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If x and y are different positive integers, which of the
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28 Oct 2018, 14:11
28 Oct 2018, 14:11
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If x and y are different positive integers, which of the following COULD be true:
Select all that apply.
A) When x is divided by y, the remainder is x
B) When 2x is divided by y, the remainder is x
C) When x+y is divided by x , the remainder is x-y
ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.
Answer:
Select all that apply.
A) When x is divided by y, the remainder is x
B) When 2x is divided by y, the remainder is x
C) When x+y is divided by x , the remainder is x-y
ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.
Answer:
Show: ::
A, C
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x and y are different positive integers, which of the
[#permalink]
30 Oct 2018, 13:26
30 Oct 2018, 13:26
3
GreenlightTestPrep wrote:
If x and y are different positive integers, which of the following COULD be true:
Select all that apply.
A) When x is divided by y, the remainder is x
B) When 2x is divided by y, the remainder is x
C) When x+y is divided by x , the remainder is x-y
Select all that apply.
A) When x is divided by y, the remainder is x
B) When 2x is divided by y, the remainder is x
C) When x+y is divided by x , the remainder is x-y
A) When x is divided by y, the remainder is x
This occurs any time x < y
For example, if x = 5 and y = 7, then statement A becomes: When 5 is divided by 7, the remainder is 5
So TRUE!
-----------------------------------------------------
B) When 2x is divided by y, the remainder is x
Nice rule: 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.
So, from statement B, we can say: some possible values of 2x are: x, x + y, x + 2y, x + 3y, . . . etc
Let's examine the first option: 2x = x. Solve to get x = 0, but we're told x is POSITIVE No good.
Check the second option: 2x = x + y. Solve to get x = y. This means the remainder is y (aka x), but the remainder CANNOT be greater than the divisor. See the rule below:
When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
Check the third option: 2x = x + 2y. Solve to get x = 2y.
This means the remainder = 2y, which means the remainder is greater than the divisor (see rule above). No good.
In fact, we can see that, with all of the possible values of 2x, the remainder will be greater than the divisor.
So, statement B is NOT TRUE
-----------------------------------------------------
C) When x+y is divided by x, the remainder is x-y
Some possible values of x+y are: (x-y), (x-y)+x, (x-y)+2x, (x-y)+3x, . . . etc
Let's examine the first option: x+y = x-y
Solve to get y = 0. No good.
Check the second option: x+y = (x-y)+x
Simplify: x+y = 2x - y
Solve to get: x = 2y
So, one possible case is: x = 6 and y = 3
Statement C becomes: When (6 + 3) is divided by 6, the remainder is 3
So TRUE!
------------------------------
Answer: A, C
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Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
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Re: If x and y are different positive integers, which of the
[#permalink]
20 Feb 2021, 11:58
20 Feb 2021, 11:58
2
GreenlightTestPrep wrote:
If x and y are different positive integers, which of the following COULD be true:
Select all that apply.
A) When x is divided by y, the remainder is x
B) When 2x is divided by y, the remainder is x
C) When x+y is divided by x , the remainder is x-y
ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.
Answer:
Select all that apply.
A) When x is divided by y, the remainder is x
B) When 2x is divided by y, the remainder is x
C) When x+y is divided by x , the remainder is x-y
ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.
Answer:
Show: ::
A, C
Given: \(x > 0\) and \(y > 0\)
A. Let \(x = 6\) and \(y = 7\)
Then, \(\frac{6}{7}\) will give a remainder as 6
B. \(x = 6\) and \(y = 7\)
Then, \(\frac{12}{7}\) will give a remainder as 5
As a matter of fact, pick any value of \(x < 7\), you will never get the remainder as the same number
C. \(x = 10\) and \(y = 5\) ................ {x has to be grater than y}
Then, \(\frac{15}{10}\) will give a remainder of 5, which is equal to \((10 - 5)\) only
Hence, options A and C
