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What is the correct choice?

Expert replies
by way12go » Mon Nov 04, 2013 10:12 pm
If y is an odd integer and the product of x and y equals 222, what is the value of x?

(1) x is a prime number.

(2) y is a 3 digit number.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient to answer the question asked
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
=====================
Answer
=====================
C is the correct answer. If Y is odd then prime number x can only be 2 and if Y is three digit 111 then X can only be two with both the choices X=2 and Y=111 is clear and no negative numbers. So C is the answer.By the usual definition of prime for integers, negative integers can not be prime.

By this definition, primes are integers greater than one with no positive divisors besides one and itself. Negative numbers are excluded. In fact, they are given no thought.If you take y=37 then x=6 is true so C is right choice
If you take y=111 then x=2 prime number is the only choice no negative integers. So C is correct.
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Source: — Data Sufficiency |

by theCodeToGMAT » Mon Nov 04, 2013 11:06 pm
Are you sure the OA is [spoiler]{C}[/spoiler]

According to me:

y = ODD INT
So, X must be EVEN (if given it's an integer)

(x)(y) = 222 = 2 x 3 x 37

To find: Value of "x"

Statement 1:

X is prime number..
Only X = 2
SUFFICIENT


Statement 2:
y = 3 digit number
y can be = 111, x = 2
y can be = 333, x = 222/333
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]
Last edited by theCodeToGMAT on Mon Nov 04, 2013 11:17 pm, edited 1 time in total.
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by way12go » Mon Nov 04, 2013 11:09 pm
The option 1 doesn't state x is 2, x can be 3 too
so C is the correct answer.
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by theCodeToGMAT » Mon Nov 04, 2013 11:17 pm
way12go wrote:The option 1 doesn't state x is 2, x can be 3 too
so C is the correct answer.
Question says that "y" is ODD and xy = 222(EVEN)

For Statement 1: we know that "x" is an PRIME INTEGER
We know that
(ODD) x (EVEN) = EVEN
(ODD) x (ODD) = ODD

So, "X" must be EVEN Integer.. The only possible value of "x" is "2"

Also, it satisfies the given case = (2) x (111)
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by way12go » Mon Nov 04, 2013 11:36 pm
Option A is correct. x has to be even and only 2 is even and prime.

You are correct.
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by theCodeToGMAT » Mon Nov 04, 2013 11:40 pm
way12go wrote:Option A is correct. x has to be even and only 2 is even and prime.

You are correct.
Yep ;)
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by Matt@VeritasPrep » Tue Nov 05, 2013 4:16 pm
The key here is that S1 tells you that x is an integer and S2 doesn't. Fom S1, we have (prime) * (odd) = 222. The product of two integers is only even if at least one of those integers is even, so our prime number must be even and hence must be 2. The second statement is sneaky, as it doesn't imply that x is an integer, so we could have y = 555 and x = (2/5), for instance.
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