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# How many of the positive integers less than 25 are 2 less than an inte

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VP
Joined: 31 Oct 2013
Posts: 1116
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
How many of the positive integers less than 25 are 2 less than an inte  [#permalink]

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09 Feb 2019, 23:40
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:02) correct 38% (01:20) wrong based on 8 sessions

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How many of the positive integers less than 25 are 2 less than an integer multiple of 4?

A)2
B)3
C)4
D)5
E)6
Director
Joined: 09 Mar 2018
Posts: 909
Location: India
Re: How many of the positive integers less than 25 are 2 less than an inte  [#permalink]

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09 Feb 2019, 23:47
selim wrote:
How many of the positive integers less than 25 are 2 less than an integer multiple of 4?

A)2
B)3
C)4
D)5
E)6

Keyword: positive integers less than 25

4*6 = 24 -2 = 22
4*5 = 20 -2 =18
4*4 = 16-2 =14
4*3 =12-2 = 10
4*2 = 8-2 =6
4*1 =4- 2 = 2

6
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How many of the positive integers less than 25 are 2 less than an inte  [#permalink]

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10 Feb 2019, 04:10

Solution

To find:
• The number of positive integers, which are less than 25, and also 2 less than an integer multiple of 4

Approach and Working:
As the number is 2 less than an integer multiple of 4, we can write the generalised form of the number as 4k – 2, where k is a positive integer.

• When k = 1, the number is 4 x 1 – 2 = 2
• When k = 2, the number is 4 x 2 – 2 = 6
• When k = 3, the number is 4 x 3 – 2 = 10
• When k = 4, the number is 4 x 4 – 2 = 14
• When k = 5, the number is 4 x 5 – 2 = 18
• When k = 6, the number is 4 x 6 – 2 = 22
• When k = 7, the number is 4 x 7 – 2 = 26, which is not possible as the number is less than 25

Hence, the correct answer is option E.

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How many of the positive integers less than 25 are 2 less than an inte   [#permalink] 10 Feb 2019, 04:10
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