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# If B is a positive integer such that the difference between its only t

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If B is a positive integer such that the difference between its only t  [#permalink]

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10 Oct 2018, 02:04
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:01) correct 21% (01:12) wrong based on 43 sessions

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If B is a positive integer such that the difference between its only two distinct factors is odd, what is the value of B+1?

A. 2
B. 3
C. 5
D. 6
E. 8
Math Expert
Joined: 02 Sep 2009
Posts: 58335
If B is a positive integer such that the difference between its only t  [#permalink]

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10 Oct 2018, 02:14
rencsee wrote:
If B is a positive integer such that the difference between its only two distinct factors is odd, what is the value of B+1?

A. 2
B. 3
C. 5
D. 6
E. 8

What do we know from the stem?

B has two factors. This means:
Only primes have two factors so B is prime.
Since 1 is a factor of every integer, then one of the factors of B is 1.

The difference between the two factors is odd:
x - 1 = odd;
x = odd + 1 = even.

So, B is a prime, which has a factor which is even. Therefore, B = 2.

B + 1 = 3.

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Re: If B is a positive integer such that the difference between its only t  [#permalink]

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10 Oct 2018, 03:56
rencsee wrote:
If B is a positive integer such that the difference between its only two distinct factors is odd, what is the value of B+1?

A. 2
B. 3
C. 5
D. 6
E. 8

NOTE: B has only 2 factor. B must be a prime.

Only even prime is 2. All other primes are odd.

If B is 2:

Factors: 1 and 2 and their difference is odd . 2 -1 =1.

If B is 3: factors: 1 and 3 . Difference is even. 3 - 1 = 2.

So , B must be 2.

B + 1 = 2 + 1 = 3 .

Re: If B is a positive integer such that the difference between its only t   [#permalink] 10 Oct 2018, 03:56
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