GMAT Challenge Question: Blackout Dates

GMAT PrepHappy Thanksgiving, everyone!  With today as one of the busiest travel dates of the year, and undoubtedly a blackout date for your frequent-flier or rewards-miles program, we’ll offer this Data Sufficiency question for which blackouts can play a prominent role.

We’ll explain what we mean later today; for now, please enter your solutions in the comments field and we’ll be back this evening with an explanation and takeaway for which you’ll be thankful!

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

Update: Solution.  Much of this problem’s difficulty derives from the fact that it is hard for us to forget what we’ve already been told.   On Data Sufficiency questions, it’s therefore important to practice “Memory Blackout” when reading statement 2 – we must assess statement 2′s sufficiency on its own by blacking out everything we’ve learned from statement 1.
Here, statement 1 tells us that x is prime, and we already know that y is odd.  For an odd y to multiply by x and produce 222, an even number, x must be even.  Therefore, if x is both even and prime, x must be 2, and the statement is sufficient.

Attacking statement 2, we no longer know that x is prime – nor do we even know that x is an integer. We ONLY know that y is a 3-digit odd number.  You may be baited into thinking that x is an integer, bringing all or some of what you’ve learned from statement 1 into the process, but we  don’t know that at all.  y could be 333 and x could be 2/3 and statement 2 is still satisfied. Or, as you were probably trapped into predicting, y could be 111 and x could be 2.  But because we can’t know for certain in this case that x is an integer, the statement is not sufficient, and the correct answer is A.

9 Responses

  1. Rosaura says:

    Answer D: Each statement alone is sufficient.

  2. Katerina says:

    for 222 all factors will be: 1, 2, 3, 111, 222. y should be odd, so y can be 1,-1 3,-3,111, -111 and possible variants for x : 222, -222, 74,-74, 2, -2 respectively (for their product to be 222
    1) x-prime, therefore, for there is only one pair that will fit: y=111, x=2 – SUFFICIENT
    2) y-three digit number gives us 2 variants x=2 y=111 and x=-2, y=-111 NOT SUFFICIENT

  3. Pardeep says:

    1 is suff.

    As x can only be equal to 2.

    2 is insuff. as y can be 111 and 222!

    Answer is A

  4. meenakshi says:

    Let N = X*Y = 222, where y is odd, so we need to factorize N in such a way that we get 1 odd factor.
    Now, 222 = 2*111 or 6*37

    From 1) x can be 2 only and y=111. hence sufficient
    From 2) y is a three digit odd no. only solution is y=111, which leaves x=2

    Hence, both statements are sufficient on their own to find x

  5. Balaji says:


    y- is odd


    Therefore, X-even number

    A) X-prime

    the only even prime is 2

    Hence A is sufficient

    B) Y is a three digit number.

    y- 111 or -111

    This gives two values for x. (2, -2)

    Hence not sufficient

  6. Ankit says:

    For the product of x & y to be even (222), x has to be an even integer (y is an odd integer).
    1) x can be prime, i.e., 2 iff y is 3-digit, i.e., 111

  7. aftab ahmed says:

    since y is an odd integer so y can be 3 ,37 or 111.
    condition1 :x is a prime number so x can be 2 ,3 or 37.but y can be an odd integer only if x=2 and then and y = condition 1 is sufficient.
    condition 2:y is a 3 digit number only possibility is y=111 and for that condition 2 alone is also sufficient to find out the value of x

  8. Javier says:

    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

    From the statement, xy = 222 being x an odd integer

    If you find the factors of 222 these are 2,3, 37, and 1, so the possible factors to obtain 222 are:
    1 x 222
    2 x 111
    3 x 74
    6 x 37

    (1) considers x as a primer number. Three of the options above meet this criteria, so statement (1) is not sufficient. Discard option a and c (each statement alone is sufficient)

    (2) considers y as a three-digit number. Two of the options above meet this criteria, so statement (2) is not sufficient. Discard option b

    If the two statements are considered, only one option meet the criteria: 1 x 222
    1 is an odd number
    1 is a primer number
    222 is a three-digit number

    Given the result above, answer e (statements 1 and 2 are not sufficient to answer the question) is discarded.

    I am sure there are shorter routes to get this one solved but I took the GMAT almost three years ago, so I hope I see other ways to get around this problem!

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