When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?
A. 5
B. 7
C. 11
D. 14
E. 21
Answer: B
Source: Veritas
When positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?
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Say k = 35q + 14; where q is a positive integerBTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:44 pmWhen positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?
A. 5
B. 7
C. 11
D. 14
E. 21
Answer: B
Source: Veritas
=> k = 7(5q + 2)
=> k must be divisible by 7. Sufficient.
Correct answer: B
Hope this helps!
Jay
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When it comes to remainders, we have a nice rule that says:BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:44 pmWhen positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?
A. 5
B. 7
C. 11
D. 14
E. 21
Answer: B
Source: Veritas
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
When positive integer k is divided by 35, the remainder is 14.
So, some possible values of k are: 14, 49, 84, 119, . . . etc
Let's test some values.
If k = 14, then we can ELIMINATE A, C and E, since they are not divisors of 14, and the questions says "Which of the following MUST be a divisor of k?
We're left with answer choices B and D
Let's test another value.
If k = 49, then we can ELIMINATE D, since 14 is not a divisor of 49.
By the process of elimination, we're left with B
Answer: B
Cheers,
Brent
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Solution:BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:44 pmWhen positive integer k is divided by 35, the remainder is 14. Which of the following must be a divisor of k?
A. 5
B. 7
C. 11
D. 14
E. 21
Answer: B
We can create the equation where q is the quotient:
k/35 = q + 14/35
k = 35q + 14
k= 7(5q + 2)
We see that 7 must be a divisor of k since k is a multiple of 7.
Answer: B
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