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If B = 12 x 15 x 34, then all of the following answer choices are inte 10 Jul 2020, 04:49
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

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89% (01:08) correct 11% (01:35) wrong based on 61 sessions

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If B = 12 x 15 x 34, then all of the following answer choices are integers EXCEPT:

A. B/18
B. B/30
C. B/32
D. B/36
E. B/72
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C
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If B = 12 x 15 x 34, then all of the following answer choices are inte 10 Jul 2020, 04:53
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Option C!

Check one by one each option, starting from middle. All other options, on solving gives us an integer value.
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If B = 12 x 15 x 34, then all of the following answer choices are inte 10 Jul 2020, 04:54
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Prime Factorization of B = 12 x 15 x 34
= 3*2*2*3*5*2*17
The non integer value among options =
A. B/18 = 3*2*2*3*5*2*17/18
=> 3*2*2*3*5*2*17/2*3*3
=> Integer

B. B/30 = 3*2*2*3*5*2*17/30
=> 3*2*2*3*5*2*17/2*3*5
=> Integer

C. B/32 = 3*2*2*3*5*2*17/32
=> 3*2*2*3*5*2*17/2*2*2*2*2
=> Non-Integer

D. B/36 = 3*2*2*3*5*2*17/36
=> 3*2*2*3*5*2*17/2*2*3*3
=> Integer

E. B/72 = 3*2*2*3*5*2*17/72
=> 3*2*2*3*5*2*17/2*2*2*3*3
=> Integer

Answer is C

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If B = 12 x 15 x 34, then all of the following answer choices are inte 10 Jul 2020, 05:06
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If B = 12 x 15 x 34, then all of the following answer choices are integers EXCEPT:

A. B/18 18=6*3, we take 6 from 12 and 3 from 15 to get 18.
B. B/30 30=6*5, we take 6 from 12 and 5 from 15 to get 30.
C. B/32 8*4, we take 4 from 12, we can not take an even number from 15 and we can take only 2 from 34. answer C
D. B/36 36=6*6, we take 6 from 12, 3 from 15 and 2 from 34 to get 36
E. B/72 it is D*2 (36*2) , we take all numbers from D above and 2 from 12 to get 72.
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If B = 12 x 15 x 34, then all of the following answer choices are inte 11 Jul 2020, 00:38
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Bunuel
If B = 12 x 15 x 34, then all of the following answer choices are integers EXCEPT:

A. B/18
B. B/30
C. B/32
D. B/36
E. B/72
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Solution


    • \(B = 12*15*34 = (2^2*3)*(3*5)*(2*17) = 2^3*3^2*5*17\)
    • So, If B is divided by any integer whose prime factorization either contains prime numbers other than 2, 3, 5, and 17 or it has powers of at least one of 2, 3, 5, and 17 more than that in B, then the result will be non-integer.
    • So, let’s check the answer options:
      o Option A : B/18
         \(18 = 2*3^2\)
         Since powers of 2 and 3 are less than or equal to that in B, so B/18 it will be an integer.
      o Option B: B/30
         30 = 2*3*5
         Since powers of 2, 3 and 5 are less than or equal to that in B, So, B/30 will be an integer.
      o Option C: B/32
         \(32 = 2^5\)
         Since powers of 2 is more than that of the power of 2 in B. Hence, B/32 will not be an integer.
Thus, the correct answer is Option C.
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