If (z + 3)/5 is an integer, what is remainder when z is divided by 5?

Question

A. 2
B. 3
C. 4
D. 5
E. 6

g106 · Answer

Assume the answer choices as the value of z

A) 2; (2+3)/5 = 1 satisfies the equation
B) 3; (3+3)/5 = 1.2 Not an integer
C) 4; (4+3)/5 = 1.4 Not an integer
D) 5; (5+3)/5 = 1.6 Not an integer
E) 6; (6+3)/5 = 1.8 Not an integer

Ans A

PareshGmat · Answer

Answer = A. 2

Let z = 2, gives  \frac{2+3}{5} = integer

For  \frac{2}{5} , remainder = 2

sunaimshadmani · Answer

(z+3)/5 is an integer, which means that remainder must be a multiple of 5.
Eq can be written as z/5 + 3/5,
3/5 gives a remainder of 3, which means that z must be 5n+2, where n is an integer.
Answer is A.

Konstantin1983 · Answer

From the question we can see that if (z+3)/5 is an integer it means that z+3 should be a multiple of 5. Hence z=2 or z=7 or z=12 and so on. Hence if,for example, z=7 then (7/5) leaves a remainder of 2. If z=12 then (12/5) leaves a remainder of 2 again. Hence answer A.

manpreetsingh86 · Answer

(z+3)/5 = I
z+3=5I
adding two on both sides we have
z+3+2 = 5I+2
z+5=5I+2
z=5I-5+2
=5(I-1)+2

thus z when divided by 5 will always gives a remainder of 2.

rakshithbabu · Answer

(z + 3)/5 is an Integer.
Lets say K+1
(z + 3)/5 = k+1
z+3 = 5k+5
z=5k+5-3
z=5k+2

So when z is divided by 5 reminder is 2.

mvictor · Answer

Z is an integer that needs 3 to be divisible by 5
in that case, whatever number Z is, the remainder will always be 2.

Abhishek009 · Answer

Since (z + 3)/5 is an integer ,  \frac{(z + 3)}{5}  is an integer must be divisible by 5

The least possible value of z must be 2

\frac{2}{5}  - reminder is 2 ( Answer choice A)

Hence the correct answer is A

kashifgolf · Answer

Solution:

The question states that z+3/5 is an integer, therefore we know that z+3 is a multiple of 5. Now to solve this question we can plug in a value for z+3 to arrive at the solution.
Lets assume z+3 to be any multiple of 5. Let say z+3 = 15, then z = 12. The question asks what is the remainder when z is divided by 5. When 12/5 we know the remainder is 2. If we plug in any other multiples of 5 for z+3, then too we will get a remainder of 2 when z is divided by 5. Therefore our answer is A.

Mo2men · Answer

(z + 3)/5 = Integer......Then z could be 2,7,12,17...etc

In the above.........z /5 .......reminder is 2

Answer: A

pierjoejoe · Answer

negative remainder theorem is very important

if (z+3)/5 = K where K is a integer

than
z = 5K-3

we now divide z by 5
z/5 = (5K-3)/5 = K - 3/5
 
for the negative remainder properties (still need to figure them out well tho) --> the remainder is
5-3 = 2

3mrecan · Answer

z/5 + 3/5 = # (1)

z = 2

z/5 = 2

BrushMyQuant · Answer

(z + 3)/5 is an integer

=> (z+3)/5 = k (where k is an integer)
=> z + 3 = 5k
=> z = 5k - 3

What is remainder when z is divided by 5?

Remainder of z by 5 = Remainder of (5k - 3) by 5 = Remainder of 5k by 5 + Remainder of -3 by 5 = 0 + (-3 + 5) = 2

So,  Answer will be A 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

If (z + 3)/5 is an integer, what is remainder when z is divided by 5?

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If (z + 3)/5 is an integer, what is remainder when z is divided by 5?

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