Explanation required for OG 12 Problem.

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pratyoosh: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat Apr 10, 2010 6:20 am

by pratyoosh » Tue Aug 17, 2010 12:22 pm

Hello Guys,

Am unable to comprehend the explanation for the below OG 12 DS problems, can anyone out there offer a better explanation than the one mentioned in OG?

Q1. If n is a positive integer, what is the tens digit of n ?
(1) The hundreds digit of 10n is 6.
(2) The tens digit of n + 1 is 7.

Answer - A.

Q2. Are all of the numbers in a certain list of 15 numbers
equal?
(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.

Answer - B

Thanks in advance,
Pratyoosh.

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Source: Beat The GMAT — Data Sufficiency | Tue Aug 17, 2010 12:22 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Tue Aug 17, 2010 5:22 pm

Q1. If n is a positive integer, what is the tens digit of n ?
(1) The hundreds digit of 10n is 6.
(2) The tens digit of n + 1 is 7.

Explanation:

(1) The hundreds digit of 10n is 6 means 10n = 6(tens place)(units place); tens place can take the digits from 0 to 9 but units place has to be the digit 0 as n is a positive integer.
So, n = 6(tens place)
We can see that the tens digit of n will always be 6.
[If not clear take an example: Let 10n = 620, then n = 62. If we take 10n = 602 then n cannot be an integer as n = 602/10 = 60.2]
So, (1) is SUFFICIENT.

2) The tens digit of n+1 is 7 so N can be 69 to 78, so tenth place of n is either 6 or 7. Since we don't have a unique answer, so (2) is NOT SUFFICIENT.

The correct answer is [spoiler](A)[/spoiler].

Does that help?

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pratyoosh: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat Apr 10, 2010 6:20 am

by pratyoosh » Tue Aug 17, 2010 9:40 pm

Thanks a lot, does make it clear now. I was able to reach part of the solution myself but didn't get round ALL possibilities.

Regards,
Pratyoosh.

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ketandoshi: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sat May 15, 2010 3:30 pm; Location: Houston, TX; Thanked: 1 times

by ketandoshi » Wed Aug 18, 2010 2:41 pm

For the 2nd question should the ans be D? I am confused...
Here is my explaination......

(1) The sum of all the numbers in the list is 60. Let the #s be X so, the sum of all the # is 15X=60 or X=4,

(2) The sum of any 3 numbers in the list is 12. Let the #s be X so, the sum of the # is X+X+X=12 i.e X=4

Please somebody correct my explaintion.

Thanks

ketan

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honeysn: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Wed May 06, 2009 5:00 pm; Thanked: 1 times

by honeysn » Wed Aug 18, 2010 6:01 pm

I guess for second question, Answer is B.

We cannot have sum of "any" 3 number =12 if we do not have all numbers equal (in this case equal to 4)

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Wed Aug 18, 2010 6:22 pm

Q2. Are all of the numbers in a certain list of 15 numbers
equal?
(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.

Stmt1,

Sum of all numbers=60

All numbers can be 4 or different numbers with sum 60.

Insuff

stmt2,

Sum of any 3 numbers=12

This is possible if we assume all numbers as 4 only.

Suff.

Pick B

--Anand--

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pratyoosh: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sat Apr 10, 2010 6:20 am

by pratyoosh » Thu Aug 19, 2010 11:32 am

@ ketan - I think selango's explanation answers your query.

@ selango - I am not clear on your explanation. Whilst 12 needs to be a sum of "any" 3 numbers, why are we assuming its always 4 + 4 + 4? Why can it not be 5 + 6 + 1 or 3 + 8 + 1 ?

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Thu Aug 19, 2010 6:12 pm

pratyoosh,

Sum of any 3 numbers is 12.

If we assume 5 6 1 or 3 8 1

{5,6,1,3,8,1......}This is the list

Now take any 3 numbers

5+6+1=12

3+8+1=12

6+1+3=10

1+1+3=5

As you can see if we assume all numbers as 4 only the sum of any 3 numbers can be 12.

--Anand--

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