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Which of the following CANNOT result in an integer?

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Which of the following CANNOT result in an integer?  [#permalink]

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New post 05 Nov 2018, 23:28
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Which of the following CANNOT result in an integer?

A. The product of two integers divided by the reciprocal of a different integer
B. An even integer divided by 7
C. The quotient of two distinct prime numbers
D. A multiple of 11 divided by 3
E. The sum of two odd integers divided by 2

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Re: Which of the following CANNOT result in an integer?  [#permalink]

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New post 06 Nov 2018, 01:11
Bunuel wrote:
Which of the following CANNOT result in an integer?

A. The product of two integers divided by the reciprocal of a different integer
B. An even integer divided by 7
C. The quotient of two distinct prime numbers
D. A multiple of 11 divided by 3
E. The sum of two odd integers divided by 2



A. The product of two integers divided by the reciprocal of a different integer

\(\frac{2*3}{(\frac{1}{5})} = 2*3*5\) (an integer)

B. An even integer divided by 7

\(\frac{14}{7} = 2\) (an integer)

C. The quotient of two distinct prime numbers

When one prime number is divided by another, the answer cannot be an integer (though I wouldn't call it quotient since that implies quotient-remainder set up). One prime number is never divisible by another prime number since prime number has only two divisors - 1 and itself.

D. A multiple of 11 divided by 3

\(\frac{33}{3} = 11\) (an integer)

E. The sum of two odd integers divided by 2

\(\frac{(3 + 5)}{2} = 4\) (an integer)

Answer (C)
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Re: Which of the following CANNOT result in an integer?  [#permalink]

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New post 20 Nov 2018, 02:20
VeritasKarishma wrote:
Bunuel wrote:
Which of the following CANNOT result in an integer?

A. The product of two integers divided by the reciprocal of a different integer
B. An even integer divided by 7
C. The quotient of two distinct prime numbers
D. A multiple of 11 divided by 3
E. The sum of two odd integers divided by 2



A. The product of two integers divided by the reciprocal of a different integer

\(\frac{2*3}{(\frac{1}{5})} = 2*3*5\) (an integer)

B. An even integer divided by 7

\(\frac{14}{7} = 2\) (an integer)

C. The quotient of two distinct prime numbers

When one prime number is divided by another, the answer cannot be an integer (though I wouldn't call it quotient since that implies quotient-remainder set up). One prime number is never divisible by another prime number since prime number has only two divisors - 1 and itself.

D. A multiple of 11 divided by 3

\(\frac{33}{3} = 11\) (an integer)

E. The sum of two odd integers divided by 2

\(\frac{(3 + 5)}{2} = 4\) (an integer)

Answer (C)



Quotient will not be 0 here ?
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Which of the following CANNOT result in an integer?  [#permalink]

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New post 31 Dec 2018, 08:14
VeritasKarishma wrote:
Bunuel wrote:
Which of the following CANNOT result in an integer?

A. The product of two integers divided by the reciprocal of a different integer
B. An even integer divided by 7
C. The quotient of two distinct prime numbers
D. A multiple of 11 divided by 3
E. The sum of two odd integers divided by 2



A. The product of two integers divided by the reciprocal of a different integer

\(\frac{2*3}{(\frac{1}{5})} = 2*3*5\) (an integer)

B. An even integer divided by 7

\(\frac{14}{7} = 2\) (an integer)

C. The quotient of two distinct prime numbers

When one prime number is divided by another, the answer cannot be an integer (though I wouldn't call it quotient since that implies quotient-remainder set up). One prime number is never divisible by another prime number since prime number has only two divisors - 1 and itself.

D. A multiple of 11 divided by 3

\(\frac{33}{3} = 11\) (an integer)

E. The sum of two odd integers divided by 2

\(\frac{(3 + 5)}{2} = 4\) (an integer)

Answer (C)


Hello!

How did you understand that one prime number is dividing another prime number?

I am a bit confused with the wording of the question.

Can´t it be like the following?

2*3 divided by 6 = quotient would be 1.

Regards!
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Re: Which of the following CANNOT result in an integer?  [#permalink]

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New post 01 Jan 2019, 02:35
jfranciscocuencag wrote:
VeritasKarishma wrote:
Bunuel wrote:
Which of the following CANNOT result in an integer?

