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# M14-19

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:53
2
13
00:00

Difficulty:

95% (hard)

Question Stats:

44% (01:12) correct 56% (01:47) wrong based on 190 sessions

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If among the first ten cyclists who crossed the finish line, 4 were Italians and 8 represented Telefonica team, how many cyclists who represented Telefonica team and finished in the top ten were not Italians?

(1) 2 Italians who finished in the top ten did not represent Telefonica team.

(2) Each of the top ten finishers either was an Italian or represented Telefonica team or both.

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16 Sep 2014, 00:53
2
4
Official Solution:

(1) 2 Italians who finished in the top ten did not represent Telefonica team. Since 2 Italians did not represent Telefonica team, then remaining 2 Italians did represent Telefonica team, hence out of 8 cyclists who represented Telefonica team $$8 - 2 = 6$$ were not Italians. Sufficient.

(2) Each of the top ten finishers either was an Italian or represented Telefonica team or both. So, $$\{Total\} = \{Italians\} + \{Telefonica\} - \{Both\}$$: $$10 = 4 + 8-\{Both\}$$, which gives $$\{Both\} = 2$$. So, 2 cyclists represented Telefonica and were Italians, which means that $$8 - 2 = 6$$ cyclists represented Telefonica but were not Italians. Sufficient.

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26 Jan 2015, 20:12
I think this question is good and helpful.
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10 Feb 2015, 04:52
1
With the box approach statement (2) might be way easier to comprehend for some people:

ITAL NO ITAL TOTAL

TELE 2 6 8

NO TELE 2 0 (!) 2

4 6 10
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03 May 2015, 10:16
3
Bunuel wrote:
Official Solution:

(1) 2 Italians who finished in the top ten did not represent Telefonica team. Since 2 Italians did not represent Telefonica team, then remaining 2 Italians did represent Telefonica team, hence out of 8 cyclists who represented Telefonica team $$8 - 2 = 6$$ were not Italians. Sufficient.

(2) Each of the top ten finishers either was an Italian or represented Telefonica team or both. So, $$\{Total\} = \{Italians\} + \{Telefonica\} - \{Both\}$$: $$10 = 4 + 8-\{Both\}$$, which gives $$\{Both\} = 2$$. So, 2 cyclists represented Telefonica and were Italians, which means that $$8 - 2 = 6$$ cyclists represented Telefonica but were not Italians. Sufficient.

Neither the question stem nor the first option state that first ten cyclists consist exclusively of Italians, Telefonica team, or both. This information is given only in option 2. How is option 1 sufficient if there is no information whether there are cyclists among top ten who belong to neither of two groups?
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18 Sep 2015, 14:30
Bunuel wrote:
If among the first ten cyclists who crossed the finish line, 4 were Italians and 8 represented Telefonica team, how many cyclists who represented Telefonica team and finished in the top ten were not Italians?

(1) 2 Italians who finished in the top ten did not represent Telefonica team.

(2) Each of the top ten finishers either was an Italian or represented Telefonica team or both.

Why Stat.1 is Sufficient ? It is only statement 2 that complete the question by stating the actual type of participants i.e. either Italian or Telefonica or both and no one else.
Stat 1...gives Quantity
Stat 2....gives Type

Stat 1+2 gives OA....C.........

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12 Nov 2015, 08:59
2
manish8383 wrote:
Bunuel wrote:
If among the first ten cyclists who crossed the finish line, 4 were Italians and 8 represented Telefonica team, how many cyclists who represented Telefonica team and finished in the top ten were not Italians?

(1) 2 Italians who finished in the top ten did not represent Telefonica team.

(2) Each of the top ten finishers either was an Italian or represented Telefonica team or both.

Why Stat.1 is Sufficient ? It is only statement 2 that complete the question by stating the actual type of participants i.e. either Italian or Telefonica or both and no one else.
Stat 1...gives Quantity
Stat 2....gives Type

Stat 1+2 gives OA....C.........

Hi

I have compiled a small matrix box because this tool is the best to most overlapping sets problems - venn diag are ambigious for me.

NOTE: we do not need to know for the Statement 1 whether there is a "NONE" GROUP - YOU WILL SEE IN THE MATRIX. Statement 2 virtually states that there is none of "NONE" because everyone belongs either to both sets or at least to one of the sets:

"Each of the top ten finishers either was an Italian or represented Telefonica team or both."
>> !!!

