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The variables a, b, and c are distinct factors of 24. Which of the fol 25 Jul 2018, 21:57
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D
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79% (01:35) correct 21% (01:26) wrong based on 208 sessions

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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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D
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The variables a, b, and c are distinct factors of 24. Which of the fol Updated on: 25 Jul 2018, 22:07
Originally posted by StudiosTom on 25 Jul 2018, 22:01.
Last edited by StudiosTom on 25 Jul 2018, 22:07, edited 1 time in total.
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Bunuel
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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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

Answer:D
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The variables a, b, and c are distinct factors of 24. Which of the fol 25 Jul 2018, 22:05
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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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The variables a, b, and c are distinct factors of 24. Which of the fol 25 Jul 2018, 22:07
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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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The variables a, b, and c are distinct factors of 24. Which of the fol 25 Jul 2018, 22:40
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Bunuel
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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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.

The best answer is D.
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The variables a, b, and c are distinct factors of 24. Which of the fol 26 Jul 2018, 00:46
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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.

Answer: D
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The variables a, b, and c are distinct factors of 24. Which of the fol 30 Jul 2018, 11:28
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Bunuel
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
Show more

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.

Answer: D
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The variables a, b, and c are distinct factors of 24. Which of the fol 13 Oct 2019, 12:39
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