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Min Max problem

Expert replies
by gdshamain » Tue May 13, 2014 9:30 am
6 countries in a certain region sent a total of 75 representatives to international congress and no 2 countries sent the same number. Of the 6 countries, if country A sent the 2nd greatest number of representatives, did A send at least 10 representatives?

A) One of the 6 sent 41 reps to congress

B)A sent less than 12 reps to congress
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Source: — Data Sufficiency |

by GMATinsight » Tue May 13, 2014 10:27 am
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by Matt@VeritasPrep » Tue May 13, 2014 12:50 pm
One nice way of solving this is trying cases. Since we want to know if A sent at least 10 representatives, we'll try both 9 reps and 10 reps and see if each case is possible. If each one works, then we know the statements are INSUFFICIENT; if only one works, then the statement(s) are SUFFICIENT.

Given S1, let's see if we can make A send exactly 9 reps. The conditions we have to observe are these: (i) A sends the second most reps; (ii) another country sends 41; (iii) each of the six countries sends a unique number of reps; (iv) 75 reps are sent in total.

If have the countries send 41, 9, 8, 7, 6, and 4 reps, respectively, we've observed all the conditions and we don't have A sending at least 10 reps.

On the other hand, the countries could send 41, 10, 8, 7, 6, and 3 reps, respectively.

So it's possible for A to send 9 reps or for A to send 10 reps, so S1 is INSUFFICIENT.

With S2 and with the two statements together we can use the exact same two cases we just used, as both will still be valid. Hence we don't know if A sent at least two reps, and the two statements together are INSUFFICIENT.
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by gdshamain » Tue May 13, 2014 1:12 pm
Thanks, it is clear now!
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by unknown13 » Tue May 13, 2014 7:55 pm
IMO option E (both are insufficient)
logic
if highest is 41 then to reject the assumption of A not sending 10
41+9+8+7+6+5 = 76 means Yes or No with first premise of highest is 41
second premise says A has send less than 12 which again gives Yes or No
and if consider both at same time then if highest is 41 and A less than 12 can have value either higher than 10 or 10 or less than 10 so again Yes or No

Option E is good to go
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