Less than an integer multiple of 4

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sat Feb 22, 2014 11:04 am

Hello,

Can you please assist with this:

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

(A) Two
(B) Three
(C) Four
(D) Five
(E) Six

OA: E

Thanks,
Sri

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Source: Beat The GMAT — Problem Solving | Sat Feb 22, 2014 11:04 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Feb 22, 2014 11:11 am

gmattesttaker2 wrote:How many of the positive integers less than 25 are 2 less than an integer multiple of 4?

(A) Two
(B) Three
(C) Four
(D) Five
(E) Six

When we check the answer choices, we see that all of the answers are very small.
So, it's not unreasonable to start listing the values that satisfy the given conditions.

Positive multiples of 4: 4, 8, 12, 16, 20, 24, 28, etc

So, integers that are 2 less than multiples of 4 are: 4-2, 8-2, 12-2, 16-2, 20-2, 24-2, 28-2, etc
Simplify to get: 2, 6, 10, 14, 18, 22, 26, etc..

We want those values that are LESS THAN 25. So, we have: 2, 6, 10, 14, 18 and 22

There are 6 such values.

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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parveen110: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Fri Jan 17, 2014 7:34 am; Thanked: 7 times

by parveen110 » Wed Feb 26, 2014 4:51 am

gmattesttaker2 wrote:Hello,

Can you please assist with this:

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

(A) Two
(B) Three
(C) Four
(D) Five
(E) Six

OA: E

Thanks,
Sri

Hi Sri,

There is an altenative approach as well.

The question is essentially asking us, how many numbers less than 25 are of the form 4k+2.

We can see that 4*6+2=26. Therefore we'll choose integers less than 6 for k i.e. 0,1,2,3,4,5 to satisfy the given condition.

Total positive integers of the form 4k+2 less than 25 = 6.

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Wed Feb 26, 2014 8:48 am

gmattesttaker2 wrote:How many of the positive integers less than 25 are 2 less than an integer multiple of 4 ?

First of all define the set of Numbers -

S = { 4 , 8 , 12 , 16 ,20 , 24 }

Now if we subtract 2 from theses numbers we obtain a positive Number ( Even from the lowest Number - 4 )

Count the elements in the set..

The answer is without any hesitation [spoiler](6)[/spoiler]

Abhishek

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