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

Question

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.

mau5 · Accepted Answer

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.

Mo2men · Answer

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

Answer: A

Chiranjeevee · Answer

IMO, D. In any case 1 or 2, value of x will be 2.
btw, what is OA?

way12go · Answer

If y= -111 then what?
C is the correct answer.

mau5 · Answer

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

Please verify the OA.

Chiranjeevee · Answer

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

Bunuel · Answer

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.

Chiranjeevee · Answer

Yes, understood. missed that one :roll:

thanks

way12go · Answer

Option A is correct. x has to be even and only 2 is even and prime.

chetan2u · Answer

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

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

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