BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Less than an integer multiple of 4

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
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
Image
Top
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.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 359
Joined: Wed Mar 11, 2009 4:37 am
Location: Kolkata, India
Thanked: 50 times
Followed by:2 members

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
Top
Post new topic Post Reply
• Page 1 of 1