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# Six countries in a certain region sent a total of 75

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Director
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Six countries in a certain region sent a total of 75  [#permalink]

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27 Apr 2010, 08:57
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55% (hard)

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66% (02:30) correct 34% (02:36) wrong based on 1475 sessions

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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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27 Apr 2010, 11:42
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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 $$A\geq{10}$$: $$x_1=2$$, $$x_2=3$$, $$x_3=8$$, $$x_4=10$$, $$A=11$$ --> $$sum=34$$ (answer to the question YES);
Can $$A<{10}$$: $$x_1=4$$, $$x_2=6$$, $$x_3=7$$, $$x_4=8$$, $$A=9$$ --> $$sum=34$$ (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 $$12>A\geq{10}$$: $$x_1=2$$, $$x_2=3$$, $$x_3=8$$, $$x_4=10$$, $$A=11$$, $$x_6=41$$ --> $$sum=75$$ (answer to the question YES);
Can $$A<{10}$$: $$x_1=4$$, $$x_2=6$$, $$x_3=7$$, $$x_4=8$$, $$A=9$$, $$x_6=41$$ --> $$sum=75$$ (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.

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Director
Joined: 03 Sep 2006
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28 Apr 2010, 02:21
Bunuel wrote:
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 $$A\geq{10}$$: $$x_1=2$$, $$x_2=3$$, $$x_3=8$$, $$x_4=10$$, $$A=11$$ --> $$sum=34$$ (answer to the question YES);
Can $$A<{10}$$: $$x_1=4$$, $$x_2=6$$, $$x_3=7$$, $$x_4=8$$, $$A=9$$ --> $$sum=34$$ (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 $$12>A\geq{10}$$: $$x_1=2$$, $$x_2=3$$, $$x_3=8$$, $$x_4=10$$, $$A=11$$, $$x_6=41$$ --> $$sum=75$$ (answer to the question YES);
Can $$A<{10}$$: $$x_1=4$$, $$x_2=6$$, $$x_3=7$$, $$x_4=8$$, $$A=9$$, $$x_6=41$$ --> $$sum=75$$ (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.

Excellent explanation. Thanks very much.
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10 May 2010, 20:45
1
Bunuel wrote:
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 $$A\geq{10}$$: $$x_1=2$$, $$x_2=3$$, $$x_3=8$$, $$x_4=10$$, $$A=11$$ --> $$sum=34$$ (answer to the question YES);
Can $$A<{10}$$: $$x_1=4$$, $$x_2=6$$, $$x_3=7$$, $$x_4=8$$, $$A=9$$ --> $$sum=34$$ (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 $$12>A\geq{10}$$: $$x_1=2$$, $$x_2=3$$, $$x_3=8$$, $$x_4=10$$, $$A=11$$, $$x_6=41$$ --> $$sum=75$$ (answer to the question YES);
Can $$A<{10}$$: $$x_1=4$$, $$x_2=6$$, $$x_3=7$$, $$x_4=8$$, $$A=9$$, $$x_6=41$$ --> $$sum=75$$ (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.

Why and how is it obvious that obviously $$x_6=41$$
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11 May 2010, 01:55
LM wrote:
Bunuel wrote:
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 $$A\geq{10}$$: $$x_1=2$$, $$x_2=3$$, $$x_3=8$$, $$x_4=10$$, $$A=11$$ --> $$sum=34$$ (answer to the question YES);
Can $$A<{10}$$: $$x_1=4$$, $$x_2=6$$, $$x_3=7$$, $$x_4=8$$, $$A=9$$ --> $$sum=34$$ (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 $$12>A\geq{10}$$: $$x_1=2$$, $$x_2=3$$, $$x_3=8$$, $$x_4=10$$, $$A=11$$, $$x_6=41$$ --> $$sum=75$$ (answer to the question YES);
Can $$A<{10}$$: $$x_1=4$$, $$x_2=6$$, $$x_3=7$$, $$x_4=8$$, $$A=9$$, $$x_6=41$$ --> $$sum=75$$ (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.

Why and how is it obvious that obviously $$x_6=41$$

Only the country which sent greatest number of representatives ($$x_6$$) could have sent 41, as 41 is more than half of the total (75).
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24 Sep 2010, 13:59
2
Thanks for the explanation

I got tripped when doing this in GMAT Prep as well.
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15 Jan 2012, 17:26
3
I understand by putting the values we can get but during exam its tough to out so many values and get it. I am thinking can there any other simpler and quick solution.

