O(x) represents the least odd integer greater than x, whereas o(x)

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

Kudos for a correct  solution .

SumitojSingh · Answer

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

took me ~120 seconds to solve,

O(3.2) = 5
E(–1.7)= 0
o(–1.3)=-3
e(2.7)=2

O(3.2) + E(–1.7) + o(–1.3) + e(2.7) = 5+0-3+2=4 option C

Bambaruush · Answer

If it is too complicated, you can draw the number line. Everything will be clear

5 + 2 + (-3) + 2 = 6 Hehe, too short comment. I hope it won't be deleted.

SumitojSingh · Answer

Thanks Bambaruush ... 0 is neither Even nor Odd.

ENGRTOMBA2018 · Answer

Any number that can be written in the form : x/1 is an integer. As 0 = 0/1 or 5= 5/1 etc , yes 0 is an integer.

Additional properties of 0:

1. 0/0 is not defined
2. 0 is a multiple of all numbers
3. 0 is NOT a factor of any number
4. 0 is Even
5. 0 is neither positive nor negative

ENGRTOMBA2018 · Answer

That is incorrect.

0 is always an  even integer .

I think you are confusing with the property of a '0' that it is neither positive nor negative.

kunal555 · Answer

O(3.2) + E(–1.7) + o(–1.3) + e(2.7
or 5 + 0 + (-3) + 2
= 4

Answer:- C

Bambaruush · Answer

Sorry, you were right. I googled and found out that it is indeed even integer. So you're right

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

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).

MathRevolution · Answer

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

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

By the definitions, O(3.2) > 3.2 and O(3.2) is odd integer --> O(3.2)=5
Similarly E(-1.7) > -1.7 and E(-1.7) is even integer --> E(-1.7)=0
o(-1.3) < -1.3 and o(-1.3) is odd integer --> o(-1.3)=-3
e(2.7) < 2.7 and e(2.7) is even integer --> e(2.7)=2

So O(3.2)+E(-1.7)+o(-1.3)+e(2.7)=5+0-3+2= 4. That is the answer is (C) 4.

EncounterGMAT · Answer

An easy one (and require keen concentration). 5 + 0 - 3 + 2 = 4 Answer is option C.

KarishmaB · Answer

What each definition means on the number line:

O(x) represents the least odd integer greater than x - O(x) is the first (so that it is smallest) odd number to the right (so that it is greater than x) of x. So O(3.2) = 5
o(x) represents the greatest odd integer less than x - o(x) is the first (so that it is greatest) odd number to the left (so that it is smaller than x) of x. So o(–1.3) = -3
E(x) represents the least even integer greater than x - E(x) is the first (so that it is smallest) even number to the right (so that it is greater than x) of x. So E(-1.7) = 0
e(x) represents the greatest even integer less than x - e(x) is the first (so that it is greatest) even number to the left (so that it is smaller than x) of x. So e(2.7) = 2

Sum = 5 - 3 + 0 + 2 = 4
Answer (C)

yashna36 · Answer

Hi,
the problem is pretty staright forward. However, this question aside, does GMAT considers negative integers to be odd or even?

vishalkazone · Answer

O(3.2) = 5 (east odd integer greater than 3.2)
E(–1.7) = 0 (least even integer greater than -1.7)
o(–1.3) = -3 (the greatest odd integer less than -1.3)
 e(2.7) = 2 (the greatest even integer less than 2.7)

5+0-3+2= 4
Answer C

Bunuel · Answer

Yes, negative integers can also be even or odd.

An even number is an   integer   that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., -4, -2, 0, 2, 4, ... are all even integers.

An odd number is an   integer   that is not evenly divisible by 2. So, ..., -3, -1, 1, 3, 5, ... are all odd integers.

For more check here:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

Archit3110 · Answer

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

took me ~120 seconds to solve,

O(3.2) = 5
 E(–1.7)= 0
 o(–1.3)=-3
 e(2.7)=2

O(3.2) + E(–1.7) + o(–1.3) + e(2.7) = 5+0-3+2=4 option C

KanishkM · Answer

O(3.2) + E(–1.7) + o(–1.3) + e(2.7)
5 + 0 -3 +2
4

rahulm3564 · Answer

My solution:

Important: all should be integers.

End result will be Odd + Even + Odd + Even = Even. So clearly cancel out B and D.

O(3.2) is something just more than 3.2. Can be 5
E(-1.7) = 0
o(-1.3) = -3
e(2.7) = 2

sp result is 5+0-3+2 = 4

bumpbot · Answer

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O(x) represents the least odd integer greater than x, whereas o(x)

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O(x) represents the least odd integer greater than x, whereas o(x)

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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