If N divided by 5 leaves a remainder of 4, and N divided by 2 leaves a remainder of 1 , then the one’s digit of N is?

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Concept: Concept of expressing division in dividend, divisor, quotient and remainder will be used.
Dividend = Divisor

\times

Quotient + Remainder
Complete step-by-step answer:
First,
using the statement I
N, when divided by 2, leaves a remainder 1.
N = 2

\times

X + 1
Using this statement, it can be concluded that the number “N” is an odd number as it is not divisible by 2.
Now using the statement II
N divided by 5 leaves a remainder 4.
N = 5

\times

X’ + 4
It is known that a number is divisible by 5 if its unit digit is either 5 or 0.
So, analyzing the case by taking the unit digit of the largest number which is divisible by 5 and less than N.
Case I, is when the unit digit of the largest number which is divisible by 5 and less than N be 0. So, the unit digit of N shall be 0 + 4 = 4. But unit digit 4 implies N is even, Hence, this case is not possible.
Case II, We will consider the unit digit of the largest number which is divisible by 5 and less than N be 5. Hence, the unit digit of N will be 5+4 = 9, which is a possible case.
Therefore, It can be concluded that the one’s digit of N is 9.
Hence the answer is option 2.

Watch 3-min video & get full concept clarity