Is abc = 2?

Is \(abc = 2\)?

We must determine whether \(abc = 2\).

Statement 1 says that \(ab = 2\). Since this gives us no information about \(c\), there is no way to determine whether \(abc = 2\). If \(c = 1\), then \(abc = 2\); if \(c = 2\), then \(abc = 4\). Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice must be B, C, or E.

Statement 2 says that \(bc = 2\). In this case, we are given no information about \(a\), and so there is no way to determine whether \(abc = 2\). If \(a = 1\), then \(abc = 2\); if \(a = 2\), then \(abc = 4\). Statement 2 is NOT sufficient to answer the question. Eliminate answer choice B. The correct answer choice must be either C or E.

Taking the statements together, we know that \(ab = 2\) and \(bc = 2\). Note that if \(a = 1\), \(b = 2\), and \(c = 1\), then both statements are satisfied and \(abc = 2\). However, if \(a = 4\), \(b = 0.5\) and \(c = 4\), then both statements are still satisfied, only now \(abc = 8\). Together, the statements are NOT sufficient.

Answer: E.

Statement 1 and 2, are by themselves not sufficient to conclusively say whether abc =2 or not .

Combining 1 and 2.

If a = 1, b= 2 and c = 1, we can say abc = 2 . True
If a =sqrt(2), b=sqrt(2) and c = sqrt(2), then abc = 2* sqrt(2). False

Hence the answer is E

from 1 : ab = 2
multiplying both sides by c, we get
=> abc = 2c

Value of c is not known, hence 1 is insufficient

from 2: bc = 2
multiplying both sides by a, we get
=> abc = 2a

Value of a is unknown, hence 2 is also insufficient

Combining 1 and 2,

abc = 2c
abc = 2a

=> 2c = 2a
=> c=a
hence abc = ab[a] = [a^2]*b
which is not equal to 2 since we do not know the value of a and b separately



Hence E is the answer