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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
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16 Sep 2014, 00:28
Official Solution: 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 and factor out \(a\): \(a(bc)=0\): either \(a=0\) or \(b=c\). (1) \(c=1\). If \(a=0\) then \(b\) can take any value irrespective of the value of \(c\). Not sufficient. (2) \(a\) is a prime number and \(c\) is NOT a prime number. Now, \(a=\text{prime}\) means that \(a \ne 0\), so it must be true that \(b=c\). Now, since also given that \(c \ne \text{prime}\) then \(b\) is also not equal to a prime number so it cannot equal a prime number 2. Sufficient. Answer: B
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Re: M0624
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04 Nov 2015, 19:26
Hi,
I'm struggling with understanding the answer explanation. For (2), if c is not a prime and thus b is not a prime either, why does that mean that b (and c) needs to be 2 necessarily? Can it not be any other nonprime numbers such as 4 or 6?



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Re: M0624
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04 Nov 2015, 21:56
rammangst wrote: Hi,
I'm struggling with understanding the answer explanation. For (2), if c is not a prime and thus b is not a prime either, why does that mean that b (and c) needs to be 2 necessarily? Can it not be any other nonprime numbers such as 4 or 6? hi, the stat 2 tells us (2) a is a prime number and c is NOT a prime number and it is given that " ab=ac ".. or abac=0.. a(bc)=0.. this means either a=0, b=c, or all three could be 0.. statement 2 gives us 'a' is a prime number, so' a' cannot be 0, therefore b=c... also it is given that 'c' is not a prime number, so 'b' is also not a prime number, so 'b' cannot be 2.... therefore statement 2 is suff to ans the question with 'NO'.. hope it helped
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Re: M0624
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17 Nov 2015, 17:26
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 nonprime. 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.
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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
Explanation ab=ac >a(bc)=0 1)c=1 ,from (1) we cant confirm whether b=2 or not. 2)a is a prime number and c is NOT a prime number This implies a is not 0 and b=c .Further since c is NOT a prime number ,c is not equal to 2.Hence sufficient.
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Re: M0624
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11 Jan 2016, 14:50
Statement 2 is tricky! At first I thought it was insufficient since C is infinite but on second glance it clearly answers the statement!



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Bunuel wrote: Official Solution:
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 and factor out \(a\): \(a(bc)=0\): either \(a=0\) or \(b=c\). (1) \(c=1\). If \(a=0\) then \(b\) can take any value irrespective of the value of \(c\). Not sufficient. (2) \(a\) is a prime number and \(c\) is NOT a prime number. Now, \(a=\text{prime}\) means that \(a \ne 0\), so it must be true that \(b=c\). Now, since also given that \(c \ne \text{prime}\) then \(b\) is also not equal to a prime number so it cannot equal a prime number 2. Sufficient.
Answer: B From Stat 1, how can b take any value when it is given as c=1 ?



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17 Jun 2016, 06:20
avdgmat4777 wrote: Bunuel wrote: Official Solution:
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 and factor out \(a\): \(a(bc)=0\): either \(a=0\) or \(b=c\). (1) \(c=1\). If \(a=0\) then \(b\) can take any value irrespective of the value of \(c\). Not sufficient. (2) \(a\) is a prime number and \(c\) is NOT a prime number. Now, \(a=\text{prime}\) means that \(a \ne 0\), so it must be true that \(b=c\). Now, since also given that \(c \ne \text{prime}\) then \(b\) is also not equal to a prime number so it cannot equal a prime number 2. Sufficient.
Answer: B From Stat 1, how can b take any value when it is given as c=1 ? It says: for c=1, IF a=0, then b can take any value.
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M0624
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Updated on: 16 Aug 2016, 00:26
from ab = ac; => a(bc) = 0; it means either a=0 or b=c.
Now, from stat 1 we do not know what would be the value of a ? if a = 0 then b can be take any value and equation ab = ac will still satisfy.right ! so stat 1 not sufficient.
from stat 2 we are given that a is not zero. now if a is not zero, we can say b = c; (from either a= 0 or b = c). and c is not a prime number, then b also wont be a prime number. is b = 2 ? NO! (2 is a prime) stat 2 is sufficient.
Originally posted by minhaz3333 on 14 Aug 2016, 05:45.
Last edited by minhaz3333 on 16 Aug 2016, 00:26, edited 1 time in total.



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15 Aug 2016, 05:16
I think this is a highquality question and I agree with explanation.



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30 Aug 2016, 05:11
I think this is a highquality question and I agree with explanation.



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Re: M0624
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31 Jan 2018, 12:15
Hi Bunuel,
From the question stem, we already got that a = 0 and b = c. This is what we derived and is valid.
But in statement 2, we have information that a is prime and obviously prime number is only positive and can't be zero. Ok.. now a is not equal 0 , but from question stem we have concluded that a is zero but this statement 2 is showing as a is +ve and this statement is contracting with the question stem. Do we get such question really in GMAT.



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31 Jan 2018, 12:25
msk0657 wrote: Hi Bunuel,
From the question stem, we already got that a = 0 and b = c. This is what we derived and is valid.
But in statement 2, we have information that a is prime and obviously prime number is only positive and can't be zero. Ok.. now a is not equal 0 , but from question stem we have concluded that a is zero but this statement 2 is showing as a is +ve and this statement is contracting with the question stem. Do we get such question really in GMAT. From the stem we got that a = 0 OR b = c (OR not AND). So, if b = c, a is not necessarily 0. From (2) \(a=\text{prime}\) means that \(a \ne 0\), so it must be true that \(b=c\).
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Re: M0624
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17 Feb 2018, 00:45
Good question. I missed to consider a=0 in option A and considered it as sufficient and marked C as answer incorrectly.
Thanks Bunuel for explanation



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18 Mar 2019, 19:44
I think this is a highquality question and I agree with explanation. Really good question !!!



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29 May 2019, 03:40
Bunuel, if division by 0 is not allowed then why is it being assessed in this question? I thought the only time we really need to worry about the sign or value of a variable is during inequalities, since we may need to flip the signs etc.



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29 May 2019, 03:43
dcummins wrote: Bunuel, if division by 0 is not allowed then why is it being assessed in this question? I thought the only time we really need to worry about the sign or value of a variable is during inequalities, since we may need to flip the signs etc. Can you please reread the solution and then rephrase your question? Where are we dividing by 0? Where are we concerned about the sign?
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29 May 2019, 04:00
Bunuel wrote: dcummins wrote: Bunuel, if division by 0 is not allowed then why is it being assessed in this question? I thought the only time we really need to worry about the sign or value of a variable is during inequalities, since we may need to flip the signs etc. Can you please reread the solution and then rephrase your question? Where are we dividing by 0? Where are we concerned about the sign? I reread the solution and understand it, but I still think the phrase "since a can be zero and division by zero is not allowed" is confusing since it's more to do with the fact that a can be 0, making (0)b=(0)c, then it has to do with any "division by zero"



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17 Jun 2019, 08:07
I think this is a highquality question and I agree with explanation. Oh boi







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