BTGModeratorVI wrote: ↑Tue Dec 15, 2020 7:02 am
If x and y are positive integers, is the product xy divisible by 9?
(1) The product xy is divisible by 6.
(2) x and y are perfect squares.
Answer:
C
Source: Veritas Prep
Kudos for a correct solution.[/quote]
Target question: Is the product xy divisible by 9?
Given: x and y are positive integers
Statement 1: The product xy is divisible by 6
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 3 and y = 6, in which case
xy IS divisible by 9
Case b: x = 2 and y = 3, in which case
xy is NOT divisible by 9
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: The largest and smallest of the numbers are odd
This statement doesn't FEEL sufficient either, so I'll TEST some values.
Case a: x = 1 and y = 9, in which case
xy IS divisible by 9
Case b: x = 1 and y = 4, in which case
xy is NOT divisible by 9
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that either p or q is divisible by 3
Statement 2 tells us that both p and q are perfect squares. So, whichever number is divisible by 3 must ALSO be divisible by 9. Since one of the values (x or y) must be divisible by 9, we can be CERTAIN that
the product xy is divisible by 9
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