A. The product of two integers divided by the reciprocal of a different integer
B. An even integer divided by 7
C. The quotient of two distinct prime numbers
D. A multiple of 11 divided by 3
E. The sum of two odd integers divided by 2



A. The product of two integers divided by the reciprocal of a different integer

\(\frac{2*3}{(\frac{1}{5})} = 2*3*5\) (an integer)

B. An even integer divided by 7

\(\frac{14}{7} = 2\) (an integer)

C. The quotient of two distinct prime numbers

When one prime number is divided by another, the answer cannot be an integer (though I wouldn't call it quotient since that implies quotient-remainder set up). One prime number is never divisible by another prime number since prime number has only two divisors - 1 and itself.

D. A multiple of 11 divided by 3

\(\frac{33}{3} = 11\) (an integer)

E. The sum of two odd integers divided by 2

\(\frac{(3 + 5)}{2} = 4\) (an integer)

Answer (C)


Hello!

How did you understand that one prime number is dividing another prime number?

I am a bit confused with the wording of the question.

Can´t it be like the following?

2*3 divided by 6 = quotient would be 1.

Regards!


The wording of the question is not perfect.

It should read something like this: The result when one prime number is divided by a different prime number.

One prime number will never be divisible by a different prime number because a prime is divisible by only two numbers - 1 and itself.
So the result will never be an integer.

e.g. 3/2 or 5/7 or 13/5 etc

Note that 2*3 is not a prime number.

Also, quotient of a division is always an integer. The remainder is also an integer. Together, you get the result of division which may or may not be an integer.

So 13/5 gives quotient 2 and remainder 3.
But 13/5 = 2.6 (not an integer)
Hence, the use of the term quotient is also not right.
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Re: Which of the following CANNOT result in an integer?  [#permalink]

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New post 01 Jan 2019, 12:15
[/quote]The wording of the question is not perfect.

It should read something like this: The result when one prime number is divided by a different prime number.

One prime number will never be divisible by a different prime number because a prime is divisible by only two numbers - 1 and itself.
So the result will never be an integer.

e.g. 3/2 or 5/7 or 13/5 etc

Note that 2*3 is not a prime number.

Also, a quotient of a division is always an integer. The remainder is also an integer. Together, you get the result of division which may or may not be an integer.

So 13/5 gives quotient 2 and remainder 3.
But 13/5 = 2.6 (not an integer)
Hence, the use of the term quotient is also not right.[/quote]

Thank you! Now everything is very clear :).
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Re: Which of the following CANNOT result in an integer?  [#permalink]

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New post 15 Jan 2019, 05:09
Bunuel wrote:
Which of the following CANNOT result in an integer?

A. The product of two integers divided by the reciprocal of a different integer
B. An even integer divided by 7
C. The quotient of two distinct prime numbers
D. A multiple of 11 divided by 3
E. The sum of two odd integers divided by 2

\(?\,\,:\,\,\,{\rm{cannot}}\,\,{\rm{be}}\,\,{\rm{integer}}\)

\(\left( {\rm{A}} \right)\,\,\,\left( {0 \cdot 0} \right) \div {1^{ - 1}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{A}} \right)\,\,\,{\rm{refuted}}\)

\(\left( {\rm{B}} \right)\,\,\,0 \div 7\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{B}} \right)\,\,\,{\rm{refuted}}\)

\(\left( {\rm{D}} \right)\,\,0 \div 3\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{D}} \right)\,\,\,{\rm{refuted}}\)

\(\left( {\rm{E}} \right)\,\,\left( {1 + 1} \right) \div 2\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{E}} \right)\,\,\,{\rm{refuted}}\)

Conclusion: (C) is the corrrect answer by exclusion.

POST-MORTEM:

\(\left( {\rm{C}} \right)\,\,\,{{{p_1}} \over {{p_2}}} \ne {\mathop{\rm int}} \,\,\,\,:\,\,\,\,\,{\rm{if}}\,\,\,\,{{{p_1}} \over {{p_2}}} = {\mathop{\rm int}} \,\,\,\,\left\{ \matrix{
{p_1}\,\,,{p_2}\,\, > 0\,\,\,\, \Rightarrow \,\,\,{\mathop{\rm int}} \,\, \ge 1\,\,\,\,\left( * \right) \hfill \cr
{p_1} \ne {p_2}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,{\mathop{\rm int}} \,\, \ge 2 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{p_1} = {\mathop{\rm int}} \,\, \cdot {p_2}\,\,\,\,\,\,\,\,\)

\(\,\mathop \Rightarrow \limits_{{p_2}\,\, \ge \,\,2}^{{\mathop{\rm int}} \,\, \ge \,\,2} \,\,\,\,\,\,\,\,{p_1}\,\,{\rm{not}}\,\,{\rm{prime}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{impossible}}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Which of the following CANNOT result in an integer? &nbs [#permalink] 15 Jan 2019, 05:09
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Which of the following CANNOT result in an integer?

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