If p is a positive integer, is p even?
(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1
The OA is the option B .
Why is sufficient the second statement? How can I get an answer? Help!!!
If p is a positive integer, is p even?
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Target question: Is p even?VJesus12 wrote:If p is a positive integer, is p even?
(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1
Statement 1: p divided by 3 leaves a remainder of 1
In other words, p is 1 greater than some multiple of 3
There are several values of p that satisfy this condition. Here are two:
Case a: p = 4. In this case, the answer to the target question is YES, p is even
Case b: p = 7. In this case, the answer to the target question is NO, p is not even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: p divided by 4 leaves a remainder of 1
In other words, p is 1 greater than some multiple of 4
So, we can say that: p = 4k + 1 for some integer k
Since 4k must be EVEN, we can conclude that 4k+1 must be ODD
In other words, p MUST be ODD
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
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Hello Vjesus12.VJesus12 wrote:If p is a positive integer, is p even?
(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1
The OA is the option B .
Why is sufficient the second statement? How can I get an answer? Help!!!
Let's take a look.
We have to say if p is even or not.
This implies that $$p=3\cdot k+1,\ \ \ \ k\in\mathbb{Z}.$$ Now,(1) p divided by 3 leaves a remainder of 1
1- If k=1 then p=4, that is to say, p is EVEN.
2- If k=2 then p=7, that is to say, p is ODD.
NOT SUFFICIENT.
This implies that $$p=4\cdot k+1,\ \ \ \ k\in\mathbb{Z}.$$ Now, since 4k is always an even number, then 4k+1 will be always an ODD number. Hence, p is always ODD.(2) p divided by 4 leaves a remainder of 1
Therefore, the answer to the question "is p even?" is NO, it isn't.
SUFFICIENT.
So, the correct answer is the option B.
I hope it helps.
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Target question: Is p EVEN?VJesus12 wrote:If p is a positive integer, is p even?
(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1
ASIDE: Another way to handle statement 2 is to apply a useful rule:
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.
Statement 2: p divided by 4 leaves a remainder of 1
So, some possible values of p are: 1, 5, 9, 13, 17, 21, 25, 29, ...etc
We can see that, if we continue listing possible values of p, all of those values will be ODD
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Cheers,
Brent
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We need to determine whether positive integer p is even.VJesus12 wrote:If p is a positive integer, is p even?
(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1
Statement One Alone:
p divided by 3 leaves a remainder of 1
We see that p could be 4 or p could be 7. Statement one is not sufficient to answer the question.
Statement Two Alone:
p divided by 4 leaves a remainder of 1
See see that p is 1 more than any multiple of 4. Since all multiples of 4 are even, p must be odd. Statement two is sufficient to answer the question.
Answer: B
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