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

Question

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 :-)

PareshGmat · Accepted Answer

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

masoomjnegi · Answer

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

ScottTargetTestPrep · Answer

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

IanStewart · Answer

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.

KanishkM · Answer

Series will begin from 5,13,21

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

A

vasu1104 · Answer

since remainder is 5 when divided by 8, the first num needs to be 5 itself.

now remainder is 5 that means each num after 5 will be 8 higher than preceding num.

so our sequence will be = 5,13,21,29,...

we need to find 76th num in sequence.

we can easily use the formula of an = a1 + (n-1)d

here d= 8 (13-5)
a1= 5
n = 76

a76 = 5 + (76-1) *8

a76 = 605

choice A

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards