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

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## Question

O(x) represents the least odd integer greater thanx, whereaso(x) represents the greatest odd integer less thanx.Likewise,

E(x) represents the least even integer greater thanx, wherease(x) represents the greatest even integer less thanx.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 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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## 5 comments

Swarna on August 27th, 2010 at 12:44 pm

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

Makarand on August 27th, 2010 at 10:00 pm

I was under the impression that 0 is neither even nor odd

so i got :

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

julia on August 27th, 2010 at 10:14 pm

Nice work swarna..

julia on August 27th, 2010 at 10:15 pm

Very Effective site to learn about GMAT

ron on August 28th, 2010 at 12:42 am

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