How many positive integers less than 100 have a remainder of 2 when divided by 13?

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GMATprofessional21: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Wed Aug 05, 2020 2:05 am

by GMATprofessional21 » Wed Aug 05, 2020 2:22 am

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How many positive integers less than 100 have a remainder of 2 when divided by 13?

A 6
B 7
C 8
D 9
E 10

The possible numbers that fulfill this criteria are 2, 15, 28,41,54,67,80,93. This is 8 numbers, so the answer is C

Source: Beat The GMAT — Problem Solving | Wed Aug 05, 2020 2:22 am

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Re: How many positive integers less than 100 have a remainder of 2 when divided by 13?

by Scott@TargetTestPrep » Mon Aug 10, 2020 3:24 am

GMATprofessional21 wrote: ↑
Wed Aug 05, 2020 2:22 am
How many positive integers less than 100 have a remainder of 2 when divided by 13?

A 6
B 7
C 8
D 9
E 10

Solution:

The first positive integer that has a remainder of 2 when divided by 13 is 2. The greatest positive integer less than 100 that has a remainder of 2 when divided by 13 is 93.

So, the total number of numbers that have a remainder of 2 when divided by 13 is (93 - 2)/13 + 1 = 7 + 1 = 8.

Answer: C

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