When m is divided by 7, the remainder is 5. When m is divided by 13, t

Question

When m is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < m < 200, what is the greatest possible value of m?

A. 5
B. 19
C. 61
D. 74
E. 110

chetan2u · Answer

The simplest way would be to test the options.

Since we are looking for largest, start from 110.

110-5 or 105 should be divisible by 7....yes
110-6 or 104 should be divisible by 13...yes

E

Aswin12 · Answer

You can use the method of finding a common equation that solves for both the given equation 
we know from the question that m= 7k+5 and m=13y+6 
in this case it would be
m=(LCM of 7,13)*x + first common digit in the above patterns (m= 7k+5 and m=13y+6)
 19 ,26,.......]
 19 ,32,........]
Therefore the common equation in this case would be  m=91x +19 
and substituting different values of x we can get the answer ,which in this case is 110 which we get by substituting x=1 
 
Or we can do this by blunt force
by checking if all the numbers satisfy both the divisibility conditions mentioned in the question

BrushMyQuant · Answer

Let's solve the problem using two methods.

Method 1: Testing answer choices.

Let's try with the biggest number as we need to find the greatest possible value

E. 110

110 when divided by 7 gives 5 remainder which is correct.
110 when divided by 13 gives 6 remainder which is correct.
=> 110 is the solution

Method 2: Algebra

When m is divided by 7, the remainder is 5.

Dividend = Divisor * Quotient + Remainder

m = 7*a + 5 (where a is an integer) = 7a + 5 ...(1)

When m is divided by 13, the remainder is 6.

m = 13*b + 6 (where b is an integer) = 13b + 6 ...(2)

If 1 < m < 200, what is the greatest possible value of m?

From (1) and (2) 12 get

m = 7a + 5 = 13b + 6
=> a = \(\frac{13b + 1}{7}\)

Only those values of b which will also make a an integer will give us the possible values of m

=> b = 1, 8 will give us integer values for a
=> b=1, = 13*1 + 6 = 19
=> b=8, = 13*8 + 6 = 110

So, Answer will be E
Hope it helps!

Watch the following video to MASTER Remainders

bumpbot · Answer

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When m is divided by 7, the remainder is 5. When m is divided by 13, t

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When m is divided by 7, the remainder is 5. When m is divided by 13, t

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