A box contains 10 tablets of medicine A and 15 tablets

Question

A box contains 10 tablets of medicine A and 15 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.

A)12
B)15
C)17
D)19
E)21

A. 12
B. 15
C. 17
D. 19
E. 21

Bunuel · Accepted Answer

Extracting 12 tablets does not guarantee having at least 2 of each type, because all 12 could be medicine B. In such problems you have to consider the worst case scenario. Similar questions to practice: 12-easy-pieces-or-not-126366.html#p1033935 in-his-pocket-a-boy-has-3-red-marbles-4-blue-marbles-and-85216.html of-the-science-books-in-a-certain-supply-room-50-are-on-131100.html in-a-deck-of-52-cards-each-card-is-one-of-4-different-color-83183.html a-box-contains-10-red-pills-5-blue-pills-12-yellow-56779.html each-of-the-integers-from-0-to-9-inclusive-is-written-on-130562.html a-student-is-asked-to-pick-marbles-from-a-bag-that-contains-72390.html of-the-science-books-in-a-certain-supply-room-50-are-on-131100.html Hope it helps.

Bunuel · Answer

The worst-case scenario would occur if we remove all 15 tablets of medicine B first. In this scenario, we would still not have any tablets of medicine A. However, the next two tablets we remove must be of Medicine A. Therefore, to  guarantee  that at least two tablets of each type will be taken, we should remove a minimum of  15+2=17  tablets.

Answer: C

Asifpirlo · Answer

if we extract 12 then it can be all B, but if 17 then 2kinds of each must have to be there like 15B+2A.....

schittuluri · Answer

I didnt understand ...
if there should be two from each box , the total number shoukdnt be EVEN??

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Asifpirlo · Answer

At least two means 2,3,4,5 etc, so not just even.

12 tablets = 12 B but no A 
17 tablets = 15 B and 2 A (even if 15 B extracted)

pick 12 tablets out of the box, chances are that all the 12 tablets are B.
so we have 12 B tablets, not at least two of each kind.

but if we pick 17 tablets out of the box, then even after 15 B we can still have 2 tablets of A.

i mean pick 17 then you have to pick at least 2 from A as well as at least 2 from B.

rcformba · Answer

why cant we take all of 10 A and then next 2 will be B tablets so total will be 12 and it is the least to ensure we have at least 2 of each type?

ScottTargetTestPrep · Answer

Let’s consider the worst possible scenario: It’s possible to take out 15 tablets and all of them are medicine B. In this case, we only take out one kind of medicine instead of both. Therefore, we need to take out at least 15 + 2 = 17 tablets (all 15 of medicine B and 2 of medicine A) to ensure that at least two tablets of each kind are extracted.

Answer: C

Answer: C

MathRevolution · Answer

Extract 15 tablets of Medicine B. This gives at least '2' of medicine B.

Add '2' for Medicine A.

=> 15 + 2 = 17

Answer C

gmatpro15 · Answer

Think of least possible way which is getting 15 tablets of B and 2 tablets of A

So 15+2 = 17

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pikachu9 · Answer

We can also take 10 medicines of A and then for tablet B we can have 10+2=12

A box contains 10 tablets of medicine A and 15 tablets

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A box contains 10 tablets of medicine A and 15 tablets

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