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

This topic has 3 expert replies and 0 member replies

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

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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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GMAT/MBA Expert

Post
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.

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GMAT/MBA Expert

Post
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

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GMAT/MBA Expert

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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
jeff@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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