magpie16 wrote:For nonnegative integers x and y, what is the remainder when x is divided by y?
(1) x/y = 13.8
(2) The numbers x and y have a combined total of less than 5 digits.
Target question:
What is the remainder when x is divided by y?
Statement 1: x/y = 13.8
In other words, x/y = 13 4/5
Or . . . x/y = 69/5
At this point, we can see that there are several pairs of values that meet this condition. Here are three:
Case a: x = 69 and y = 5, in which case
the remainder is 4 when x is divided by y
Case b: x = 138 and y = 10, in which case
the remainder is 8 when x is divided by y
Case c: x = 1380 and y = 100, in which case
the remainder is 80 when x is divided by y
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The numbers x and y have a combined total of less than 5 digits.
There are several pairs of values that meet this condition. Here are two:
Case a: x = 2 and y = 2, in which case
the remainder is 0 when x is divided by y
Case b: x = 3 and y = 2, in which case
the remainder is 1 when x is divided by y
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 1 tells us that x and y must be such that x/y = 69/5, so x and y could equal
69 and 5, or
138 and 10, or
207 and 15, or
276 and 20, etc . . .
Statement 2 tells us that the number pair must have a total of 2, 3 or 4 digits.
Only the first pair of values meets this second criterion, so
it must be the case that x = 69 and y = 5
Since we can now answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
