Bunuel wrote:
If a is a 3-digit integer and b is a 3-digit integer, is the units digit of the product of a and b greater than 5?
(1) The units digit of a is 4.
(2) The units digit of b is 7.
Target question: Is the units digit of the product of a and b greater than 5? Given: a is a 3-digit integer and b is a 3-digit integer Statement 1: The units digit of a is 4 There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 104 and b = 102. In this case the product ab = (104)(102) = ----
8. So,
the units digit of ab IS greater than 5Case b: a = 104 and b = 100. In this case the product ab = (104)(100) = ----
0. So,
the units digit of ab is NOT greater than 5Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
ASIDE: When I write that the product ab = (104)(102) = ----
8, I'm ignoring all digits in the product OTHER THAN the units digit, since that's all we care about.
Statement 2: The units digit of b is 7 There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 104 and b = 107. In this case the product ab = (104)(107) = ----
8. So,
the units digit of ab IS greater than 5Case b: a = 100 and b = 107. In this case the product ab = (100)(107) = ----
0. So,
the units digit of ab is NOT greater than 5Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that a = --
4Statement 2 tells us that b = --
7So, ab = (--
4)(--
7) = -----
8So,
the units digit of ab IS greater than 5Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer:
Cheers,
Brent