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abc0 is a positive, four-digit integer, where a, b and c are 1-digit

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Math Revolution GMAT Instructor
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abc0 is a positive, four-digit integer, where a, b and c are 1-digit  [#permalink]

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New post 10 May 2018, 07:57
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[GMAT math practice question]

abc0 is a positive, four-digit integer, where a, b and c are 1-digit positive integers. Is abc0 divisible by 4?

1) ab is an odd number
2) bc is an odd number

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Re: abc0 is a positive, four-digit integer, where a, b and c are 1-digit  [#permalink]

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New post 10 May 2018, 09:00
MathRevolution wrote:
[GMAT math practice question]

abc0 is a positive, four-digit integer, where a, b and c are 1-digit positive integers. Is abc0 divisible by 4?

1) ab is an odd number
2) bc is an odd number


abc0 will be divided by 4, when the number made by the last 2 digis is divided by 4
( Reason : as 100 is always divided by 4, abc0 can be written as : ab*100+ c*10 + 0....thus c*10 + 0 must be divisible by 4)

Now c*10 + 0 is divisible by 4 when c is even .
( Reason : when c is even c*10 + 0 = 20 or 40 or 60 or 80... this can also be deduced assuming c=2n+1(o)& c=2n(e))

1) ab is an odd number ==> no information about c( it could be odd/even).... Thus (NS)
1) bc is an odd number ==> hence, c is odd ... thus c*10 + 0 is not divisible by 4 .... Thus (S)

Hence I would go for option B.
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Re: abc0 is a positive, four-digit integer, where a, b and c are 1-digit  [#permalink]

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New post 10 May 2018, 10:08
Divisibility by 4 - last two digits need to be divisible by 4

Here means c0 has to be divisible by 4

I) no info about c
Insufficient

II) bc is odd
Means both b and c are odd
With zero as unit digit only even digit at tens place is divisible by 4
Eg 20,30,40,60

10,30,50 are not divisible by 4

Hence sufficient

B is answer

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Re: abc0 is a positive, four-digit integer, where a, b and c are 1-digit  [#permalink]

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New post 13 May 2018, 18:40
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

We can determine whether an integer is divisible by 4 from its final two digits.
Thus, abc0 is divisible by 4 if and only if c0 is divisible by 4.
Condition 1) tells us nothing about the value of c, so it is not sufficient.
Condition 2) tells us that both b and c are odd numbers.
If c is an odd number, then 10*c + 0 = 10*c is not a multiple of 4, and so abc0 is not a multiple of 4. The answer is ‘no’.
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient.

Therefore, B is the answer.

Answer: B
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Re: abc0 is a positive, four-digit integer, where a, b and c are 1-digit &nbs [#permalink] 13 May 2018, 18:40
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