Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.110)

110. 

A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:

[A]. 214
[B]. 476
[C]. 954
[D]. 1908

Answer: Option A

Explanation:

 4 | x            z = 6 x 1 + 4  = 10
 -----------
 5 | y -2         y = 5 x z + 3  = 5 x 10 + 3  = 53
 -----------
 6 | z - 3        x = 4 x y + 2  = 4 x 53 + 2  = 214
 -----------
   | 1 - 4
   
Hence, required number = 214.

Aman said: (Mar 7, 2012)  
Not able to understand this question, what is asking, please discuss.

Divya said: (Sep 3, 2012)  
Let the no. is x.
according to question,x=4a+2.
a=5b+3.
b=6c+4
By solving this, we get
x=4[5(6c+4)+3]+2 (since a=5b+3,b=6c+4)
x=120c+94
Now for checking the answer we put c=1
x = 214 i.e. ans.

M.Stoica said: (Jul 28, 2014)  
214 divided by 5 how the remainder can be 3?

Maahi said: (Aug 26, 2014)  
If we take, x=4a+2 then a=5b+3 and b=6c+4. How does it come?

Pooja said: (Feb 2, 2015)  
We don't need to divide 214 by 5 but quotient obtain by dividing 214 by 4, i.e. 53. Further you will get 3 as remainder.

Onyi said: (May 4, 2015)  
I thought the same way as @M.Stoica, then I saw the word "successively". I think it simply means 'in succession' hence, it is the quotient obtained from the first division that you then divide by 5 and the next quotient result, you divide by 6 having this in mind, then go through the calculations by @Divya or the calculations provided after the answer, I'm sure you will understand.

Bhavna said: (Oct 27, 2015)  
Not able to understand the solution elaborate it please.

Anil Jangid said: (Feb 3, 2016)  
Sir I have other problem, please help me.

(5)x + (12)x = (13)x.

x is power of numbers. Then what would be value of x?

Dhanya said: (May 4, 2016)  
Can anyone elaborate it step by step?

Santha said: (Jun 9, 2016)  
If x is a power of numbers, then.

(5^2) + (12^2) = 25 + 144 = 169.

Which is equal to 13^2 = 169.

So, the value of x is 2.

Manju said: (Jul 22, 2016)  
@Divya could you please elaborate your explanation?

How a = 5b + 3?

Manju said: (Jul 22, 2016)  
Dividend = divisor * quotient + remainder.

So let the number be X.

=> X = 4a + 2--->1st eq (here a is quotient of 1st division , this will be divided by 5).
=> a = 5b + 3 (b is 2nd quotient, similarly).
=> b = 6c + 4

Considering 1st equation.
X = 4[5(6c + 4) + 3] + 2.
X = 120c + 94 ( here I did'nt get about 94).

Can anyone please explain it?

And rest calculations are like as Divya explained

Vivek Gupta said: (Jul 28, 2016)  
Wrong answer.

How can remainder will be 3 when 214 is divided by 5?

The Correct answer should be 60k-2.

Where k is any integer.

Nikhil Kumar said: (Sep 19, 2016)  
Let, p be the number.

Suppose,
p ÷ 4 = q
p ÷ 4 = q, remainder = 2.

q ÷ 5 = r
q÷5=r, remainder = 3.

r ÷ 6 = s
r ÷ 6=s, remainder = 4.

Then,
r = 6s + 4
q = 5r + 3
q = 5r + 3= 5(6s + 4) + 3 = 30s + 23.
p = 4q + 2 = 4 (30s + 23) + 2 = 120s + 94

Suppose the final quotient,

s = 1.
Then,
p = 120 * 1 + 94 = 214

214 is one of the choices given and hence it is the answer.

Manikandan said: (Nov 21, 2016)  
How is the s value equal to 1? Please explain.

Vijay Mittal said: (Dec 9, 2016)  
In this question 214 is correct if only 214 is divided by 4, 5, 6. Orderly using the quotient of the previous solution. But in question, there is no explanation about this.

Bikas Khan said: (Mar 14, 2017)  
I can't understand it please explain simple.

Shadab said: (Apr 25, 2017)  
The Number is 4 5 6 And their Remainder in 2 3 4 On just multiplying we got the answer like this [(6+4) * (5)+(3) * (4)+(2)] = 214.

Sarthaksaxena said: (Aug 12, 2017)  
I guess this is wrong question as how it is possible to get 3 as a remainder when 214 is divisible by 5? Please tell me.

D Priya said: (Jan 24, 2018)  
@Sarthaksaxen.

This is successive division not normal division.

Tapan said: (Mar 8, 2018)  
I think it is right. Because 214 first divided by 4 then the quotient is 53 remainder is 2, then 53 is divided by 5 then the quotient is 10 remainder is 3, and then 10 is divided by 6 then the reminder is 4.

Debdas Biswas said: (Jan 18, 2019)  
Thanks all for explaining this.

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