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

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

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New post 27 Oct 2014, 10:21
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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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New post 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

Answer = A
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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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New post 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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New post 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.

Answer: A
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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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New post 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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New post 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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