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If ab is divisible by c, which of the following cannot be t [#permalink]
07 Aug 2017, 13:08
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If ab is divisible by c, which of the following cannot be true? A. a is divisible by c. B. a is not divisible by c. C. c is a prime number. D. ab + c is odd and c is odd. E. ab + c is odd and c is even.
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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
10 Jan 2018, 00:21
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This can be solved by substituting values for a,b and c.
For options A Lets consider a =4, b=1 and c=2 now a is divisible by c. This is possible
For option B Lets consider a =1, b=4 and c=2 now a is not divisible by c. This is possible
For option C in the above two examples c is a prime number (c=2). Thus this is possible
For option D and E let us consider a = 2, b=3 and c = 3 Now ab+c = 2*3 + 3 = 9 which is odd but c is odd as well. In no case can ab+c be odd and c be even. Thus D is possible while E is not.
Hence E is the answer.



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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
22 Feb 2018, 18:19
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answer: E ab is an integer which a is the tens digit and b is a unit digit. It is divisible by c so: ab / c = x and (c * x) = ab now we try to find a condition for each of the options to be true A: a= 30 and c = 3. Then a is divisible by c. B: a= 12 and c=4. Then a is not divisible by c. C: a= even and c=2. Then c is prime. D: ab=30 and c=3. Then both ab+c=33 and c are odd. In the other words: (ab+c)= (c*x+c)= c*(x+1) if x is even and c is odd then ab+c is odd and it’s possible. F: as said in D, ab+c = c*(x+1). If ab+c is odd then c*(x+1) is odd. It means that c is odd and x is even. So it is impossible for c to be even when ab+c is odd.
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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
23 Feb 2018, 09:04
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According to question, ab is divisible by c. Thus, either a is divisibe by c and/or b is divisible by c. Considering the options:
A: a might or might not be divisible by c. It is not necessarily false. B: same reasoning as A C: Let c be a prime number, it can still divide ab D: If c is odd; ab+c =ck+c =c(k+1) Since, value of k is unknown, we cannot say that k+1 is even or odd. Thus, ab+c might be even or odd. E: If c is even; ab+c =ck+c =c(k+1) Since, c is even, the value c(k+1) is also even. Hence, ab+c is also even. Thus, it is this option which is false.
Answer: E



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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
07 Jul 2018, 11:25
FatemehAsgarinejad wrote: answer: E ab is an integer which a is the tens digit and b is a unit digit. It is divisible by c so: ab / c = x and (c * x) = ab now we try to find a condition for each of the options to be true A: a= 30 and c = 3. Then a is divisible by c. B: a= 12 and c=4. Then a is not divisible by c. C: a= even and c=2. Then c is prime. D: ab=30 and c=3. Then both ab+c=33 and c are odd. In the other words: (ab+c)= (c*x+c)= c*(x+1) if x is even and c is odd then ab+c is odd and it’s possible. F: as said in D, ab+c = c*(x+1). If ab+c is odd then c*(x+1) is odd. It means that c is odd and x is even. So it is impossible for c to be even when ab+c is odd.
Could you please explain it more clearly?



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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
07 Dec 2019, 09:23
Carcass wrote: If ab is divisible by c, which of the following cannot be true? A. a is divisible by c. B. a is not divisible by c. C. c is a prime number. D. ab + c is odd and c is odd. E. ab + c is odd and c is even. Official Explanation If ab is divisible by c, then a might be divisible by c (e.g., if a = 8, b = 3, and c = 2). Choice (A) is possible and thus incorrect. Additionally, this numeric example demonstrates that choice (C) is possible and thus incorrect, since 2 is a prime number. If ab is divisible by c, then a might also not be divisible by c (for example, if a = 3, b = 4, and c = 6). Choice (B) is possible and thus incorrect. In choice (D), if c is odd and ab + c is odd, then ab must be even. An even divided by an odd can result in an integer (e.g., if ab = 12 and c = 3). Choice (D) is possible and thus incorrect. Finally, in choice (E), if c is even and ab + c is odd, then ab must be odd. An odd divided by an even will never result in an integer; that is, if ab is odd and c is even, ab will never be divisible by c. Choice (E) is impossible and therefore is the correct answer.
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Re: If ab is divisible by c, which of the following cannot be t
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07 Dec 2019, 09:23





