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mcelroytutoring
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Six countries in a certain region sent a total of 75 representatives 05 Jun 2022, 13:51
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In my opinion, this is the type of DS question that is easy enough to get away with doing in your head (mental math), but you can always test cases if you are unsure.

1) Six different numbers a,b,c,d,e add up to 75. A is the 2nd greatest number. One of them is 41, meaning that the remaining 5 numbers add up to 31. Can a be LESS than 10? Yes. Can a be MORE than 10? Yes. Not Sufficient.

2) Six different numbers a,b,c,d,e add up to 75. A is the 2nd greatest number. A < 12. Can a be LESS than 10? Yes. Can a be MORE than 10? Yes. Not sufficient.

C) Six different numbers a,b,c,d,e add up to 75. A is the 2nd greatest number. One of them is 41. A < 12. Can a be LESS than 10? Yes. Can a be MORE than 10? Yes. Not sufficient.

Thus, Choice E is correct.
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Six countries in a certain region sent a total of 75 representatives 10 Dec 2022, 09:38
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Hello, thanks for the explanation. I am wondering why you assumed x1<x2<x3 < x4 < A < x6. It is x1 != x2 !=.....x6 rather.

Bunuel
Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if Country A sent the second greatest number of representatives, did Country A send at least 10 representatives?

Given: \(x_1<x_2<x_3<x_4<A<x_6\) and \(x_1+x_2+x_3+x_4+A+x_6=75\). Q: is \(A\geq{10}\)


(1) One of the six countries sent 41 representatives to the congress --> obviously \(x_6=41\) --> \(x_1+x_2+x_3+x_4+A=34\).

Can \(A\geq{10}\)? Yes. For example: \(x_1=2\), \(x_2=3\), \(x_3=8\), \(x_4=10\), \(A=11\) --> \(sum=34\) (answer to the question YES);
Can \(A<{10}\)? Yes. For example: \(x_1=4\), \(x_2=6\), \(x_3=7\), \(x_4=8\), \(A=9\) --> \(sum=34\) (answer to the question NO).


(2) Country A sent fewer than 12 representatives to the congress --> \(A<{12}\).

The same breakdown works here as well:
Can \(12>A\geq{10}\)? Yes. For example: \(x_1=2\), \(x_2=3\), \(x_3=8\), \(x_4=10\), \(A=11\), \(x_6=41\) --> \(sum=75\) (answer to the question YES);
Can \(A<{10}\)? Yes. For example: \(x_1=4\), \(x_2=6\), \(x_3=7\), \(x_4=8\), \(A=9\), \(x_6=41\) --> \(sum=75\) (answer to the question NO).


(1)+(2) The given examples fit in both statements and A in one is more than 10 and in another less than 10. Not sufficient.

Answer: E.
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Six countries in a certain region sent a total of 75 representatives 21 Mar 2025, 07:56
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May I ask what the contents of options a, b, c, d and e are and where can I find them?

LM
Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if Country A sent the second greatest number of representatives, did Country A send at least 10 representatives?

(1) One of the six countries sent 41 representatives to the congress
(2) Country A sent fewer than 12 representatives to the congress
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Six countries in a certain region sent a total of 75 representatives 21 Mar 2025, 08:27
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illiya
May I ask what the contents of options a, b, c, d and e are and where can I find them?

LM
Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if Country A sent the second greatest number of representatives, did Country A send at least 10 representatives?

(1) One of the six countries sent 41 representatives to the congress
(2) Country A sent fewer than 12 representatives to the congress
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Hi,

This is a data sufficiency question. Options for DS questions are always the same and usually omitted on the site.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Hope this helps.­
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Six countries in a certain region sent a total of 75 representatives 22 May 2025, 21:26
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spent like 4.5 mins in this

however probably an easier way is

75-41 = 34
so take one case where A = 9 and one where A =10
Other 4 countries = 25 if A = 9 (which is on an avg closer to 6) as all can't be equal
4+6+7+8 (all nos around -2/+2 around avg)
if A = 10 then
other 4 countries = 24
so, 3+6+7+8 (just subtract 1 from any of the above)


so statement 1 not suff.

statement 2 :
A < 12, curtails the cases discussed above so not suff.

together,
same cases. Not suff.

hence E.

LM
Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if Country A sent the second greatest number of representatives, did Country A send at least 10 representatives?

(1) One of the six countries sent 41 representatives to the congress
(2) Country A sent fewer than 12 representatives to the congress
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