Let S be the set of all positive integers that, when divided

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Mike@Magoosh: GMAT Instructor; Posts: 768; Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members; Location: Berkeley, CA; Thanked: 387 times

by Mike@Magoosh » Mon Oct 27, 2014 9:23 am

Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 76th number in this set?
(A) 605
(B) 608
(C) 613
(D) 616
(E) 621

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Source: Beat The GMAT — Problem Solving | Mon Oct 27, 2014 9:23 am

abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 amFollowed by: 11 members; Location: NY; Thanked: 28 times

by abhasjha » Fri Oct 31, 2014 7:00 am

To get the numbers in set S use .... N= 8A+5 . putting A=0 we get the first number as 5 .putting A = 1 we get the number = 13 ....

first of such number is 5 ...
next number 13 and next number 21 .....

An Arithmetic series then follows . (one way to look at remainder problems is all remainder problems are in a way arithmetic progessions !)

So there are 76 terms in the series with a common difference of 8.

so tn = a+(n-1)d
= 5+ (75)x8
= 5+600
= 605
Answer A

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Mon Nov 10, 2014 11:52 am

If the first multiple of 8 is 0, then the 75th true multiple of 8 gives:
75 x 8 + 5 has last digit 5
Answer = A

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masoom j negi: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Thu Dec 20, 2018 2:09 am

by masoom j negi » Fri Dec 21, 2018 9:09 pm

S = 8x + 5
So, terms in S are in A.P. with first term = 5 and common difference = 8
76th term = a + (76 - 1)d = 5+ (75)8= 605

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8196; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Feb 18, 2019 6:03 pm

Mike@Magoosh wrote:Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 76th number in this set?
(A) 605
(B) 608
(C) 613
(D) 616
(E) 621

The first number in the set is 5, since 5/8 = 0 remainder 5.

The second number in the set is 5 + 1(8).

The third number in the set is 5 + 2(8).

The fourth number in the set is 5 + 3(8).

Continuing the pattern established, we see that the 76th number in the set is 5 + 75(8) = 605.

Answer: A

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