DS INTEGER

[[email protected]]

Q: IS THE POSITIVE INTEGER X A PRIME NO.

A: 3X + 1 IS A PRIME NO
B: 5X + 1 IS A PERFECT SQUARE

[cans]

a) 3x + 1 is prime. also as x is integer, 3x+1 can't be 2.
thus 3x+1 is odd or 3x is even. this x is even. x=2 - prime. x=6, not prime
Insufficient
b)5x + 1 is perfect square.
x=16 (81 is perfect square)
x=3 (16 is perfect square)
not sufficient
a&b) x is even. thus 5x+1 is odd and 5x is multiple of 10.
thus 5x+1 =81.
sufficient
IMO C

[TwiceBitten]

Cans,

You are assuming that x is 16. in that case 3x+1 would be 49, and it is not prime.
so x can not be 16.

I think the answer is E, but i am not sure.

[cans]

thanks for that mistake. x should not be 16.
but then also c) is sufficient.
because a) says that 3x+1 is prime and it means x is even. (which includes 2 also)
and with b we can say that 5x+1 is not square when x=2. Thus x=2 is invalid.
Thus x is even >2. Thus x is not prime
IMO C

[prateek_guy2004]

Q: IS THE POSITIVE INTEGER X A PRIME NO.

A: 3X + 1 IS A PRIME NO

Example
If x is 2 then its suff
If x is 5 it isint

Not Suff

B: 5X + 1 IS A PERFECT SQUARE

Example

If x = 3 Its suff

If x = 2 it isint

Not suff

If we conclude both the statements

We can solve for x

Hence C

[Whitney Garner]

Q: IS THE POSITIVE INTEGER X A PRIME NO.

A: 3X + 1 IS A PRIME NO
B: 5X + 1 IS A PERFECT SQUARE

Hi [email protected]!

Statement (1):
There are 2 basic cases possible: either 3X+1=2, or 3X+1= any other (odd) prime.

If 3X+1=2
3X = 1
X = 1/3, BUT, X is an integer so this case is NOT possible, so it must be the case that 3X+1=odd prime. Let's see what values are possible when we solve that for X:

3X+1 = odd prime
3X = odd prime - 1 (so, because an odd-1 is an even)
3X = even
X = even.

So X will be an even number, because there is one prime even number we must test that:

Let X=2, then 3X+1 = 3(2)+1 = 6+1 = 7 (PRIME), so 3X+1 is prime when X=2 (prime) so the answer to the original question is YES, X is Prime!
Let X=4, then 3X+1 = 3(4)+1 = 12+1 = 13 (PRIME), so 3X+1 is prime when X=4 (non-prime) so the answer to the original question is NO, X is NOT Prime!

We have 2 different answers from statement (1), so NOT sufficient!


Statement (2):
Now for the tougher statement - if 5X+1=perfect square, let's take a look at what this means for X. Call the perfect square Y^2.

5X+1 = Y^2
5X = Y^2 - 1
X = (Y^2 - 1)/5

So, we can find values of INTEGER X by finding perfect squares that are 1 more than a multiple of 5 (so that they will divide evenly). Let's list the perfect squares up to 12 (since we should have those memorized):
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

From this list, 16, 36, 81 and 121 are the ones that are 1 more than a multiple of 5. So

X = (16-1)/5 = 15/5 = 3 Prime!
X = (36-1)/5 = 35/5 = 7 Prime!
X = (81-1)/5 = 80/5 = 16 NOT Prime!

We showed two different answers from statement (2) so NOT sufficient!


Statement (1+2):
From statement (1): Integer X is even
From statement (2): Integer X could be several numbers, some even and some odd, but the smallest values is 3.

Putting this together, X is an even number but cannot be 2 so we have our answer - Integer X is NOT a Prime number, therefore, the statements together are Sufficient!

The correct answer is C.

I hope this helps!

Whit

[[email protected]]

Q: IS THE POSITIVE INTEGER X A PRIME NO.

A: 3X + 1 IS A PRIME NO
B: 5X + 1 IS A PERFECT SQUARE

Hi [email protected]!

Statement (1):
There are 2 basic cases possible: either 3X+1=2, or 3X+1= any other (odd) prime.

If 3X+1=2
3X = 1
X = 1/3, BUT, X is an integer so this case is NOT possible, so it must be the case that 3X+1=odd prime. Let's see what values are possible when we solve that for X:

3X+1 = odd prime
3X = odd prime - 1 (so, because an odd-1 is an even)
3X = even
X = even.

So X will be an even number, because there is one prime even number we must test that:

Let X=2, then 3X+1 = 3(2)+1 = 6+1 = 7 (PRIME), so 3X+1 is prime when X=2 (prime) so the answer to the original question is YES, X is Prime!
Let X=4, then 3X+1 = 3(4)+1 = 12+1 = 13 (PRIME), so 3X+1 is prime when X=4 (non-prime) so the answer to the original question is NO, X is NOT Prime!

We have 2 different answers from statement (1), so NOT sufficient!


Statement (2):
Now for the tougher statement - if 5X+1=perfect square, let's take a look at what this means for X. Call the perfect square Y^2.

5X+1 = Y^2
5X = Y^2 - 1
X = (Y^2 - 1)/5

So, we can find values of INTEGER X by finding perfect squares that are 1 more than a multiple of 5 (so that they will divide evenly). Let's list the perfect squares up to 12 (since we should have those memorized):
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

From this list, 16, 36, 81 and 121 are the ones that are 1 more than a multiple of 5. So

X = (16-1)/5 = 15/5 = 3 Prime!
X = (36-1)/5 = 35/5 = 7 Prime!
X = (81-1)/5 = 80/5 = 16 NOT Prime!

We showed two different answers from statement (2) so NOT sufficient!


Statement (1+2):
From statement (1): Integer X is even
From statement (2): Integer X could be several numbers, some even and some odd, but the smallest values is 3.

Putting this together, X is an even number but cannot be 2 so we have our answer - Integer X is NOT a Prime number, therefore, the statements together are Sufficient!

The correct answer is C.

I hope this helps!

Whit

Ms. GARNER, THANKS. THIS IS REALLY A NICE EXPLANATION FOR THIS QUESTION. I SOLVE THIS QUESTIONS BY PUTTING VALUES. BUT YOUR METHOD IS GREAT AND SAVES TIME. THANK-YOU