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Retired Moderator
Joined: 19 Nov 2020
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GRE 1: Q160 V152
What is the number of odd integers ...
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30 Jul 2021, 15:50
30 Jul 2021, 15:50
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What is the number of odd integers that are greater than \(116,999\) and less than \(117,289\)?
(A) 147
(B) 146
(C) 145
(D) 144
(E) 143
(A) 147
(B) 146
(C) 145
(D) 144
(E) 143
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What is the number of odd integers ...
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30 Jul 2021, 19:49
30 Jul 2021, 19:49
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motion2020 wrote:
What is the number of odd integers that are greater than \(116,999\) and less than \(117,289\)?
(A) 147
(B) 146
(C) 145
(D) 144
(E) 143
(A) 147
(B) 146
(C) 145
(D) 144
(E) 143
To find the number of terms in a range;
Case I: when we have an odd and an even number as first and last term, the number of odd numbers and even numbers are same
Case II: when we have both first and last terms as odd or both even, the number of terms will have 1 more odd or even term.
Here, a number greater than 116,999 means 117,000 (First term)
and, less than 117,289 means 117,288 (Last term)
So, Case II applies
Number of even terms = \(\frac{Last - First}{2}\) + 1 = \(\frac{288}{2}\) + 1 = 145 terms
Number of odd terms = 288 - 145 = 143 terms
Hence, option E
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
What is the number of odd integers ...
[#permalink]
30 Jul 2021, 21:45
30 Jul 2021, 21:45
1
you are including two evens, before adding 1
formula for interval that is the spaced order defined exclusively is (A-B)/2 - 1 too
To find the number of terms in a range;
Case I: when we have an odd and an even number as first and last term, the number of odd numbers and even numbers are same
Case II: when we have both first and last terms as odd or both even, the number of terms will have 1 more odd or even term.
Here, a number greater than 116,999 means 117,000 (First term)
and, less than 117,289 means 117,288 (Last term)
So, Case II applies
Number of terms = \(\frac{Last - First}{2}\) + 1 = \(\frac{288}{2}\) + 1 = 145 terms
Hence, option C
formula for interval that is the spaced order defined exclusively is (A-B)/2 - 1 too
KarunMendiratta wrote:
motion2020 wrote:
What is the number of odd integers that are greater than \(116,999\) and less than \(117,289\)?
(A) 147
(B) 146
(C) 145
(D) 144
(E) 143
(A) 147
(B) 146
(C) 145
(D) 144
(E) 143
To find the number of terms in a range;
Case I: when we have an odd and an even number as first and last term, the number of odd numbers and even numbers are same
Case II: when we have both first and last terms as odd or both even, the number of terms will have 1 more odd or even term.
Here, a number greater than 116,999 means 117,000 (First term)
and, less than 117,289 means 117,288 (Last term)
So, Case II applies
Number of terms = \(\frac{Last - First}{2}\) + 1 = \(\frac{288}{2}\) + 1 = 145 terms
Hence, option C
