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The integers r, s, and t all have the same remainder when divided by 5 https://gmatclub.com/forum/theintegersrsandtallhavethesameremainderwhendividedby318380.html 
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Author:  Bunuel [ 13 Mar 2020, 01:48 ] 
Post subject:  The integers r, s, and t all have the same remainder when divided by 5 
The integers r, s, and t all have the same remainder when divided by 5. What is the value of t ? (1) r + s = t (2) 20 ≤ t ≤ 24 Are You Up For the Challenge: 700 Level Questions 
Author:  GMATinsight [ 13 Mar 2020, 05:09 ] 
Post subject:  Re: The integers r, s, and t all have the same remainder when divided by 5 
Bunuel wrote: The integers r, s, and t all have the same remainder when divided by 5. What is the value of t ? (1) r + s = t (2) 20 ≤ t ≤ 24 Given: The integers r, s, and t all have the same remainder when divided by 5 I.e. r = 5a+p I.e. s = 5b+p I.e. t = 5c+p where p is the remainder. Question: t = t = 5c+p = ? Statement 1: r + s = t I.e. (5a+p) + (5b+p) = 5c+p I.e. 5(a+b) + p = 5c I.e. p must be zero and t must be a multiple of 5 but c is unknown hence value of t can not be calculated NOT SUFFICIENT Statement 2: 20 ≤ t ≤ 24 t can be 20 or 21 or 22 etc hence NOT SUFFICIENT Combining the statements t is a multiple of 5 and 20 ≤ t ≤ 24 I.e. t = 20 SUFFICIENT Answer: Option C 
Author:  exc4libur [ 09 Jun 2020, 09:45 ] 
Post subject:  Re: The integers r, s, and t all have the same remainder when divided by 5 
Bunuel wrote: The integers r, s, and t all have the same remainder when divided by 5. What is the value of t ? (1) r + s = t (2) 20 ≤ t ≤ 24 r/5=5p+x s/5=5q+x t/5=5r+x 0 ≤ remainder x ≤ 4 (1) insufic 5p+x+5q+x=5r+x 5p+5q+x=5r only multi of 5 for x is 0 5(p+q)=5r no info about r (2) insufic (1/2) sufic 20≤5r+x≤24 20≤5r≤24 4≤r<5 r=integer=4 Ans (C) 
Author:  Tonkotsu [ 21 Jan 2021, 13:22 ] 
Post subject:  Re: The integers r, s, and t all have the same remainder when divided by 5 
GMATinsight wrote: Statement 1: r + s = t I.e. (5a+p) + (5b+p) = 5c+p I.e. 5(a+b) + p = 5c I.e. p must be zero and t must be a multiple of 5 but c is unknown hence value of t can not be calculated Hi GMATinsight Thank you so much for the help. Actually, this all the sudden makes sense to me. I forgot that there is an unwritten constraint for p p must be less than 5. Furthermore, the LHS of this equation below must be a multiple of 5, which subsequently points to p equaling 0. 5(a+b) + p = 5c My apologies. 
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Post subject:  Re: The integers r, s, and t all have the same remainder when divided by 5 
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