Primes & Divisibility

Expert replies

shanice: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Apr 05, 2012 8:48 amFollowed by: 1 member; Thanked: 3 times

by shanice » Thu Apr 05, 2012 10:19 pm

Hello, everyone. I'll be taking my GMAT within 2 months and I'm struggling with the Primes & Divisibility topic. I heard about your site and hope you guys could help me out.

My question is on Remainders. I know this is the formula for remainders - [b]y=xn+r[/b]. I know that r is the remainder, n is the divisor, x is the quotient and y is dividend. I don't understand how to apply this formula to a question below:-

If x is an integer and y=3x+2, which of the following cannot be a divisor of y?

A) 4
B) 5
C) 6
D) 7
E) 8

I read the explanation on this site but I still don't understand. What is the connection of remainder to divisor or dividend and vice-versa.What does the formula mean?

Thanks in advance.

[Moderator Edit: Moved the post to a relevant forum - neelgandham]

Source: Beat The GMAT — Problem Solving | Thu Apr 05, 2012 10:19 pm

killer1387: Legendary Member; Posts: 581; Joined: Sun Apr 03, 2011 7:53 amFollowed by: 5 members; Thanked: 52 times

by killer1387 » Thu Apr 05, 2012 10:38 pm

If x is an integer and y=3x+2, which of the following cannot be a divisor of y?

A) 4
B) 5
C) 6
D) 7
E) 8

you have a number y that is 3x+2,

put x=0,1,2,3.......
you have y= 2,5,8,11,14=> these numbers are divisible by 4,5,8,7

hence 6 will be the answer

hope this helps..!!

shanice: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Apr 05, 2012 8:48 amFollowed by: 1 member; Thanked: 3 times

by shanice » Fri Apr 06, 2012 12:53 am

Thank you for your quick reply,killer1387.

Is there any other way than plugging in numbers? Please explain in detail.

By the way,when the question says "x is an integer", it means x is a whole number (non-fraction or non-decimal right) right?

Thank you.

seal4913: Master | Next Rank: 500 Posts; Posts: 106; Joined: Wed Mar 23, 2011 4:56 pm; Thanked: 8 times

by seal4913 » Fri Apr 06, 2012 4:40 pm

shanice wrote:By the way,when the question says "x is an integer", it means x is a whole number (non-fraction or non-decimal right) right?

Yes, an interger is a whole number therefore a number that is not a fraction. Non decimal, I mean 1 is an interger and 1.0 is the same... but 1.1 isn't an interger

shanice: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Apr 05, 2012 8:48 amFollowed by: 1 member; Thanked: 3 times

by shanice » Fri Apr 06, 2012 5:37 pm

Thank you very much, Seal4913.

Mr Smith: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Fri Apr 06, 2012 1:27 amFollowed by: 1 member; Thanked: 5 times; GMAT Score:770

by Mr Smith » Fri Apr 06, 2012 8:03 pm

Strictly speaking,
Whole numbers are integers but all integers are not whole numbers.
Whole Numbers: 0,1,2,3,4,5,6,7,8,9,10,11,12,13....100.. etc.
Integers: .........-100, .....-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0, 1,2,3,4,5,6,7,8,9,10,11,12,13....100..
Whole numbers are a subset of the numbers.

Ok regarding the original question:
Since y = 3x +2 where x is integer, y is 2 plus a multiple of 3. clearly y is not divisible by 3 and thus not by divisible by the multiples of 3 too.
6 is a multiple of 3, hence 6 is not the divisor of the number.

shanice: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Apr 05, 2012 8:48 amFollowed by: 1 member; Thanked: 3 times

by shanice » Sat Apr 07, 2012 2:02 am

Thank you for the explanation, Mr.Smith.

Everyone in "Beat The Gmat" are so supportive and helpful. I'm glad I joined it.

Thanks, again.

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review