If a positive integer n, divided by 5 has...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

If a positive integer n, divided by 5 has...

by BTGmoderatorLU » Sat Nov 11, 2017 8:11 am

If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?

I n is odd.
II n+1 cannot be a prime number.
III n+2 divided by 7 has remainder 2.

A. none.
B. I only.
C. I and II only.
D. II and III only.
E. I, II and III.

The OA is A.

Please, can any expert assist me with this PS question? I'm really confused with it. Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sat Nov 11, 2017 8:11 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sun Nov 12, 2017 9:33 am

Hello LUANDATO.

We only have to find an integer "n" that help us in each case.

For example, let's take n=12.

When we divide 12 by 5 the remainder is 2, and:

- 12 is NOT odd. So, option I is out.

- n+1=12+1=13, and 13 is a prime number. So, option II is out too.

- n+2 = 12+2=14. When we divide 14 by 7 the remainder is 0. So, option III is out.

So, none option is correct.

The correct answer is A .

I hope this may help you. Feel free to ask me again if you have a doubt.

Regards.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

If a positive integer n, divided by 5 has...

by Brent@GMATPrepNow » Mon Nov 13, 2017 2:09 pm

LUANDATO wrote:If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?

I n is odd.
II n+1 cannot be a prime number.
III n+2 divided by 7 has remainder 2.

A. none.
B. I only.
C. I and II only.
D. II and III only.
E. I, II and III.

-----------------ASIDE----------------------------------
When it comes to remainders, we have a nice rule that says:

If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
------ONTO THE QUESTION!!!------------------------

Positive integer n, divided by 5 has a remainder 2
Some possible values of n: 2, 7, 12, 17, 22, 27, 32, 37, . . . etc

Now let's examine the statements:
I. n is odd.
This need not be true.
Among the possible values of n, we see that n need not be odd
So statement 1 is FALSE

II. n+1 cannot be a prime number.
Not true.
Among the possible values of n, we see that n COULD equal 2
2+1 = 3, and 3 IS a prime number
So, n+1 CAN BE a prime number
So statement 2 is FALSE

NOTE: Since statements I and II are false, we need not examine statement III, since there are no answer choices that suggest that only statement III is true.
So, the correct must be A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

hi

by Jeff@TargetTestPrep » Mon Dec 18, 2017 9:39 am

LUANDATO wrote:If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?

I n is odd.
II n+1 cannot be a prime number.
III n+2 divided by 7 has remainder 2.

A. none.
B. I only.
C. I and II only.
D. II and III only.
E. I, II and III.

We can express n as:

n = 5q + 2

Let's now analyze each Roman numeral:

I. n is odd

If q = 2, then 5q + 2 = 12, so n does not have to be odd.

II. n+1 cannot be a prime number

If q = 2, then 5q + 2 = 12, so n + 1 = 13, which is prime. So II does not have to be true.

III. (n+2) divided by 7 has remainder 2

n + 2 = 5q + 4

If q = 2, then 5q + 4 = 14, which has a remainder of zero when divided by 7. So III does not have to be true.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]