Brent@GMATPrepNow wrote: ↑

Thu Sep 23, 2021 10:13 am

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?
I. a < b
II. c < d
III. b < d

A) II only
B) III only
C) I and II
D) II and III
E) I and III

Answer: A

Source: GMATPrepNow.com

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