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When integer n is divided by 15, the remainder is 5. Which of the foll
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13 Jul 2021, 04:37
13 Jul 2021, 04:37
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When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3n
II. 5n
III. 4n + 10
A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
I. 3n
II. 5n
III. 4n + 10
A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: When integer n is divided by 15, the remainder is 5. Which of the foll
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13 Jul 2021, 05:03
13 Jul 2021, 05:03
Carcass wrote:
When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?
I. 3n
II. 5n
III. 4n + 10
A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
I. 3n
II. 5n
III. 4n + 10
A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Many integer properties questions can be solved by testing values
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 integer n is divided by 15, the remainder is 5.
So, some possible values of n are: 5, 20, 35, 50, 65, ....
Which of the following has a remainder of 10 when divided by 15 ?
Let's test a possible value of n.
Try n = 5
I. 3n = 3(5) = 15. When we divide 15 by 15, we get remainder 0. So, statement I does NOT satisfy the requirement.
ELIMINATE answer choices A, D and E
II. 5n = 5(5) = 25. When we divide 25 by 15, we get remainder 10. So, statement II DOES satisfy the requirement. This means we can't eliminate anything.
III. 4n + 10 = 4(5) + 10 = 30. When we divide 30 by 15, we get remainder 0. So, statement III does NOT satisfy the requirement.
ELIMINATE answer choice C
Answer: B
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When integer n is divided by 15, the remainder is 5. Which of the foll
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10 Jan 2022, 10:37
10 Jan 2022, 10:37
1
When integer n is divided by 15, the remainder is 5
Theory: Dividend = Divisor*Quotient + Remainder
n -> Dividend
15 -> Divisor
a -> Quotient (Assume)
5 -> Remainders
=> n = 15*a + 5 = 15a + 5
Which of the following has a remainder of 10 when divided by 15
I. 3n
3n = 3*(15a + 5) = 45a + 15 = 15*(3a+1)
=> 3n when divided by 15 gives 3a+1 as quotient and 0 as remainder => FALSE
II. 5n
5n = 5*(15a + 5) = 75a + 25 = 75a + 15 + 10 = 15*(5a+3) + 10
=> 5n when divided by 15 gives 5a+3 as quotient and 10 as remainder => TRUE
III. 4n + 10
4n + 10 = 4*(15a + 5) + 10 = 60a + 20 + 10 = 15*4a + 30 = 15*(4a + 2)
=> 4n + 10 when divided by 15 gives 4a + 2 as quotient and 0 as remainder => FALSE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
Theory: Dividend = Divisor*Quotient + Remainder
n -> Dividend
15 -> Divisor
a -> Quotient (Assume)
5 -> Remainders
=> n = 15*a + 5 = 15a + 5
Which of the following has a remainder of 10 when divided by 15
I. 3n
3n = 3*(15a + 5) = 45a + 15 = 15*(3a+1)
=> 3n when divided by 15 gives 3a+1 as quotient and 0 as remainder => FALSE
II. 5n
5n = 5*(15a + 5) = 75a + 25 = 75a + 15 + 10 = 15*(5a+3) + 10
=> 5n when divided by 15 gives 5a+3 as quotient and 10 as remainder => TRUE
III. 4n + 10
4n + 10 = 4*(15a + 5) + 10 = 60a + 20 + 10 = 15*4a + 30 = 15*(4a + 2)
=> 4n + 10 when divided by 15 gives 4a + 2 as quotient and 0 as remainder => FALSE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Remainders
