Aptitude - Numbers - Discussion

The correct answer is 214 only, the remaining options will not satisfy the condition, let me break it down, { In the question they have given successive divisions which means the first number's quotient will be the numerator for the next division and it goes on like that.

Let's see it with an example}

Option 4: 1908 when divided by 4, the remainder is 0 ( expected remainder 2), so it's incorrect.
Option 3: 1) 954 when divided by 4, the remainder is 2 ( as expected ), Quotient is 238
2) Now 238 when divided by 5, the remainder is 3( as expected), Quotient is 47
3) Now again when 47 is divided by 6, the remainder is 5 ( expected remainder 4), So it is incorrect.


Option 2: 476 When divided by 4, the remainder is 0 (expected 2), So it's incorrect.
Option 1: 1) 214 when divided by 4, the remainder is 2 ( as expected ), Quotient is 53,
2) Now 53 when divided by 5, the remainder is 3( as expected), Quotient is 10,
3) Now again when 10 is divided by 6, the remainder is 4 ( as expected), So it is the correct answer.

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

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.

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.

Yes, 214 was first divided by 4 and then the quotient is 53 remainder is 2 then 53 is divided by 5 and then the quotient is 10 remainder is 3, and and then 10 is divided by 6 the reminder is 4.

So, 254 is correct.

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.

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.

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.

Why not 954?

954 = 233 * 4 + 2
233 = 46 * 5 + 3
46 = 6 * 7 + 4
It satisfies the condition same as 214. Then why not 954 instead of 214?

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.