Manhattan GMAT Challenge Problem of the Week – 27 Aug 2010:

by on August 27th, 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!


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


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).

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  • It's a simple one!!

    The expression to be evaluated = O(3.2) + E(–1.7) + o(–1.3) + e(2.7)
    O(x) is least odd integer greater than x. as given the expression, x = 3.2.
    Now , Integers greater than 3.2 are 4, 5... and so on. we need to pick one of these.

    least odd integer = 5

    o(x) represents greatest odd integer less than x.
    x= -1.7 , integers less than x are -2, -3, -4
    greatest odd is -3

    Similarly, E(x) = 0 , e(x) = 2

    summing them all = 5 + (-3) + 0 + 2 = 4

  • I was under the impression that 0 is neither even nor odd
    so i got :

    5 +(-3)+2+2=6

  • Nice work swarna..

  • Very Effective site to learn about GMAT

  • This same problem is also in the OG 12th edition Problem Solving section. Its amazing how you can see patterns from doing all the problems in the OG

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