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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If a, b, c and d are positive integers such that a divided by b equals
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23 Sep 2021, 08:50
23 Sep 2021, 08:50
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If a, b, c and d are positive integers such that a divided by b equals c with remainder d, which of the following COULD be true?
A) II only
B) I and II
C) II and III
D) I and III
E) I, II and III
- I. a < b
II. c < d
III. b < d
A) II only
B) I and II
C) II and III
D) I and III
E) I, II and III
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If a, b, c and d are positive integers such that a divided by b equals
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24 Sep 2021, 05:12
24 Sep 2021, 05:12
1
GreenlightTestPrep wrote:
If a, b, c and d are positive integers such that a divided by b equals c with remainder d, which of the following COULD be true?
A) II only
B) I and II
C) II and III
D) I and III
E) I, II and III
- I. a < b
II. c < d
III. b < d
A) II only
B) I and II
C) II and III
D) I and III
E) I, II and III
I. a < b
If a is less than b, then the larger number will divide into the smaller number ZERO times.
For example, 3 divided by 7 equals 0 with remainder 3.
In this example, a = 3, b = 7, c = 0 and d = 3
Since we're told c is a positive integer, it can't be the case that c = 0
In general, if a < b, then a divided by b equals 0 with remainder a.
So, a < b is impossible, which means statement I can't be true.
II. c < d
This is possible.
For example, 7 divided by 4 equals 1 with remainder 3.
In this example, a = 7, b = 4, c = 1 and d = 3, which means c < d.
So statement II CAN be true.
III. b < d
Useful property: 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
So, for the given information, we can conclude that d < b, which is the OPPOSITE of what statement III is saying.
In other words, statement III can't be true.
Answer: A
Re: If a, b, c and d are positive integers such that a divided by b equals
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12 Jan 2023, 16:32
12 Jan 2023, 16:32
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
