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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If ab is divisible by c, which of the following cannot be t  Question banks Downloads My Bookmarks Reviews Important topics
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Founder  Joined: 18 Apr 2015
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If ab is divisible by c, which of the following cannot be t [#permalink]
Expert's post 00:00

Question Stats: 61% (01:12) correct 38% (01:16) wrong based on 102 sessions

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.
[Reveal] Spoiler: OA

_________________ Intern Joined: 20 Sep 2017
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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
1
KUDOS
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. Manager Joined: 22 Feb 2018
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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
2
KUDOS
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.

_________________ Intern Joined: 17 Jun 2017
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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
1
KUDOS
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.

Intern Joined: 14 Jun 2018
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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
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?
Director  Joined: 22 Jun 2019
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Re: If ab is divisible by c, which of the following cannot be t [#permalink]
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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