Happy 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.