Manhattan GMAT Challenge Problem of the Week – 27 Aug 2010

by Manhattan Prep, Aug 27, 2010

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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!

Question

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:

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

Answer

To ensure that we grasp the four definitions, we might restate themtaking 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 lets 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).

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