Which of the following CANNOT result in an integer?

Question

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

KarishmaB · Answer

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)

priyanknema · Answer

Quotient will not be 0 here ?

jfranciscocuencag · Answer

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!

KarishmaB · Answer

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.

jfranciscocuencag · Answer

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. Thank you! Now everything is very clear

.

fskilnik · Answer

?\,\,:\,\,\,{m{cannot}}\,\,{m{be}}\,\,{m{integer}}

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

\left( {m{B}} ight)\,\,\,0 \div 7\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {m{B}} ight)\,\,\,{m{refuted}}

\left( {m{D}} ight)\,\,0 \div 3\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {m{D}} ight)\,\,\,{m{refuted}}

\left( {m{E}} ight)\,\,\left( {1 + 1} ight) \div 2\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {m{E}} ight)\,\,\,{m{refuted}}

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

POST-MORTEM:

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

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

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

Regards, 
Fabio.

ScottTargetTestPrep · Answer

Recall that a prime number is a number that has only two factors: 1 and itself. Therefore, the quotient of two distinct prime numbers, such as 2/7 or 13/11, can’t be an integer since the two prime numbers can’t be multiples of each other.

Answer: C

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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?

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