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

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Math Expert
Joined: 02 Sep 2009
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O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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01 Sep 2015, 22:28
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55% (hard)

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62% (01:45) correct 38% (02:01) wrong based on 280 sessions

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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.

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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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02 Sep 2015, 02:57
1
O(x) represents the least odd integer greater than x - O(3.2) = 5,
o(x) represents the greatest odd integer less than x - o(–1.3) = -3,
E(x) represents the least even integer greater than x - E(–1.7) = 0 ,
e(x) represents the greatest even integer less than x - e(2.7) = 2.

The value of O(3.2) + E(–1.7) + o(–1.3) + e(2.7) = 4

But not sure about E(x)
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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02 Sep 2015, 03:29
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.
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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02 Sep 2015, 03:36
Thanks Bambaruush ... 0 is neither Even nor Odd.
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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02 Sep 2015, 03:39
1
Bambaruush wrote:
SumitojSingh wrote:
O(x) represents the least odd integer greater than x - O(3.2) = 5,
o(x) represents the greatest odd integer less than x - o(–1.3) = -3,
E(x) represents the least even integer greater than x - E(–1.7) = 0 ,
e(x) represents the greatest even integer less than x - e(2.7) = 2.

The value of O(3.2) + E(–1.7) + o(–1.3) + e(2.7) = 4

But not sure about E(x)

Is 0 even integer?

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
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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02 Sep 2015, 03:41
SumitojSingh wrote:
Thanks Bambaruush ... 0 is neither Even nor Odd.

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.
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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02 Sep 2015, 09:38
1
Bunuel wrote:
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.

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

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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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02 Sep 2015, 13:06
SumitojSingh wrote:
Thanks Bambaruush ... 0 is neither Even nor Odd.

Sorry, you were right. I googled and found out that it is indeed even integer. So you're right
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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06 Sep 2015, 06:00
1
Bunuel wrote:
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.

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).
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O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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06 Sep 2015, 06:20
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.
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O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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Updated on: 15 Sep 2019, 01:00
An easy one (and require keen concentration). 5 + 0 - 3 + 2 = 4 Answer is option C.
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Originally posted by EncounterGMAT on 18 Oct 2018, 00:00.
Last edited by EncounterGMAT on 15 Sep 2019, 01:00, edited 3 times in total.
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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18 Oct 2018, 02:29
1
Bunuel wrote:
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.

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
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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07 Nov 2018, 23:00
Hi,
the problem is pretty staright forward. However, this question aside, does GMAT considers negative integers to be odd or even?
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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07 Nov 2018, 23:05
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
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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07 Nov 2018, 23:32
yashna36 wrote:
Hi,
the problem is pretty staright forward. However, this question aside, does GMAT considers negative integers to be odd or even?

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:
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Hope it helps.
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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08 Nov 2018, 03:35
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
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Re: O(x) represents the least odd integer greater than x, whereas o(x)  [#permalink]

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03 Feb 2019, 10:51
Bunuel wrote:
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

O(3.2) + E(–1.7) + o(–1.3) + e(2.7)
5 + 0 -3 +2
4
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Re: O(x) represents the least odd integer greater than x, whereas o(x)   [#permalink] 03 Feb 2019, 10:51
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