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Number properties question

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Number properties question

by sukh » Sun Aug 07, 2011 1:22 am
If after a number was added to a set consisting of all one-digit prime integers, the median of the set grew by 25%, which of the following cannot be the value of the number added? (A) 4.8 (B) 5.0 (C) under-root 29 (D) 7.7 (E) 49/4


A box contains 10 tablets of medicine A and 15 tablets of medicine B. If N tablets are taken from the box at random, what is the least possible N that ensures that at least two tablets of each kind are among the extracted? (A) 12 (B) 15 (C) 17 (D) 19 (E) 21

After M students took a test, there was a total of 64% of correct answers. If the test contains 50 questions, what is the least number of questions that the next student have to get right to bring the total of correct answers to 70% ? (A) 3M + 20 (B) 3M + 35 (C) 4M + 15 (D) 4M + 20 (E) 4M + 45
Last edited by sukh on Tue Aug 09, 2011 4:58 am, edited 1 time in total.
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by sumgb » Mon Aug 08, 2011 3:19 pm
1. set contains 2,3,5,7. median = 4. now, say number 'n' is added then the median becomes 1.25 x 4 = 5. so n >= 5. hence answer choice A (n cannot be less than 5)

2. could not understand " what is the least possible that ensures " ... sorry.

3. total correct answers = 50M * .64 = 32M; if after next students attempt total % needs to be 70 then, 50(M+1) * 0.7 = 35M + 35; so next student needs to answer 35M + 35 - 32M = 3M + 35 correctly so ans choice B
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by sukh » Tue Aug 09, 2011 5:00 am
In the worst possible scenario, the first 15 tablets will be of kind B . To ensure that there are at least two tablets of each kind we have to take out 17 tablets. The correct answer is C.
However I did not understand this explaination
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by sumgb » Tue Aug 09, 2011 8:56 am
Ok. That makes sense now. Let's through each answer choice... since we need to know the least value of N, let's start from A which is 12
A. 12, now you could have all type B tablets and none type A tablets. So 12 is not the least number. it should be more than 12

B. 15, now same as A, you could have all 15 of type B and none of type A, so insuff.

C. 17, if you take out 17 tablets, you can have max of 15 type B tablets and 2 of type A tablets. hence 17 tablets will ensure you have at least 2 of each type pf tablets. hence the answer.

ans choices 19 and 21 are also correct but we need least number of tablets to ensure 2 of each type hence 17 wins.

I feel in problems like this you must maximize the max of two no.s to ensure you meet the required condition. maximize type B tablets and add minimum no of type A tablets. you get an answer of 17 :-) hurrrayy

hope this helps..
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