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16 Sep 2014, 00:28
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If \(ab=ac\), is \(b=2\)?
(1) \(c = 1\)
(2) \(a\) is a prime number and \(c\) is NOT a prime number
(1) \(c = 1\)
(2) \(a\) is a prime number and \(c\) is NOT a prime number
16 Sep 2014, 00:28
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Official Solution:
If \(ab=ac\), is \(b=2\)?
Notice that, we cannot simply cancel out \(a\) from both sides of \(ab=ac\) to conclude that \(b=c\) since \(a\) could be zero and division by zero is not allowed. Instead, we can rearrange the equation as follows:
\(a(b-c)=0\)
This implies that either \(a=0\) or \(b=c\).
(1) \(c=1\).
If \(a=0\), then \(b\), irrespective of the value of \(c\), can take any value, including 2. Therefore, this statement alone is not sufficient to determine whether \(b=2\) or not.
(2) \(a\) is a prime number and \(c\) is NOT a prime number.
Since \(a\) is a prime number, it cannot be zero, and therefore \(b=c\). Since \(c\) is not a prime number, we know that \(b\) is also not a prime number and hence cannot be 2. Therefore, this statement alone is sufficient to determine that \(b\) is not equal to 2. Sufficient
Answer: B
If \(ab=ac\), is \(b=2\)?
Notice that, we cannot simply cancel out \(a\) from both sides of \(ab=ac\) to conclude that \(b=c\) since \(a\) could be zero and division by zero is not allowed. Instead, we can rearrange the equation as follows:
\(a(b-c)=0\)
This implies that either \(a=0\) or \(b=c\).
(1) \(c=1\).
If \(a=0\), then \(b\), irrespective of the value of \(c\), can take any value, including 2. Therefore, this statement alone is not sufficient to determine whether \(b=2\) or not.
(2) \(a\) is a prime number and \(c\) is NOT a prime number.
Since \(a\) is a prime number, it cannot be zero, and therefore \(b=c\). Since \(c\) is not a prime number, we know that \(b\) is also not a prime number and hence cannot be 2. Therefore, this statement alone is sufficient to determine that \(b\) is not equal to 2. Sufficient
Answer: B
General Discussion
17 Nov 2015, 17:26
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B it is!
First step, Try solving or simplifying the question stem. When ab = ac, we cannot cancel out 'a' until we know the value of 'a'. So first thought should be what if if a=0? In this case we cannot divide both sides by a.
Statement 1: Value of 'c' only won't help to find out value of b. As explained above, if a=0, then LHS=RHS irrespective of values of b and c. Clearly insufficient.
Statement 2: a is a prime number and c is NOT a prime number.
This means a is not zero, rather a positive number. So let's cancel on both sides. Thus b=c. Now, c is given to be non-prime. So whatever be it's value, it is certainly not 2 or 3 or 5 or 7 or so on. Therefore, we can conclude that b (which is equal to c) is also not equal to 2. Sufficient.
First step, Try solving or simplifying the question stem. When ab = ac, we cannot cancel out 'a' until we know the value of 'a'. So first thought should be what if if a=0? In this case we cannot divide both sides by a.
Statement 1: Value of 'c' only won't help to find out value of b. As explained above, if a=0, then LHS=RHS irrespective of values of b and c. Clearly insufficient.
Statement 2: a is a prime number and c is NOT a prime number.
This means a is not zero, rather a positive number. So let's cancel on both sides. Thus b=c. Now, c is given to be non-prime. So whatever be it's value, it is certainly not 2 or 3 or 5 or 7 or so on. Therefore, we can conclude that b (which is equal to c) is also not equal to 2. Sufficient.
