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product of x and y equals 222

by sanju09 » Mon Feb 21, 2011 2:17 am
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.
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by Night reader » Mon Feb 21, 2011 2:36 am
IOM C
hey sanju, tricky problem!
given: y is odd integer, x*y=222, find x-?
st(1) x is prime, if x is prime the only way x*y=222 is when 222/x=y, but we don't know y otherwise we could find x=222/y, hence Not Sufficient.
st(2) y is three-digit number (ABC) obviously Not Sufficient, as we don't know x, BUT y is odd and x*y for y to be three-digit integer only possible when y=111 and x can be infinite number of values. Not Sufficient.
Combined st(1&2): x is prime and y is three-digit number odd, x*y=222 --> x=2, y=111 Sufficient;
sanju09 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.
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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by sanju09 » Mon Feb 21, 2011 2:51 am
Night reader wrote:answer B - changed my answer from C Sad
given: y is odd integer, x*y=222, find x-?
st(1) x is prime, if x is prime the only way x*y=222 is when 222/x=y, but we don't know y otherwise we could find x=222/y, hence Not Sufficient.
st(2) y is three-digit number (ABC) obviously Sufficient, as we don't know x, BUT y is odd and x*y for y to be three-digit integer only possible when y=111 and x=2
sanju09 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.

222 = 2 × 3 × 37 = x y, what is x?

(1) If x is a prime then it could be any of 2, 3, or 37. Insufficient.
(2) If y is a 3-digit number, it could either be 222 giving x = 1, or 111 giving x = 2. Insufficient
Taking together, if x is prime and y is a 3-digit number, then x can only be equal to 2.

[spoiler]Sufficient

C[/spoiler]
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by Night reader » Mon Feb 21, 2011 3:06 am
it's posted above
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by rohu27 » Mon Feb 21, 2011 5:56 am
I have a diff answer here :(

y is an odd integere and xy=222, so it can be tht 111*2=333*2/3=222
but st 1 says x is a prime number, so x has to be 2.
2*111=222
A is suffcient.

st 2 says y is a three digit number but nothing abt x. it can be anyhtng.

sanju09 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.
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by gmatmachoman » Mon Feb 21, 2011 6:13 am
sanju09 wrote:
Night reader wrote:answer B - changed my answer from C Sad
given: y is odd integer, x*y=222, find x-?
st(1) x is prime, if x is prime the only way x*y=222 is when 222/x=y, but we don't know y otherwise we could find x=222/y, hence Not Sufficient.
st(2) y is three-digit number (ABC) obviously Sufficient, as we don't know x, BUT y is odd and x*y for y to be three-digit integer only possible when y=111 and x=2
sanju09 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.

222 = 2 × 3 × 37 = x y, what is x?

(1) If x is a prime then it could be any of 2, 3, or 37. Insufficient.
(2) If y is a 3-digit number, it could either be 222 giving x = 1, or 111 giving x = 2. Insufficient
Taking together, if x is prime and y is a 3-digit number, then x can only be equal to 2.

[spoiler]Sufficient

C[/spoiler]
@Sanju,

are u sure?? IMO u never tend to make mistakes..but here is one !! [spoiler]Guess, u missed Y to be a odd integer!![/spoiler]
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by Night reader » Mon Feb 21, 2011 6:16 am
@rohu: I said this one is tricky, tempting many ways :) --> the best answer to your question is prime factorization of 222
111*2, and 111 isn't prime, so 222=3*37*2 falls into three possible prime factors 2, 3 and 37 if you take 2*3 then one number, then this cannot be x as x is a prime number, and this cannot be y as y is odd; so we have the only option 3*37 which makes 111 and 2 for y and x respectively.

So basically yes, A is the only correct answer for this DS if its content doesn't change.

@sanju, did you make this problem yourself? What's OA and source?
rohu27 wrote:I have a diff answer here :(

y is an odd integer and xy=222, so it can be the 111*2=333*2/3=222
but st 1 says x is a prime number, so x has to be 2.
2*111=222
A is sufficient.

st 2 says y is a three digit number but nothing about x. it can be any thing.

sanju09 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.
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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by Ashish8 » Tue Feb 22, 2011 11:28 am
I got B.

