Manhattan GMAT Challenge Problem of the Week – 27 Aug 2010:
Here is a new Challenge Problem! If you want to win prizes, try entering our Challenge Problem Showdown. The more people enter our challenge, the better the prizes.
As always, the problem and solution below were written by one of our fantastic instructors. Each challenge problem represents a 700+ level question. If you are up for the challenge, however, set your timer for 2 mins and go!
O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x.
Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x.
According to these definitions, the value of O(3.2) + E(–1.7) + o(–1.3) + e(2.7) is:
To ensure that we grasp the four definitions, we might restate them—taking care to preserve the meaning precisely.
O(x) rounds x up to the nearest odd integer, whereas o(x) rounds x down to the nearest odd integer. The two E-functions do the same thing, except that the outcome is even integers.
Now let’s write the terms one at a time and apply the functions.
O(3.2) = 5 (notice that we must round up pretty far)
E(–1.7) = 0 (remember that the 0 is larger than –1.7)
o(–1.3) = –3 (we have to round down pretty far, and –3 is less than –1.3)
e(2.7) = 2
5 + 0 + (–3) + 2 = 4
The correct answer is (C).
Special Announcement: If you want to win prizes for answering our Challenge Problems, try entering our Challenge Problem Showdown. Each week, we draw a winner from all the correct answers. The winner receives a number of our our Strategy Guides. The more people enter, the better the prize. Provided the winner gives consent, we will post his or her name on our Facebook page.