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26 Nov 2015, 14:41
Bunuel wrote:
Official Solution:

(1) 2 Italians who finished in the top ten did not represent Telefonica team. Since 2 Italians did not represent Telefonica team, then remaining 2 Italians did represent Telefonica team, hence out of 8 cyclists who represented Telefonica team $$8 - 2 = 6$$ were not Italians. Sufficient.

(2) Each of the top ten finishers either was an Italian or represented Telefonica team or both. So, $$\{Total\} = \{Italians\} + \{Telefonica\} - \{Both\}$$: $$10 = 4 + 8-\{Both\}$$, which gives $$\{Both\} = 2$$. So, 2 cyclists represented Telefonica and were Italians, which means that $$8 - 2 = 6$$ cyclists represented Telefonica but were not Italians. Sufficient.

Hi Bunuel, I would like to get more explanation from you on why the option is D. I thought the answer is B, because Option A does not say if there were any non-Italians who were not in Telefonica team whereas option B clearly states the number as 0. If you see the question, it clearly asks "how many cyclists who represented Telefonica team and finished in the top ten were not Italians" - with option A you could have few folks who were not italians and not telefonicans. Please explain !!
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05 Jul 2016, 22:48
Hi Bunuel,
Option A is not sufficient because there could be some folks who are neither italian nor in the Telefonica team. So I think Option A is still insufficient. Can you please explain?
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05 Jul 2016, 22:49
I think this is a poor-quality question and I don't agree with the explanation. Hi Bunuel,
Option A is not sufficient because there could be some folks who are neither italian nor in the Telefonica team. So I think Option A is still insufficient. Can you please explain?
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06 Jul 2016, 07:29
apnavaibhav wrote:
I think this is a poor-quality question and I don't agree with the explanation. Hi Bunuel,
Option A is not sufficient because there could be some folks who are neither italian nor in the Telefonica team. So I think Option A is still insufficient. Can you please explain?

The question is fine. Please check here for alternative solutions: if-among-the-first-ten-cyclists-who-crossed-the-finish-line-87435.html

Hope it helps.
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11 Oct 2016, 19:19
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. for statement 1 to be true, should not statement 2 be true.
Hence, correct ans should be C.
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11 Oct 2016, 21:55
yogeshrjn wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. for statement 1 to be true, should not statement 2 be true.
Hence, correct ans should be C.

The question is fine. Please check here for alternative solutions: if-among-the-first-ten-cyclists-who-crossed-the-finish-line-87435.html

Hope it helps.
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15 Oct 2016, 19:30
The answer should be corrected to 'Statement 2 only being sufficient' here. Statement 1 states '2 Italians who finished in the top ten did not represent Telefonica team'. How can we readily assume that the other 2 represent Telefonica team? They could be representing some other team as well.
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16 Oct 2016, 03:27
satyakrishna wrote:
The answer should be corrected to 'Statement 2 only being sufficient' here. Statement 1 states '2 Italians who finished in the top ten did not represent Telefonica team'. How can we readily assume that the other 2 represent Telefonica team? They could be representing some other team as well.

The question is fine. Please check here for alternative solutions: if-among-the-first-ten-cyclists-who-crossed-the-finish-line-87435.html

Hope it helps.
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Updated on: 03 Dec 2016, 00:18
1
my solution:
1)gives c=2 so
a=4-c=2
d=2-c=0
b=8-a or b=6-d so b=6
SUFFICIENT
2) gives d=0 use b+d=6 to get b=6
SUFFICIENT
>> !!!

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Originally posted by karanchamp1 on 02 Dec 2016, 23:44.
Last edited by karanchamp1 on 03 Dec 2016, 00:18, edited 2 times in total.
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03 Dec 2016, 00:10
my solution:
>> !!!

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07 Mar 2017, 23:24
Neither the question stem nor the first option state that first ten cyclists consist exclusively of Italians, Telefonica team, or both. This information is given only in option 2. How is option 1 sufficient if there is no information whether there are cyclists among top ten who belong to neither of two groups?

I checked the thread -https://gmatclub.com/forum/if-among-the-first-ten-cyclists-who-crossed-the-finish-line-87435.html, and still cant find answer to above.
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17 Apr 2017, 05:35
The trick and confusion about this question is that at first we need to assume that there were also people who were neither Italians nor part of the Telefonica team.
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14 Oct 2017, 22:13
I think this is a high-quality question and I agree with explanation. this is a very good question!
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# M14-19

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