On Dividing A Number by 56, We Get 29 as a Remainder GMAT Problem Solving

Question: On dividing a number by 56, we get 29 as a remainder. On dividing the same number by 8, what will be the remainder?

1. 3
2. 4
3. 5
4. 7
5. 2

Answer:
Approach Solution (1):
\({N\over 56}=a+{29\over56}\)
\(N=56a+29\)
\(N=(8)(7)a+29\)
\({N\over8}=7a+{29\over8}\)
\({29\over8}=3+R5\)
Or, 8 is a factor of N, so the original remainder 29 can be divided by 8; that remainder is the answer
Correct option: C

Approach Solution (2):
As we know that:
29 + 56 = 85
Therefore,\(85\over8\)gives 5 as remainder
Correct option: C

Approach Solution (3):
We know that, Dividend = (Divisor * Quotient) + Remainder
\((56\times{Q})+29=D\rightarrow(1)\)
\(D\div{R}=R\rightarrow(2)\)
\(((56\times{Q}+29)\div8=R\)
Since 56 is already divisible by 8
\(\Rightarrow29\div8=R\)
\(\Rightarrow85\div8\)
R=5
Required remainder is 5
Correct option: C

“On dividing a number by 56, we get 29 as a remainder. On dividing the same number by 8, what will be the remainder?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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