Putting values like 4,6,7,8 and 11 is not easy.
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Re: Six countries in a certain region sent a total of 75  [#permalink]

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18 Apr 2012, 18:36
Thank you bunnel for the explanation.
I must remember to solve it logically. and see when it does fit (a = 10) and when it is not true (a=9)
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19 Apr 2012, 09:24
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sourabhsoni wrote:
I understand by putting the values we can get but during exam its tough to out so many values and get it. I am thinking can there any other simpler and quick solution.

Putting values like 4,6,7,8 and 11 is not easy.

It is when you have a plan! You should know how to manipulate numbers and examples.
Let me explain.

6 countries, 75 people. No 2 countries sent the same number of people.

Stmnt 1: One country sent 41 people.
The other 5 together sent 75 - 41 = 34 people. 'A' sent the most number of people from the remaining 5 countries. Does A need to send atleast 10?
34 divided by 5 is approximately 7. On average, every country sent 7 people so we can split it like 4, 6, 7, 8, 9 (try and split around 7 so that the average stays apprx 7). A sent 9 people here.
A could have sent more than 10 people of course (say if the other 4 countries sent 1, 2, 3 and 4)
Not sufficient.

Stmnt 2: A sent fewer than 12
A could have sent 9 people (example above) or 11 (Split is 2, 6, 7, 8, 11. Try to make minimum changes to get what you want so that you can minimize the chances of error. Since I want to increase the last number, I just reduce the first one appropriately).
Again, not sufficient.

Using both statements together, A could have sent 9 or 11 people so not sufficient.

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Re: Six countries in a certain region sent a total of 75  [#permalink]

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20 Apr 2012, 19:32
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1
Great explanation, I need to spend time checking to prove and disprove these type of questions. For some reason I have a bad habit of rushing DS questions and not thinking through.
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Re: Six countries in a certain region sent a total of 75  [#permalink]

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30 Oct 2012, 10:52
Bunuel,
Sorry :s for making this question again hehe:
Is this a word problem question or another type of question? I cannot recognize it using the MGMAT guides.
Could you provide me more links related or tell me how to find them?
Thank you!
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Re: Six countries in a certain region sent a total of 75  [#permalink]

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30 Oct 2012, 11:25
danzig wrote:
Bunuel,
Sorry :s for making this question again hehe:
Is this a word problem question or another type of question? I cannot recognize it using the MGMAT guides.
Could you provide me more links related or tell me how to find them?
Thank you!

Yes, it's a word problem but also a bit like min/max type of question.

You can find all kinds of questions in our question banks here: viewforumtags.php

DS min/max questions: search.php?search_id=tag&tag_id=42
PS min/max questions: search.php?search_id=tag&tag_id=63

Hope it helps.
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Re: Six countries in a certain region sent a total of 75  [#permalink]

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16 Jun 2013, 00:33
But I still have a question,,,,,,,
Since the question we need to anwer is : did A at least send 10 representitives?
so if I can conclude tht : yes,A at least sent 10. it is sufficient.
if I conclude tht: no, A didn't not at least send 10. it is also sufficient.
Because GMAC says if we can hve one specific answer, it is sufficient.

Well, when I consider(1), clearly I can say that: no, A didn't not at least send 10.

then why not choose A??????
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Re: Six countries in a certain region sent a total of 75  [#permalink]

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16 Jun 2013, 00:42
1
KimY wrote:
But I still have a question,,,,,,,
Since the question we need to anwer is : did A at least send 10 representitives?
so if I can conclude tht : yes,A at least sent 10. it is sufficient.
if I conclude tht: no, A didn't not at least send 10. it is also sufficient.
Because GMAC says if we can hve one specific answer, it is sufficient.

Well, when I consider(1), clearly I can say that: no, A didn't not at least send 10.

then why not choose A??????

In a Yes/No Data Sufficiency questions, statement is sufficient if the answer is “always yes” or “always no” while a statement is insufficient if the answer is "sometimes yes" and "sometimes no".

For the first statement we can have an YES as well as a No answer to the question, which means that the statement is NOT sufficient.

For example, check here: six-countries-in-a-certain-region-sent-a-total-of-93368.html#p718376 or here: six-countries-in-a-certain-region-sent-a-total-of-93368.html#p1075895

Hope it helps.
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Re: Six countries in a certain region sent a total of 75  [#permalink]

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05 May 2014, 19:12
4
I took one good look at this problem and had the word "guess" in my head. After doing this problem again, I realized that it was not as difficult as it first looked. The GMAT is definitely beatable! Not giving up.
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Re: Six countries in a certain region sent a total of 75  [#permalink]

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18 Dec 2015, 23:30
1
Well this question is really a good one!

