If ab = ac is b = 2?

Question: If ab = ac is b = 2?

1. c = 1
2. a is a prime number and c is NOT a prime number

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“If ab = ac is b = 2?" is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Notice that we cannot reduce ab = ac by a and write b = c, since a can be zero and division by zero is not allowed.

Rearrange the given expression as:

ab = ac

ab – ac = 0

a (b – c) = 0

Now, considering the statement (1), c = 1

If a = 0 then b can take any value irrespective of the value of c.

Hence, this statement is not sufficient.

Now, considering the statement (2), a is a prime number and c is NOT a prime number

a = prime means that a \(\neq \) 0, so it must be true that = c.

Now, since also given c \(\neq \) prime, then b is also not equal to a prime number so it cannot equal a prime number 2.

Hence, this statement is sufficient.

Correct Answer: B

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