Help on permutations problem

[crackgmat007]

Please solve this with steps. Thanks.

Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 159
(C) 166
(D) 285
(E) 324

answer is 324

[cramya]

Process of elimination works best for this.

Consider worst case for these prob types.

50 are on botany, 65 are on zoology50 are on geology

165

still cant guarantee 80 of same type

Rule out 166 since by taking 1 more we cant get there

No we have 90 left phy 110 chemistry i.e 200 left


Look at the next choice i.e. 285

We haev taken 165 already so to get to 285 we need 120 books

Out of 200 we could pick 120 without getting to 80 from one science

60-> chem 60->phy

Dont waste a second choose E

[PAB2706]

this is how i did it...i dnt know if the approach is right or not..but logically i found it ok..and the answer also came right.

50+65+50=165 (similarly as cramya did it)

now 110 chem and 90 phy books left....

again i considered the worst case scenario...

now there is a race for 80 btwn chem and phy books...either ways...i will take a minimum of 159 tries(if i select them alternating.........159 bcos if i start with chem i will reach to 80 mark for chem before selecting the 80th phy book so 160-1 =159)

therefore 165+159=324