For a non-negative integer n, the function mod(n, d) denotes the remai

Question

For a non-negative integer n, the function mod(n, d) denotes the remainder obtained when n is divided by positive integer d. Which of the following statements must be true?

I. mod(n, d) = mod(2n, d)
II. If mod(n, d) = 1, then mod(5n, d) = 5
III.  ^2 = mod(n^2, d)

A. I only
B. II only
C. III only
D. I, II and III
E. None of the above

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yashikaaggarwal · Answer

I. mod(n, d) = mod(2n, d)
Let N = 7 and D = 5
Remainder when 7/5 = 2
Remainder when 14/5 = 4
2≠4 (False)

II. If mod(n, d) = 1, then mod(5n, d) = 5
Let N = 6 and D = 5
Remainder when 6/5 = 1
Remainder when 30/5 = 0
1≠0 (False)

III.  ^2 = mod(n^2, d)
Let N = 8 and D = 5
Remainder when 8/5 = (3)^2 = 9
Remainder when 64/5 = 4
9≠4 (False)

None if the statements is true.
IMO E

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vipulshahi · Answer

n = non -ve int 
mod(n,d) =R, remainder
n = d*q+R

1) mod(n,d) = mod(2n,d)
mod(n,d) = n - d*q
mod(2n, d) = 2*n - d*k

n - d*q is not always equal to 2*n - d*k.
Thus, Incorrect

2) if mod(n,d) = 1 then mod(5n,d) = 5
n = d*q + 1 ; 5*n = d * k + 5 
 it depends on "k' & "q"
so n- d*q is not always equal to 5*n - d*k
Thus, Incorrect

3)  ^2 = mod(n^2 , d)

n = d*q + R1 = > R1 = n - d*q
n^2 = d*k + R2 = > R2 = n^2 - d*k

R1 & R2 will never be same
Thus , incorrect

IMO(E)

gurmukh · Answer

First case is true when d is the divisor of n and not always.
Second case is true when 5 times the remainder on LHS is less than divisor d
Third case is true when remainder is 0 or 1.

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HoneyLemon · Answer

E , imo
For a non-negative integer n, the function mod(n, d) denotes the remainder obtained when n is divided by positive integer d. Which of the following statements must be true?

I. mod(n, d) = mod(2n, d)
  -- False .. e.g. MOD (5,4) = 1 . mod(10, 4) = 2  
II. If mod(n, d) = 1, then mod(5n, d) = 5
   -- False .. e.g. MOD (5,4) = 1 . mod(25, 4) = 1

III.  ^2 = mod(n^2, d)

-- False .. e.g.   ^2 = 4 . mod(25, 3) = 1

So None is correct . 
Hence Ans is E .

ScottTargetTestPrep · Answer

Solution:

Let’s analyze each statement using numerical values for n and d.

I. mod(n, d) = mod(2n, d)

If n = 1 and d = 2, mod(1, 2) = 1 and mod(2, 2) = 0. We see that mod(1, 2) ≠ mod(2, 2). So statement I is not true.

II. If mod(n, d) = 1, then mod(5n, d) = 5

Again, we can let n = 1 and d = 2 since mod(1, 2) = 1. However, mod(5, 2) = 1 ≠ 5. So statement II is not true.

III.  ^2 = mod(n^2, d)

If n = 2 and d = 3,  ^2 = 2^2 = 4 and mod(2^2, 3) = mod(4, 3) = 1. We see that  ^2 ≠ mod(2^2, 3). So statement III is not true.

Answer: E

sambitspm · Answer

Kindly see the attachment
E

bumpbot · Answer

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For a non-negative integer n, the function mod(n, d) denotes the remai

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