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# The variables a, b, and c are distinct factors of 24. Which of the fol

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The variables a, b, and c are distinct factors of 24. Which of the fol  [#permalink]

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25 Jul 2018, 21:57
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The variables a, b, and c are distinct factors of 24. Which of the following must be true?

A. a + b + c is even.
B. a + b + c < 40
C. (a – b)/c is an integer.
D. abc is even.
E. abc is a multiple of 24

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The variables a, b, and c are distinct factors of 24. Which of the fol  [#permalink]

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Updated on: 25 Jul 2018, 22:07
2
Bunuel wrote:
The variables a, b, and c are distinct factors of 24. Which of the following must be true?

A. a + b + c is even.
B. a + b + c < 40
C. (a – b)/c is an integer.
D. abc is even.
E. abc is a multiple of 24

So take 2,3,4 and 24,12,8 or any combination which can includes 1 and 6 cases as well
A.Substitute,a+b+c=9,not even ,false
B.24+12+8>40,false case.So not necessarily true
C.(4-3)/2=0.5 ,false
D.2*3*4=24 ,true
Also 24*12*8=even,true
E.1*2*3=6,not a multiple of 24,not necessarily true

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Originally posted by AnkitOrYadav on 25 Jul 2018, 22:01.
Last edited by AnkitOrYadav on 25 Jul 2018, 22:07, edited 1 time in total.
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Re: The variables a, b, and c are distinct factors of 24. Which of the fol  [#permalink]

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25 Jul 2018, 22:05
D

Distinct factors of 24 are 1,2,3,4,6,8,12,24
Only 1 and 3 are odd numbers.
Out of a, b, and c, one of the factors has to be even. So, abc will always be even.

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Re: The variables a, b, and c are distinct factors of 24. Which of the fol  [#permalink]

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25 Jul 2018, 22:07
The variables a, b, and c are distinct factors of 24

Distinct factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

option A

a + b + c is even is false since 1 + 2 + 4 is odd

option B

a + b + c < 40 is false since 8 + 12 + 24 = 44 > 40

option C

$$\frac{a-b}{c}$$ is an integer is false since $$\frac{2-1}{3}$$ is not an integer

option D

abc is even since there are only two odd numbers and everything else is an even number

option E

abc is a multiple of 24 is false since 1 * 2 * 3 = 6 is not a multiple of 24

Hence option D
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Re: The variables a, b, and c are distinct factors of 24. Which of the fol  [#permalink]

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25 Jul 2018, 22:40
Bunuel wrote:
The variables a, b, and c are distinct factors of 24. Which of the following must be true?

A. a + b + c is even.
B. a + b + c < 40
C. (a – b)/c is an integer.
D. abc is even.
E. abc is a multiple of 24

a, b, c are distinct factors of 24.

Factors of 24 : 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24.

Note: Except 1 and 3 all are EVEN factors.

So, whenever we multiply abc , one of them must be EVEN. That makes the result Even.

So, abc = even.

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Re: The variables a, b, and c are distinct factors of 24. Which of the fol  [#permalink]

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26 Jul 2018, 00:46

Solution

Given:
• a, b, and c are distinct factors of 24

To find:
• Among the following option which one is true.

Approach and Working:

Factors of 24= 1, 2, 3, 4, 6, 8, 12, 24
Among all the factors of 24, 2 factors are odd and the rest are even.
So, whatever be the case, abc will always be even.

Hence, the correct answer is option D.

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Re: The variables a, b, and c are distinct factors of 24. Which of the fol  [#permalink]

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30 Jul 2018, 11:28
Bunuel wrote:
The variables a, b, and c are distinct factors of 24. Which of the following must be true?

A. a + b + c is even.
B. a + b + c < 40
C. (a – b)/c is an integer.
D. abc is even.
E. abc is a multiple of 24

Since the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, we see that there are only two odd factors and thus, at a minimum, one of the values of a, b, and c must be even, making the product abc even also.

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Re: The variables a, b, and c are distinct factors of 24. Which of the fol &nbs [#permalink] 30 Jul 2018, 11:28
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# The variables a, b, and c are distinct factors of 24. Which of the fol

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