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When positive integer k is divided by 35, the remainder is 14. Which o
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09 Jul 2021, 08:44
09 Jul 2021, 08:44
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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
A. 5
B. 7
C. 11
D. 14
E. 21
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: When positive integer k is divided by 35, the remainder is 14. Which o
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09 Jul 2021, 08:52
09 Jul 2021, 08:52
1
Carcass wrote:
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
A. 5
B. 7
C. 11
D. 14
E. 21
When it comes to remainders, we have a nice rule that says:
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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GMAT 1: 700 Q51 V31
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WE:Engineering (Computer Software)
Re: When positive integer k is divided by 35, the remainder is 14. Which o
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10 Jan 2022, 10:32
10 Jan 2022, 10:32
1
When positive integer k is divided by 35, the remainder is 14
Theory: Dividend = Divisor*Quotient + Remainder
k -> Dividend
35 -> Divisor
a -> Quotient (Assume)
14 -> Remainders
=> k = 35*a + 14 = 7*5a + 7*2 = 7*(5a + 2)
=> k when divided by 7 gives 5a+2 as quotient and 0 as remainder
=> k is divisible by 7
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
Theory: Dividend = Divisor*Quotient + Remainder
k -> Dividend
35 -> Divisor
a -> Quotient (Assume)
14 -> Remainders
=> k = 35*a + 14 = 7*5a + 7*2 = 7*(5a + 2)
=> k when divided by 7 gives 5a+2 as quotient and 0 as remainder
=> k is divisible by 7
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
