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# Let S be the set of all positive integers that, when divided by 8, hav

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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Let S be the set of all positive integers that, when divided by 8, hav  [#permalink]

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27 Oct 2014, 10:21
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45% (medium)

Question Stats:

63% (01:34) correct 37% (01:49) wrong based on 221 sessions

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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

For a set of practice problems on sequences, as well as the OE for this problem, see:
https://magoosh.com/gmat/2014/gmat-prac ... sequences/

Mike

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Re: Let S be the set of all positive integers that, when divided by 8, hav  [#permalink]

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27 Oct 2014, 19:05
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mikemcgarry 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

For a set of practice problems on sequences, as well as the OE for this problem, see:
https://magoosh.com/gmat/2014/gmat-prac ... sequences/

Mike

The set S = {5, 13, 21, 29, ..................... }

1st Number = 8 * 0 + 5 = 5

2nd Number = 8 * 1 + 5 = 13

3rd Number = 8 * 2 + 5 = 21

76th Number = 8 * (76-1) + 5 = 605

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Re: Let S be the set of all positive integers that, when divided by 8, hav  [#permalink]

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21 Dec 2018, 22:18
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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Re: Let S be the set of all positive integers that, when divided by 8, hav  [#permalink]

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18 Feb 2019, 19:19
mikemcgarry 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.

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Re: Let S be the set of all positive integers that, when divided by 8, hav  [#permalink]

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18 Feb 2019, 22:11
Since the use of mathematical terminology here might be confusing for some people, I'll point out that sets are, by definition, not in any order at all. It doesn't mean anything to talk about the "first element" or the "76th number" in a set; the set {a, b, c} is identical to the set {c, b, a}. An ordered list of values is a sequence, not a set.
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Re: Let S be the set of all positive integers that, when divided by 8, hav  [#permalink]

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18 Feb 2019, 22:48
mikemcgarry 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

For a set of practice problems on sequences, as well as the OE for this problem, see:
https://magoosh.com/gmat/2014/gmat-prac ... sequences/

Mike

Series will begin from 5,13,21

a_76 = a + (n-1) d
= 5 + 75 * 8
= 5+ 560 + 40
= 605

A
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Re: Let S be the set of all positive integers that, when divided by 8, hav   [#permalink] 18 Feb 2019, 22:48
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