GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2019, 17:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Which of the following CANNOT result in an integer?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59730
Which of the following CANNOT result in an integer?  [#permalink]

### Show Tags

06 Nov 2018, 00:28
1
1
1
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:02) correct 24% (00:54) wrong based on 215 sessions

### HideShow timer Statistics

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

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India
Re: Which of the following CANNOT result in an integer?  [#permalink]

### Show Tags

06 Nov 2018, 02:11
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)

_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 09 Mar 2017
Posts: 18
Re: Which of the following CANNOT result in an integer?  [#permalink]

### Show Tags

20 Nov 2018, 03:20
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)

Quotient will not be 0 here ?
Senior Manager
Joined: 12 Sep 2017
Posts: 308
Which of the following CANNOT result in an integer?  [#permalink]

### Show Tags

31 Dec 2018, 09:14
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)

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!
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India
Re: Which of the following CANNOT result in an integer?  [#permalink]

### Show Tags

01 Jan 2019, 03:35
jfranciscocuencag 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)

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.
_________________
Karishma
Veritas Prep GMAT Instructor

Senior Manager
Joined: 12 Sep 2017
Posts: 308
Re: Which of the following CANNOT result in an integer?  [#permalink]

### Show Tags

01 Jan 2019, 13:15
[/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 .
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Which of the following CANNOT result in an integer?  [#permalink]

### Show Tags

15 Jan 2019, 06:09
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.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8701
Location: United States (CA)
Re: Which of the following CANNOT result in an integer?  [#permalink]

### Show Tags

21 Jan 2019, 18:44
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

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Which of the following CANNOT result in an integer?   [#permalink] 21 Jan 2019, 18:44
Display posts from previous: Sort by