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Question Stats:
34% (01:18) correct 66% (01:22) wrong based on 94 sessions
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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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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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Re: M0624
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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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Re: M0624
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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 !!!










