If x is a positive integer less than 10, is 14,743 + x prime?

Hi Brianlab,

If X / 2 being odd, X is not neccessarily even. Concider X to be 4 or 8. X / 2 would be odd only when X is 2 or 6 and in both cases the resultant will not be a prime number.

14745 / 5 and 14749 / 7 . Hope you understood where you went wrong.

Therefore the Ans is D.

Hi asethi,

I think statement one is sufficient. 2 and 6 are valid solutions for x, and when substituted both do not yield a prime number. Hence sufficient.

Ans should be D.

Given : Integer x < 10

Question : Is 14,743 + x prime?

Statement 1: x/2 is odd.
i.e. x is an Even Number with only 1 power of 2
i.e. x may be 2, 6, 10, 14, 18... etc
14,743 + x will be an Odd Integer which may or may not be prime for some value of x
NOT SUFFICIENT


Statement 2: x^2 = 36
i.e. x = 6 (because x is positive Integer)
14,743 + x = 14,743 + 6 = 14,749 which can be identified whether it's prime or not. Hence,
SUFFICIENT

Answer: Option B

Good question. Lots os silly mistakes. Good to learn about how to avoid them.

Ans is D.

Statement 1 :
x/2 is odd.
0<x<10
possible values x=2,6
now 14743+2=14745 divisible by 5 , Not a prime number
now 14743+6=14749 divisible by 7 , Not a prime number

Sufficient

Statement 1 :
x^2 =36 =>x=6,-6 and
0<x<10
only possible value x=6
now 14743+6=14749 divisible by 7 , Not a prime number
Sufficient

Ans: D

If x is a positive integer less than 10, is 14,743 + x prime?

(1) x/2 is odd.
(2) x^2 = 36

Kudos for a correct solution.
given that :
x < 10 and x is positive .

st 1 --
x/2 = odd
x can be ----1, 2,3, 4,5, 6,7, 8,9
since x integer therefore x/2 should also be an integer---
x/2 = 1 , 3 because ( x/2 is also odd )

now
14,743 + x prime = 14,743 + 1 = 14744 ( not prime )
14,743 + x prime = 14,743 + 3 = 14746 ( not prime )

A sufficient .

st 2 -- x^2 = 36
there x = ( plus/minus) 6

but x is positive given in the statement .

x= 6

14,743 + x prime = 14,743 + 6 = 14749 (not prime )

B sufficient

Hence D ans .

Hi Abhishek,

In Statement 1: You have took the value of x/2 while calculating the final number i.e 14,743 + x

You get the answer right in this case even with the mistake.But it will not always the case.

It was a silly mistake - was too fast here. x/2=odd than x is 2 or 6 - 14745, 14749 which are divisible by 5,7. This number becomes a prime if x=10 but x must be <10 as stated in the question.

Hi GMATInsight,

In Statement 1, X=2 or 6 which yield odd number and x<10 (please review highlight parts). So No possible values for x above 10. When x=2, 14645 Not prime as 5 is a factor.
When x=6, 14749 Not prime as 7 is a factor.
In both values it is not prime.
SUFFICIENT

Statement x=6, the same as above
SUFFICIENT

So final answer is D

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No. This question asks: “Is 14,743 + x prime?”

Given information in the question stem or diagram: x is a positive integer and x < 10. That means that x = 1, 2, …, 9 and that 14743 + x will equal 14,744, 14,745, …, 14,752. Also note: It is difficult to confirm that a large prime number is prime. For instance there is no good way to determine whether 1,000,001 is prime. However, it is very easy to show that 1,000,011 is NOT prime, because you know it is divisible by 3 (as the sum of its digits is divisible by 3). So your strategy here should really be to try to prove that the possible values are not prime, by finding factors of each possible value.

Statement 2 is easier because it gives you a specific value for x, so you should begin there.

Statement 2: x^2 = 36. Normally x = 6 or -6, but you have the fact that x is positive. So x must equal 6. This statement is sufficient because when you add 6 to 14,743 you will get a single value, and that number will either be a prime number or not; you do not really care which. You only need to know that the answer will be a consistent “yes” or a consistent “no” with only one number involved. If you are interested, 14,749 is not prime as it is clearly divisible by 7 so the answer is “no”! The answer is either B or D.

Statement 1: “x/2 is odd.” With conceptual understanding you see that the only numbers less than 10 that work with this statement are even numbers (so that they can still yield and integer when divided by 2) that are not multiples of 4 (so that the integer is not an even one). So x = 2 or x = 6. This means that you would be adding either 2 or 6 to 14,743. If you add 2 then you get 14,745, which is not prime since it ends in 5. If you add 6 you get 14, 749, which is not a multiple of 2, 3, or 5. However it is a multiple of 7. A quick check of division shows that 14,749 = 7*2,107. Since neither of the numbers are prime, you have a consistent “no” and this statement is also sufficient. Again, you should note that the only plausible answer to this question will be “no” or the question would be unfair. 14,747, for instance, is prime but there is no way in two minutes you could EVER prove that, so the testmakers could not have x be 4! The correct answer is D.

Given : x is +ve integer <10
DS: 14743 + x is prime or not

Statement 1 : x/2 is odd . So can be 2 or 6 in which case x/2 is 1 or 3.
so, 14743+x can be 14745 which is not prime as it is divisible by 5 OR 14749 which is also not prime as it is clearly divisible by 7.

SUFFICIENT

Statement 2: x^2 = 36 , x = 6
so, 14743+x can be 14749 which is not prime as it is clearly divisible by 7.

SUFFICIENT

Answer D

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