Number properties

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sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 amFollowed by: 2 members; Thanked: 1 times

by sud21 » Fri Oct 09, 2015 8:00 pm

Suppose x is a positive even number, all of whose digits are either 3 or 4. If x is also divisible by both 3 and 4, how many digits are in the smallest possible value of x?

a)Three

b)Four

c)Five

d)Six

e)Seven

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Source: Beat The GMAT — Problem Solving | Fri Oct 09, 2015 8:00 pm

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Oct 09, 2015 9:01 pm

sud21 wrote:Suppose x is a positive even number, all of whose digits are either 3 or 4. If x is also divisible by both 3 and 4, how many digits are in the smallest possible value of x?

a)Three

b)Four

c)Five

d)Six

e)Seven

Since x is even so Unit digit of x must be 4 as it can't be 3

Since x is Divisible by 4 so Last two digits of x must be divisible by 4 as Last two digits can't be 34 so last two digits of x must be 44

Since x must be divisible by 3 so sum of the digits of x must be divisible by 3 so x may be 444 whose sum of digits is 12 i.e. Divisible by 3

i.e. Smallest x = 444

Answer: option A

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by [email protected] » Fri Oct 09, 2015 10:08 pm

Hi sud21,

This question is packed with Number Property and logic shortcuts that you can take advantage of. I'm going to give you some hints so that you can try this question again:

1) Each of the digits of X are either a 3 or a 4.
2) Notice how the prompt is NOT asking for the actual value of X; it's asking for the number of digits in the shortest possible answer.
3) To be divisible by 3, the sum of the digits of X must be divisible by 3.
4) To be divisible by 4, the number that is created by the last two digits of X must be divisible by 4.

Since the question asks for the X that has least digits, you can take advantage of the answers. We'll start with Answer A - can you find a 3-digit number that fits all of the above facts? If you can, then you're done. If you can't, then you should look for a 4-digit number that fits all of the above facts.

Final Answer: A

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