Can someone please give me the reasoning to this DS problem?

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daygoballa: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Thu Feb 26, 2009 10:08 am; Location: San Diego, CA

by daygoballa » Thu Mar 05, 2009 2:42 pm

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Here's the problem:

- Of the 66 people in a certain auditorium, at most 6 people have birthdays in any one given month. Does at least one person in the auditorium have a birthday in January?

(1) More of the people in the auditorium have birthdays in February than in March.

(2) five of the people in the auditorium have birthdays in March.

The answer is (D)

Thank you for you help!

Henry

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Source: Beat The GMAT — Data Sufficiency | Thu Mar 05, 2009 2:42 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Thu Mar 05, 2009 2:54 pm

Take the easier of the 2 statements

Stmt II

5 bday in March

Remaining 61
and 11 months includinbg Jan left

Atmost 6 can have a bday in any given month so there must be atleast 1 if not more having bday in Mar

SUFF

Stmt II

More of the people in the auditorium have birthdays in February than in March

Again to prove no one has a bday in jan try to maximize the 10 months which is 60 excluding March and Jan.

Since March cant have 6 as it should be less than Feb at the max March can be 5.

Still jan we have 1 bday.

SUFF

Choose D

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ranpman: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun Mar 01, 2009 2:16 pm

by ranpman » Mon Mar 23, 2009 5:58 pm

cramya wrote:Take the easier of the 2 statements

Stmt II

5 bday in March

Remaining 61
and 11 months includinbg Jan left

Atmost 6 can have a bday in any given month so there must be atleast 1 if not more having bday in Mar

SUFF

Stmt II

More of the people in the auditorium have birthdays in February than in March

Again to prove no one has a bday in jan try to maximize the 10 months which is 60 excluding March and Jan.

Since March cant have 6 as it should be less than Feb at the max March can be 5.

Still jan we have 1 bday.

SUFF

Choose D

I agree that (1) is SUFFICIENT.

However (2) states that "Five of the people in the auditorium have birthdays in March". (2) does not hay "ONLY five of the people in the auditorium have...".

In that case, isn't it possible that March could have 6 birthdays? In which case, (2) is INSUFFICIENT. What am I missing?

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TedCornell: Master | Next Rank: 500 Posts; Posts: 207; Joined: Mon Mar 09, 2009 9:33 pmFollowed by: 24 members; Thanked: 115 times; GMAT Score:750

by TedCornell » Wed Mar 25, 2009 12:26 am

On the GMAT, when you're told that 5 of the ppl have birth day in march that means exactly 5 of those people. There could be others with march birthdays, but those others cannot be among the people in the auditorium.

Similarly, if you're told "John has $10" it means he has exactly $10; he cannot have $11 or $12.

To make 6 march birthdays a possibility, the statement might've said "At least 5 of the pple have birthday in march" or "no fewer than 5 of the ppl"

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon Feb 19, 2018 9:11 pm

Hi All,

We're told that there are 66 people in a certain auditorium and 6 people AT MOST have birthdays in any one given month. We're asked if AT LEAST one person in the auditorium has a birthday in January. This is a YES/NO question and we can use a mix of logic and TESTing VALUES to answer it.

To start, since there are 66 people, no more than 6 have their birthdays in the same month and there are 12 months in a year, the ONLY WAY for one month to have 0 birthdays is if ALL of the other 11 months have 6 birthdays each. In that situation, there would be eleven 6s and one 0. By extension, if ANY month doesn't have 6 birthdays in it, then EVERY month would have at least one birthday in it.

1) More of the people in the auditorium have birthdays in February than in March.

Fact 1 tells us that March cannot possibly have 6 birthdays (it would have at most 5 - and that could only occur if February had 6 birthdays). Thus, since one month (in this case, March) doesn't have 6 birthdays, January will have at least 1 birthday.
Fact 1 is SUFFICIENT

2) Five of the people in the auditorium have birthdays in March.

The information in Fact 2 allows us to make the same deduction that we made in Fact 1: since one month (in this case, March) doesn't have 6 birthdays, January will have at least 1 birthday.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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