Bunuel's approach is excellent, but I think it would require at least 3-3.5 mins of working.
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Re: Six countries in a certain region sent a total of 75  [#permalink]

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12 Jan 2017, 17:09
For 1, country A can send 9 representatives, total number will 9+8+7+6+5+41=76>75.
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Re: Six countries in a certain region sent a total of 75  [#permalink]

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01 Feb 2018, 09:30
Hi guys, I'm certainly no math"magician" and just started studying for the GMAT and as such perhaps why I did not take the same approach to solve the question but it seems to be the answer of "E" is wrong, can anyone help figure out if I'm just insane ?

I went with a basic trial & error approach and stated the following:

75 Reps = R
Country A or A # of R cannot be = to B, C, D, E ,F
A must be # 2 in terms of high # of R and need to find out if A is = or greater than 10 ?

Condition 1: One of the six countries sent 41 representatives to the congress

So filling in the blanks by trial & error:

Country # R Ranking

A = 10 2
B = 41 1

which we know must be respected, so 75 - 51 = 24 R left, if we randomly assign countries C, D, E, F, #'s of R that are not the same, lets say like :

C = 9 3
D = 8 4
E = 4 5
F = 3 6

Then the total = 75 which makes condition # 1 work and is true ??

If we sub in condition # 2: Country A sent fewer than 12 representatives to the congress

this still holds true and you could make A = 11 and C = 9, D = 8, E= 4, F = 2 and this would still work and add up to 75 ? as well as many other combination allowing for condition 1 & 2 to hold true so it seems as though each of them alone is enough to satisfy the questions ? Am I missing something ? If someone can help clarify it would be highly appreciated

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Six countries in a certain region sent a total of 75  [#permalink]

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01 Feb 2018, 10:10
matm wrote:
Hi guys, I'm certainly no math"magician" and just started studying for the GMAT and as such perhaps why I did not take the same approach to solve the question but it seems to be the answer of "E" is wrong, can anyone help figure out if I'm just insane ?

I went with a basic trial & error approach and stated the following:

75 Reps = R
Country A or A # of R cannot be = to B, C, D, E ,F
A must be # 2 in terms of high # of R and need to find out if A is = or greater than 10 ?

Condition 1: One of the six countries sent 41 representatives to the congress

So filling in the blanks by trial & error:

Country # R Ranking

A = 10 2
B = 41 1

which we know must be respected, so 75 - 51 = 24 R left, if we randomly assign countries C, D, E, F, #'s of R that are not the same, lets say like :

C = 9 3
D = 8 4
E = 4 5
F = 3 6

Then the total = 75 which makes condition # 1 work and is true ??

If we sub in condition # 2: Country A sent fewer than 12 representatives to the congress

this still holds true and you could make A = 11 and C = 9, D = 8, E= 4, F = 2 and this would still work and add up to 75 ? as well as many other combination allowing for condition 1 & 2 to hold true so it seems as though each of them alone is enough to satisfy the questions ? Am I missing something ? If someone can help clarify it would be highly appreciated

Matt

Hi Matt

Let me try to see if I can help. Firstly, in DS questions, even if we are unable to calculate a unique value, there should at least be a unique proper answer to the question asked. Eg, if a question asks 'Is XYZ true or no' then the answer needs to be either a clear-cut YES or a clear-cut NO - then only we can say that we have got our answer.

In the given question, 'did Country A send at least 10 representatives', we can be sure that we have our answer in two situations:

Either if we can logically conclude that there were at least 10 representatives - in this case we have our answer as YES to the question asked
Or if we can logically conclude that there were less than 10 representatives for sure - in this case we have our answer as NO to the question asked

But if we cannot conclude any one (and only one) of the above two things then our conclusion would be that 'the data is insufficient to answer the question asked'.
Lets now analyse the statements.

(1) One country sent 41, if country A sent 10, then remaining 75-51 = 24; which can be divided among 4 different countries (say 3, 4, 8, 9 as you depicted).
But if country A sent 9, then remaining 75-50 = 25; this too can be divided among 4 different countries (say 4, 6, 7, 8).

So, the given condition of statement 1 is possible with country A having 10 R, and it is also possible with country A having 9 R.
Thus, we cannot say with surety whether country A has sent at least 10 R or not. That is why this condition is not sufficient to give either a clear-cut YES or a clear-cut NO to the question asked.

(2) As you have yourself said, it is possible with country A sending 11 R. But it is also possible with country A sending 4 R or 9 R (you can make various combinations as you have yourself written).
Again, since it is possible for this condition of statement 2 to hold true with both A having >= 10 R, and also possible with A having < 10 R, we cannot answer with a clear-cut YES or a clear-cut NO to the question asked. Not sufficient.

When we combine the two statements, still we could make a case with country A having 10 R or 11 R, but we could also make a case with country A having 9 R. This data is still insufficient to give us either a proper YES or a proper NO to the asked question (which was 'did Country A send at least 10 representatives'). That is why answer is E.
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