OG If a is a 3-digit integer and b is a 3-digit integer

[A AbeNeedsAnswers]

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.

C

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Hi AbeNeedsAnswers,

We're told that A is a 3-digit integer and B is a 3-digit integer. We're asked if the UNITS DIGIT of the PRODUCT of A and B is greater than 5? This is a YES/NO question and can be solved by TESTing VALUES. Since we're asked about the Units Digit of that product, we only need the Units Digits of A and B to answer this question.

1) The units digit of A is 4.

IF.... A = 104 and B = 100, then the Units Digit of the product will be (4)(0) = 0 and the answer to the question is NO.
IF.... A = 104 and B = 107, then the Units Digit of the product will be (4)(7) = 8 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) The units digit of B is 7.

IF.... A = 100 and B = 107, then the Units Digit of the product will be (0)(7) = 0 and the answer to the question is NO.
IF.... A = 104 and B = 107, then the Units Digit of the product will be (4)(7) = 8 and the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know exactly what the two Units Digits will be (4 and 7, respectively), so we know that the product will ALWAYS have a Units Digit of (4)(7) = 8.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

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.

C

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

[Brent@GMATPrepNow]

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.

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

[A AdityaBir]

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.

C

1) if unit digit of a is 4
Since unit digit of b can be anything between 0-9, so we can't determine the unit digit og ab.
Statement 1 alone is not sufficient.
2) if unit digit of b is 7
Same logic as above.
Statement 2 alone is also not sufficient.
Combining 1) and 2).
unit digit of ab comes out to be 8, which is greater than 5.
1) and 2) combined are sufficient.
Hence option C is correct.