure that one lemon is chosen, lets say the worst case happens - no lemon comes as we take one by one. i.e 43 should be taken (first 42 need not be lemon and last one will be lemon)
To be sure that one strawberry is chosen, lets say the worst case happens, the first 36 are not strawberry and 37th is strawbeery.

Hence choose - 37 for strawberry and 43 for lemon

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This question was provided by GMAT Club
for the 12 Days of Christmas Competition

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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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  • Lemon-flavored: 24 (strawberry) + 18 (orange) + 1 (lemon) = 43 candies.
  • Strawberry-flavored: 18 (lemon) + 18 (orange) + 1 (strawberry) = 37 candies.
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Why would we do a +1 at the end? Bunuel
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miniB21
Why would we do a +1 at the end? Bunuel

Try reviewing the official solution provided in the second post. You can also check other users' rationale on the previous 5 pages. Finally, you can check other Worst Case Scenario Questions from our Special Questions Directory to practice.

Hope it helps.
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Lemon Flavored:
There are 24 strawberry-flavored candies and 18 orange-flavored candies in the jar.
To ensure getting at least one lemon-flavored candy, Sarah could pick all 24 strawberry-flavored candies and all 18 orange-flavored candies first (worst-case scenario).
This means she has picked
24
+
18
=
42
24+18=42 candies, none of which are lemon-flavored.
If she picks 1 more candy after these 42, the 43rd candy must be lemon-flavored, as all non-lemon candies have already been picked.

Minimum number of candies Sarah must pick to ensure at least one lemon-flavored candy: 43.

Strawberry Flavored:
There are 18 lemon-flavored candies and 18 orange-flavored candies in the jar.
To ensure getting at least one strawberry-flavored candy, Sarah could pick all 18 lemon-flavored candies and all 18 orange-flavored candies first (worst-case scenario).
This means she has picked
18
+
18
=
36
18+18=36 candies, none of which are strawberry-flavored.
If she picks 1 more candy after these 36, the 37th candy must be strawberry-flavored, as all non-strawberry candies have already been picked.

Minimum number of candies Sarah must pick to ensure at least one strawberry-flavored candy: 37.

Final Selections:
Lemon Flavored: 43.
Strawberry Flavored: 37.
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Lemon Flavoured
Consider the worst case scenario: All non lemon candies before a lemon candy = 24 + 18 + 1 = 43

Strawberry Flavoured
Consider the worst case scenario: All non strawberry candies before a strawberry candy = 18 + 18 + 1 = 37
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Given there are 24 strawberry, 18 lemon and 18 orange
In order to ensure a lemon candy we need to pic atleast 43 candies ( 24 strawberries + 18 orange)
In order to ensure a strawberry candy we need to pic atleast 37 candies (18 lemon + 18 orange)
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