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Which of the following is true?

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Which of the following is true?  [#permalink]

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New post 18 Apr 2016, 01:05
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (02:06) correct 37% (01:46) wrong based on 82 sessions

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Which of the following is true?

A. The least common multiple of 9 and 12 is greater than the greatest common factor of 36 and 72.
B. The greatest common factor of 12 and 24 is greater than the least common multiple of 6 and 15.
C. The least common multiple of 20 and 12 is greater than the greatest common factor of 96 and 64.
D. The greatest common factor of 32 and 48 is greater than the least common multiple of 7 and 30.
E. The least common multiple of 10 and 12 is less than the greatest common factor of 60 and 45.

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Re: Which of the following is true?  [#permalink]

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New post 18 Apr 2016, 12:10
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Bunuel wrote:
Which of the following is true?

A. The least common multiple of 9 and 12 is greater than the greatest common factor of 36 and 72.
B. The greatest common factor of 12 and 24 is greater than the least common multiple of 6 and 15.
C. The least common multiple of 20 and 12 is greater than the greatest common factor of 96 and 64.
D. The greatest common factor of 32 and 48 is greater than the least common multiple of 7 and 30.
E. The least common multiple of 10 and 12 is less than the greatest common factor of 60 and 45.


A. The least common multiple of 9 and 12 is greater than the greatest common factor of 36 and 72.

LCM = 36

Greatest common factor = 36

The conclusion doesn't follow

B. The greatest common factor of 12 and 24 is greater than the least common multiple of 6 and 15.

GCF = 12

Least common multiple of 6 and 15 = 60

The conclusion doesn't follow

C. The least common multiple of 20 and 12 is greater than the greatest common factor of 96 and 64.

LCM = 60

Greatest common factor = 32

LCM > Greatest common factor The conclusion holds true

D. The greatest common factor of 32 and 48 is greater than the least common multiple of 7 and 30.

GCF = 16

LCM = 210

The conclusion doesn't follow

E. The least common multiple of 10 and 12 is less than the greatest common factor of 60 and 45.[/quote]

LCM = 60

GCF = 15

The conclusion doesn't follow


Hence the correct answer is (C) :-D :lol:
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Re: Which of the following is true?  [#permalink]

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New post 18 Apr 2016, 12:20
Easy peasy.

Starting with C, you immediatly see that 60 is greater than the greatest common factor of 96 and 64, which is 32.

Ans C
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Re: Which of the following is true?  [#permalink]

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New post 18 Apr 2016, 17:03
Let's take each statement at a time

A. LCM of 9 and 12 is greater than the GCF of 36 and 72.
LCM of 9 and 12 = 36
GCF of 36 and 72= 36
Statement A is false

B. The GCF of 12 and 24 is greater than LCM of 6 and 15.
GCF of 12 and 24 = 6
LCM of 6 and 15 = 30
Statement B is false

C. The LCM of 20 and 12 is greater than the GCF of 96 and 64.
LCM of 20 and 12 = 60
GCF of 96 and 64 = 32
Statement C is true

D. The GCF of 32 and 48 is greater than the LCM of 7 and 30.
GCF of 32 and 48 =16
LCM of 7 and 30 = 210
Statement D is false

E. The LCM of 10 and 12 is less than the GCF of 60 and 45.
LCM of 10 and 12 =60
GCF of 60 and 45 =15
Statement E is false

Correct option : C
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Re: Which of the following is true?  [#permalink]

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New post 25 Apr 2019, 05:35
Hello,

Is there a fast way to compute the LCM and GCF for each one (to save time)?

Thanks!

KHow

Bunuel wrote:
Which of the following is true?

A. The least common multiple of 9 and 12 is greater than the greatest common factor of 36 and 72.
B. The greatest common factor of 12 and 24 is greater than the least common multiple of 6 and 15.
C. The least common multiple of 20 and 12 is greater than the greatest common factor of 96 and 64.
D. The greatest common factor of 32 and 48 is greater than the least common multiple of 7 and 30.
E. The least common multiple of 10 and 12 is less than the greatest common factor of 60 and 45.
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Re: Which of the following is true?   [#permalink] 25 Apr 2019, 05:35
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