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25 Nov 2022, 06:56
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The integer k is the product of four different prime numbers. If k divided by 22 is a multiple of 13, which of the following could be equal to k divided by 11?
A. 44
B. 78
C. 143
D. 234
E. 242
A. 44
B. 78
C. 143
D. 234
E. 242
25 Nov 2022, 07:12
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K/22=13a
K=22*13*a=11*2*13*a
K/11?
K/11= 2*13*a
a has to be prime number and a multiple of 26.
a cannot be 2 (integer k is the product of four different prime numbers.
Check for a= 3/5/7
K/11= 2*13*3= 78
Option B is match!
Posted from my mobile device
K=22*13*a=11*2*13*a
K/11?
K/11= 2*13*a
a has to be prime number and a multiple of 26.
a cannot be 2 (integer k is the product of four different prime numbers.
Check for a= 3/5/7
K/11= 2*13*3= 78
Option B is match!
Posted from my mobile device
25 Nov 2022, 07:37
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Bunuel
The integer k is the product of four different prime numbers. If k divided by 22 is a multiple of 13, which of the following could be equal to k divided by 11?
A. 44
B. 78
C. 143
D. 234
E. 242
A. 44
B. 78
C. 143
D. 234
E. 242
Given
k = \(p_1 * p_2 * p_3 * p_4\)
\(p_1 , p_2 , p_3, p_4\) are prime numbers
We know that \(\frac{k }{ 22}\) is a multiple of multiple of 13
So we can infer that k has 11 * 2 * 13 in it as prime factors.
k divided by 11 will atleast be a multiple 2 * 13 and another prime factor.
ACE
A. 44 - Not a multiple of 13
B. 78 - 13 * 2 * 3
C. 143 - Not a multiple of 2
D. 234 - 13 * 3^2 * 2
E. 242 - Not a multiple of 13
Between B and D, we know that k has atleast one three. We don't know if the number has two 3s in it. Hence we can eliminate D and the answer is B.
