digits

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sumasajja: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Wed Jul 20, 2011 12:36 pm; Thanked: 2 times

by sumasajja » Sun Jul 24, 2011 8:07 pm

each of the following numbers has 2 digits blotted out.which of the numbers could be the number of hours in x days, where x is an integer?
a]25 , 06
b]50 , 26
c]56 , 02
d]62 , 50
e]65 , 20
answer e
any tricks for this problem ???please

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Source: Beat The GMAT — Problem Solving | Sun Jul 24, 2011 8:07 pm

winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Sun Jul 24, 2011 9:07 pm

What's the source?
Must be some thing relating to divisibility of 4.
As for divisibility by 24 , number of days(x) * 24 should be divisible by 4 as only E is divisible by 4 the answer is E.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jul 25, 2011 1:33 am

sumasajja wrote:each of the following numbers has 2 digits blotted out.which of the numbers could be the number of hours in x days, where x is an integer?
a]25 , 06
b]50 , 26
c]56 , 02
d]62 , 50
e]65 , 20

If x is an integer, then in x days there will be 24x hours which is also an integer. Thus, the correct option must be divisible by 24 and hence by 4 also.

Now a number is divisible by 4 only if the number formed by the last two digits of the number is divisible by 4. In this case, we know last two digits of all the options and we can easily find that only option E will be divisible by 4.

Hence, only option E could be divisible by 24.

The correct answer is E.

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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

by gmatdriller » Mon Jul 25, 2011 3:49 am

well, we know the number has to be divisible by 24 hrs per day.
But factors of 24 includes 3, 6, and 8. What motivates the choice of 4
and not 3?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jul 25, 2011 3:57 am

gmatdriller wrote:well, we know the number has to be divisible by 24 hrs per day.
But factors of 24 includes 3, 6, and 8. What motivates the choice of 4
and not 3?

Because,

1. To check whether a number is divisible by 3, we have to check whether the sum of the digits of the number is divisible by 3 or not. As we don't all the digits of the numbers, we cannot check for divisibility by 3.
2. To check whether a number is divisible by 6, we have to check whether the number is even and sum of the digits of the number is divisible by 3 or not. We can check whether the number is even by looking at last digit of the numbers but we cannot check for divisibility by 3.
3. To check whether a number is divisible by 8, we have to check whether the number formed by the last three digits of the number is divisible by 8 or not. As we don't know the last three digits of the numbers, we cannot check for divisibility by 8.

But, to check whether a number is divisible by 4, we have to check whether the number formed by the last two digits of the number is divisible by 4 or not. As we know the last two digits of each of the numbers, we can easily check for divisibility by 4.

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winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Mon Jul 25, 2011 4:17 am

Hi Anurag.
Can you please tell me if this is a Potential gmat problem?

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navami: Legendary Member; Posts: 540; Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members; Thanked: 37 times

by navami » Mon Jul 25, 2011 7:13 am

Last 2 digit should be divisible by 4 to identify the number.
Now if incase any 2 numebrs were div by 4 then check for divisibility of 8.
In that case last 3 digits should be divisible by 8.

This time no looking back!!!
Navami

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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

by gmatdriller » Thu Jul 28, 2011 3:29 pm

Hi Anurag,
that was a clear reminder on the application of divisibility rules.

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