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29 Oct 2018, 10:58
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
40% (02:20) correct
60%
(02:10)
wrong
based on 227
sessions
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If x and y are different positive integers, which of the following COULD be true:
i) When x is divided by y, the remainder is 2x
ii) When x is divided by 2y, the remainder is y
iii) When (2x + y) is divided by (x + y), the remainder is y
A) i only
B) ii only
C) iii only
D) i & ii only
E) ii & iii only
ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.
Related question: if-x-and-y-are-different-positive-integers-which-of-the-following-cou-280118.html
i) When x is divided by y, the remainder is 2x
ii) When x is divided by 2y, the remainder is y
iii) When (2x + y) is divided by (x + y), the remainder is y
A) i only
B) ii only
C) iii only
D) i & ii only
E) ii & iii only
ASIDE: Many Integer Properties questions can be solved by identifying values that satisfy some given conditions. This question is intended to strengthen that skill.
Related question: if-x-and-y-are-different-positive-integers-which-of-the-following-cou-280118.html
29 Oct 2018, 12:16
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If x and y are different positive integers, which of the following COULD be true:
i) When x is divided by y, the remainder is 2x
Remainder cannot be > than the dividend ... So not possible
ii) When x is divided by 2y, the remainder is y
when x =3y or x=5 y or x=7y and so on, this will be true
iii) When (2x + y) is divided by (x + y), the remainder is y
2x+y=x+x+y will leave a remainder of x when divided by x+y..
But it is given as y, this means x=y ..
But it is given that x and y are distinct so not possible
Only (ii)
B
i) When x is divided by y, the remainder is 2x
Remainder cannot be > than the dividend ... So not possible
ii) When x is divided by 2y, the remainder is y
when x =3y or x=5 y or x=7y and so on, this will be true
iii) When (2x + y) is divided by (x + y), the remainder is y
2x+y=x+x+y will leave a remainder of x when divided by x+y..
But it is given as y, this means x=y ..
But it is given that x and y are distinct so not possible
Only (ii)
B
Updated on: 03 Nov 2018, 09:07
Originally posted by BrentGMATPrepNow on 03 Nov 2018, 09:03.
Last edited by BrentGMATPrepNow on 03 Nov 2018, 09:07, edited 1 time in total.
Last edited by BrentGMATPrepNow on 03 Nov 2018, 09:07, edited 1 time in total.
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GMATPrepNow
i) When x is divided by y, the remainder is 2x
The remainder cannot be greater than the dividend (the number we're dividing)
For example, it CANNOT be the case that 17 divided by 5 leaves a remainder of 34
Statement i can never be true
Check the answer choices. . . . ELIMINATE A and D
ii) When x is divided by 2y, the remainder is y
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, some possible values of x are: y, y + 2y, y + 4y, y + 6y, . . . etc
Let's TEST the 1st option: x = y. No good.
The question tells us that x and y are different
So, let's TEST the 2nd option: x = y + 2y = 3y
So, how about x = 15 and y = 5
When we plug those values into statement ii, we get: When 15 is divided by 10, the remainder is 5
PERFECT!
Statement ii CAN be true.
Check the answer choices. . . . ELIMINATE C
iii) When (2x + y) is divided by (x + y), the remainder is y
When we apply the above rule, we get....
Some possible values of (2x + y) are: y, y + (x + y), y + 2(x + y), y + 3(x + y), . . . etc
Let's TEST the 1st option: (2x + y) = y.
Solve to get x = 0
No good. We're told x is POSITIVE
Let's TEST the 2nd option: (2x + y) = y + (x + y)
Solve to get: x = y
No good. The question tells us that x and y are different
Let's TEST the 3rd option: (2x + y) = y + 2(x + y)
Solve to get: y = 0
No good. We're told y is POSITIVE
Let's TEST the 4th option: (2x + y) = y + 3(x + y)
Solve to get: x = -3y
No good. If y is POSITIVE, then that means x is NEGATIVE, but we're told x is POSITIVE
Let's TEST the 5th option: (2x + y) = y + 4(x + y)
Solve to get: 2x = -4y
No good. If y is POSITIVE, then that means x is NEGATIVE, but we're told x is POSITIVE
At this point, we should recognize that, if we keep going, we'll keep running into the same problem where either x or y is NEGATIVE (which contradicts the given information.
So, statement iii can never be true
Answer: B
Cheers,
Brent
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