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

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

by GMATinsight » Thu Oct 08, 2015 10:13 am
If x is a positive integer less than 10, is 14,743 + x prime?

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

Answer: option B
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by GMATinsight » Thu Oct 08, 2015 10:14 am
GMATinsight wrote:If x is a positive integer less than 10, is 14,743 + x prime?

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

Answer: option B
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 one 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
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by rajat1994 » Mon Nov 02, 2015 9:51 pm
We are Given that x is a positive integer less than 10.

Statement 1:
x/2=odd
This is possible only when x is either 2 or 6.
When we add these numbers to 14,743, we get 14,745 and 14,749, both of which are divisible by 5 and 7 respectively, and hence aren't prime numbers. Therefore, Statement 1 is sufficient.

Statement 2: x^2=36
x can be -6 or +6. But since we know x is a positive number, x=+6.
We add six to 14,743 as we did in the previous case, obtain 14,749 ,which is divisible by 7. Hence, not prime.
Therefore, Statement 2 is sufficient.

ANSWER: Option D
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by GMATGuruNY » Tue Nov 03, 2015 1:55 am
GMATinsight wrote:If x is a positive integer less than 10, is 14,743 + x prime?

(1) x/2 is odd.
(2) x^2 = 36
If a DS problem asks whether a very large integer is prime, the answer must be NO.
The reason:
While there are straightforward ways to prove that a very large integer is NOT prime -- if the integer is even, if the units digit is 5, and so on -- there is no straightforward way to prove that a very large integer IS prime.

Thus, no work is needed here.
Since we cannot be expected to prove that 14,743 + x IS prime, each statement must provide sufficient information to determine that 14,743 + x is NOT prime.

The correct answer is D.
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by GMATGuruNY » Tue Nov 03, 2015 2:01 am
GMATinsight wrote:
Given : Integer x < 10

Statement 1: x/2 is odd.
i.e. x is an Even Number with only one power of 2
i.e. x may be 2, 6, 10, 14, 18... etc
The values in red do not satisfy the constraint that x must be less than 10.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
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