Data Sufficiency

jjjinapinch 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.

Official Guide question
Answer: C

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 5
Case 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 5
Since 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 5
Case 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 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that a = --4
Statement 2 tells us that b = --7
So, ab = (--4)(--7) = -----8
So, the units digit of ab IS greater than 5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

jjjinapinch 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.

We are given that a is a 3-digit integer and b is a 3-digit integer and need to determine whether the product of a and b is greater than 5.

Statement One Alone:

The units digit of a is 4.

Statement one alone is not sufficient to answer the question. For example, if the units digit of b is 1, then the units digit of the product of a and b is 4, which is less than 5; however, if the units digit of b is 2, then the units digit of the product of a and b is 8, which is greater than 5.

Statement Two Alone:

The units digit of b is 7.

Statement two alone is not sufficient to answer the question. For example, if the units digit of a is 1, then the units digit of the product of a and b is 7, which is greater than 5; however, if the units digit of a is 0, then the units digit of the product of a and b is 0, which is less than 5.

Statements One and Two Together:

Using the information from statements one and two, we see that since the product of the units digits of a and b is 4 x 7 = 28, the units digit of the product of a and b is 8, which is greater than 5.

Answer: C