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# If y is an odd integer and the product of x and y equals 222

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Intern
Joined: 18 Jul 2013
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If y is an odd integer and the product of x and y equals 222  [#permalink]

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Updated on: 05 Nov 2013, 00:37
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Difficulty:

95% (hard)

Question Stats:

43% (01:28) correct 57% (01:42) wrong based on 259 sessions

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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.

Originally posted by way12go on 04 Nov 2013, 23:14.
Last edited by way12go on 05 Nov 2013, 00:37, edited 4 times in total.
Intern
Joined: 28 Jan 2013
Posts: 29
Re: What is the correct choice?  [#permalink]

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05 Nov 2013, 00:01
way12go wrote:
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
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
=====================

=====================
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.

IMO, D. In any case 1 or 2, value of x will be 2.
btw, what is OA?
Intern
Joined: 18 Jul 2013
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Re: What is the correct choice?  [#permalink]

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05 Nov 2013, 00:07
If y= -111 then what?
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Re: What is the correct choice?  [#permalink]

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05 Nov 2013, 00:17
1
way12go wrote:
If y= -111 then what?

Nope. IMO the answer is neither C or D. It is a straight A.

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Re: If y is an odd integer and the product of x and y equals 222  [#permalink]

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05 Nov 2013, 00:21
1
1
way12go wrote:
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.

From F.S 1, we know that y is odd. Prime factorisation of 222: 2*3*37. Thus,

x could be 2, and y = 3*37(odd)
x could be 3, but y will now be even.
Again,the same for x=37. Thus, the only combinaiton possible is x=2, y=111.Sufficient.

From F.S 2, just as above, we can have y=111, x=2.Also, we could have y=101 and x =$$\frac{222}{101}$$. Insufficient.

A.
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Re: What is the correct choice?  [#permalink]

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05 Nov 2013, 00:21
way12go wrote:
If y= -111 then what?

I dont understand why C if u can get answer easily from A?

@Mau5: can we take 3 digit numbers as negative? If the question will be like How many three digit numbers are there? Will the answer be 1800 instead of 900?. Please make it clear if m wrong.

Thanks
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Joined: 02 Sep 2009
Posts: 56373
Re: What is the correct choice?  [#permalink]

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05 Nov 2013, 00:22
1
2
mau5 wrote:
way12go wrote:
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.

If y= -111 then what?

Nope. IMO the answer is neither C or D. It is a straight A.

Yes, A should be the answer. Edited the OA.

From (1) we have that $$xy=prime*odd=222=even$$ --> $$prime*odd=even$$ --> $$x=2$$. Sufficient.
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Re: If y is an odd integer and the product of x and y equals 222  [#permalink]

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05 Nov 2013, 00:23
mau5 wrote:
way12go wrote:
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.

From F.S 1, we know that y is odd. Prime factorisation of 222: 2*3*37. Thus,

x could be 2, and y = 3*37(odd)
x could be 3, but y will now be even.
Again,the same for x=37. Thus, the only combinaiton possible is x=2, y=111.Sufficient.

From F.S 2, just as above, we can have y=111, x=2.Also, we could have y=101 and x =$$\frac{222}{101}$$. Insufficient.

A.

Yes, understood. missed that one thanks
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Posts: 7
Re: If y is an odd integer and the product of x and y equals 222  [#permalink]

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05 Nov 2013, 00:38
Option A is correct. x has to be even and only 2 is even and prime.
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Joined: 26 Mar 2013
Posts: 2284
Re: If y is an odd integer and the product of x and y equals 222  [#permalink]

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09 Mar 2017, 14:40
2
1
If y is an odd integer and the product of x and y equals 222, what is the value of x?

Y is odd integer
xy= 222= 2*3*37

(1) x is a prime number.

The only possible is x=2 and y=3*37

Sufficient

(2) y is a 3 digit number.

If y=111, x=2, xy=222

If y=102, x=222/102 (The trick here is that it is not mentioned that x is INTEGER. one might think intuitively that x is integer because y is integer)

Insufficient

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Joined: 02 Aug 2009
Posts: 7763
Re: Quant:DS: If y is an odd integer and the product of x and y equals 222  [#permalink]

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09 Aug 2018, 23:28
ritu1009 wrote:
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 three digit number.

question is not sub-600 and is already discussed, so search before posting ..
otherwise for solution

x*y=222

1) x is a prime number.
as y is ODD, x has to be even.
but x is also prime, so ONLY way is that x is 2
suff

2) y is a three digit number.
only possibility is 111 or -111
so x can be 2 or -2
insuff

A
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Re: Quant:DS: If y is an odd integer and the product of x and y equals 222   [#permalink] 09 Aug 2018, 23:28
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