After factoring out 222 this is what I have:

1 * 222
2 * 111
3 * 74
6 * 37

The stem says that Y is an odd integer. This means that Y could be: 1,2,3,37,111.

Statement 1: X is prime. If y is odd and X is prime then x could be 2 or 3. Insufficient
Statement 2: Y is a 3-digit number. Only 111 satisfies that Y is odd and a 3-digit number

Thus x = 2.
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by Night reader » Tue Feb 22, 2011 12:00 pm
yes but y could be only 111 and 74 then, which one you chose if y is odd? :)

moreover, you make assumption in st(2) about x as an integer; x can be anything - eliminate B
Ashish8 wrote:I got B.

After factoring out 222 this is what I have:

1 * 222
2 * 111
3 * 74
6 * 37

The stem says that Y is an odd integer. This means that Y could be: 1,2,3,37,111.

Statement 1: X is prime. If y is odd and X is prime then x could be 2 or 3. Insufficient
Statement 2: Y is a 3-digit number. Only 111 satisfies that Y is odd and a 3-digit number

Thus x = 2.
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by Ashish8 » Tue Feb 22, 2011 12:12 pm
Now I'm very confused. Cause now I'm getting D. Haha

Statement 1. X is prime Y is odd. Then X = 2 Y = 111
Statement 2. Y is odd and 3 digit integer. Y = 111, Then X = 2.
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by Night reader » Tue Feb 22, 2011 12:27 pm
are you reading between the posts? x can be decimal too, it's not specified in quest.stimuli --> 222/111, 222/113, 222/115 ...
y can be only odd in st(1), if you eliminate B - we are on the same page, answer A
Ashish8 wrote:Now I'm very confused. Cause now I'm getting D. Haha

Statement 1. X is prime Y is odd. Then X = 2 Y = 111
Statement 2. Y is odd and 3 digit integer. Y = 111, Then X = 2.
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by Ashish8 » Tue Feb 22, 2011 12:35 pm
The stem says that Y is a integer. Then B states that Y is a 3-digit number, which implies Y is a 3 digit integer. Then X would have to be an integer to make a integer.
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by clock60 » Tue Feb 22, 2011 12:47 pm
here i got D as well
if x*y=222. then only 4 following combinations are possible, provided that y is odd
y=1,x=222,
y=3, x=37*2
y=37, x=2*3
y=37*3, x=2
to the statements
(1) the only possible combination in which x is prime and y odd is x=2, and y=37*3, x=2 suff
(2)y three digit number again y=37*3 and x=2 suff
guys objections are highly appreciated
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by Night reader » Tue Feb 22, 2011 12:49 pm
:) we operate with processing now
111 * 2
125 * 1,776
185 * 1,2

check please
Ashish8 wrote:The stem says that Y is a integer. Then B states that Y is a 3-digit number, which implies Y is a 3 digit integer. Then X would have to be an integer to make a integer.
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by GMATGuruNY » Tue Feb 22, 2011 12:51 pm
sanju09 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.
Given conditions:
xy = 222 = 2*3*37
y is an odd integer

Statement 1: x is prime
If x=2, then y = 3*37 = 111. This combination of values satisfies all the conditions given.
If x=3, then y = 2*37 = 74. Since y must be an odd integer, this combination of values is not allowed.
If x=37, then y = 2*3 = 6. Since y must be an odd integer, this combination of values is not allowed.
Thus, the only value of x that satisfies all the conditions given is x=2.
Sufficient.

Statement 2: y is a 3-digit integer
If y=111, then x=2.
If y=101, then x=222/101.
Since both x=2 and x=222/101 are possible, insufficient.

The correct answer is A.
Last edited by GMATGuruNY on Tue Feb 22, 2011 12:55 pm, edited 1 time in total.
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