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# If a, b, and c are multiples of 3 such that a > b > c > 0, which of th

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Joined: 02 Sep 2009
Posts: 65841
If a, b, and c are multiples of 3 such that a > b > c > 0, which of th  [#permalink]

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23 Jun 2020, 05:38
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If a, b, and c are multiples of 3 such that a > b > c > 0, which of the following values must be divisible by 3?

I. a + b + c
II. a – b + c
III. $$\frac{abc}{9}$$

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

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If a, b, and c are multiples of 3 such that a > b > c > 0, which of th  [#permalink]

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23 Jun 2020, 05:55
Bunuel wrote:
If a, b, and c are multiples of 3 such that a > b > c > 0, which of the following values must be divisible by 3?

I. a + b + c
II. a – b + c
III. $$\frac{abc}{9}$$

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Let, a = 3x, b = 3y and c = 3z

I. a + b + c = 3x+3y+3z = 3(x+y+z) = Multiple of 3
II. a – b + c = 3x-3y+3z = 3(x-y+z) = Multiple of 3
III. $$\frac{abc}{9}$$ $$= \frac{(3x)*(3y)*(3z)}{9} = 3xyz$$ Multiple of 3

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Re: If a, b, and c are multiples of 3 such that a > b > c > 0, which of th  [#permalink]

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23 Jun 2020, 06:20
Let A B And C = 9,6&3

Putting values in statements one by one,

1. A+B+C
=> 9+6+3
=> 18 is divisible by 3
=> Satisfying

2. A-B+C
=> 9-6+3
=> 6 is divisible by 3
=> Satisfying

3. ABC/9
=> 9*6*3/9
=> 18 is divisible by 3
=> Satisfying

All three values are Satisfying.

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Re: If a, b, and c are multiples of 3 such that a > b > c > 0, which of th   [#permalink] 23 Jun 2020, 06:20