Whts the Algebric way of solving this question

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[email protected]: Master | Next Rank: 500 Posts; Posts: 429; Joined: Wed Sep 19, 2012 11:38 pmFollowed by: 4 members; Thanked: 6 times

by [email protected] » Sun Mar 02, 2014 10:30 pm

When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

Ans is 3

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Mar 02, 2014 10:47 pm

k/5 = r is 2

k/6 = r is 5

To find: k/7 remainder

we know that "k" is less than 40.. so lets consider values less than 40

k/5 = r is 2

Possible values of k = 2, 7, 12, 17, 22, 27, 32, 37

k/6 = r is 5

Possible values of k = 5, 11, 17, 23, 29, 35

Common values = 17

Remainder = 17/7 = 3 remainder

R A H U L

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Mar 02, 2014 11:35 pm

Hi shibsriz,

Rahul has properly explained this question, so I won't rehash that here.

"Remainder" questions are always based on patterns, so you should put your energy into doing enough work to spot the pattern.

You'll notice, from the first group of numbers listed, that the values increase by 5 and that K has to end in EITHER 2 OR 7. You don't have to list all of the possibilities out if you don't want to, but it might make the task easier.

From the second group, you should notice, relatively quickly, that the values increase by 6, so listing them shouldn't be too difficult.

Based on the way that the question is worded, you need to find ANY value for K that fits both rules. Once you find the number 17 in the second set of values, you're ready to finish off the question.

Take advantage of the patterns behind this (and other) questions on Test Day. Many of the shortcuts that you'll find on the GMAT are based on the built-in patterns around which the question was designed.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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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 » Mon Mar 03, 2014 1:54 am

[email protected] wrote:When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

Ans is 3

Hi shibriz,

There is an alternate approach here, in case you are not interested in listing out possibilities in the two cases.

We have been given a number which is of the form:
5p+2 or 6q+5

On equating:

5p+2=6q+5

You'll find that the value of p is 3 and the required number is 17. Remainder when 17 is divided by 7 is 3.

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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 » Mon Mar 03, 2014 8:03 am

[email protected] wrote:When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

I'd like to mention that theCodeToGMAT is demonstrating a nice rule that says, If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 8 leaves a remainder of 1, then the possible values of k are: 1, 1+8, 1+(2)(8), 1+(3)(8), 1+(4)(8), . . . etc.

When positive integer k is divided by 5, the remainder is 2.
So, the possible values of k are: 2, 2+5, 2+(2)(5), 2+(3)(5), 2+(4)(5), . . . etc.
In other words, the possible values of k are: 2, 7, 12, 17, 22, etc.

See theCodeToGMAT's solution for the rest.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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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 » Mon Mar 03, 2014 8:37 am

[email protected] wrote:When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 40, what is the remainder when k is divided by 7?

Ans is 3

K = 5Q + 2

Possible values of K less than 40 are -

7 , 12 , 17 , 22 , 27 , 32 , 37

Again ,

K = 6Q + 5

Possible values of K less than 40 are -

11 , 17 , 23 , 29 , 35

We observe that in both the sets the common element is 17 , so the value of K is 17

When 17 is divided by 7 the remainder obtained is 3.

Abhishek

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