What is the remainder when 24^3*38^5 + 17^7 is divided by 3 ?

Question

What is the remainder when  24^3*38^5 + 17^7  is divided by 3 ?

A. -1
B. 0
C. 1
D. 2
E. 3

chipsy · Answer

As 24^3 is multiple of 3

Remainder for (24^3 * 38^5) is 0

Now, (17^7)/3 = 2^7/3 = 16*8/3
 = 1*2/3
 = 2 remainder

So option D

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Saransh123 · Answer

I used this approach
24*38= The unit digit is 2.

17^7= The unit digit is 3.

Therefore 3+2=5 and when 5 is divided by 3 the remainder is 2.

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QuantMadeEasy · Answer

Step1 : Understanding the question 
When 24 is divided by 3, remainder is 0
Similarly when  24^3  is divided by 3, remainder is 0
hence,  24^3∗38^5  is divided by 3, remainder is 0

When 17 is divided by 3, remainder is 2
 17^7  is divided by 3, remainder is  2^7 
 2^7 = 2^4*2^3  = 16*8
When 16 is divided by 3, remainder is 1
When 8 is divided by 3, remainder is 2
16*8 when divided by 3, leaves remainder of 1*2 = 2

Hence, when  24^3∗38^5+17^7  is divided by 3, reminder is 0+2 = 2

D is correct

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MathRevolution · Answer

24^3  is completely divisible by '3' and hence,  24^3 * 38^5  will give '0' remainder.

17 when divided by '3' gives (-1) as remainder :  (-1)^7  =  \frac{-1}{3}  = -1 + 3 = 2

Answer D

kntombat · Answer

The unit digit of  24^{3)  = 4;
The unit digit of  38^{5} = 8;
The unit digit of  17^{7} = 3;
Therefore, the remainder of  \frac{R(4*8+3)}{(2)} = \frac{R(35)}{(3)}  = 2.
 Hence the answer is D.

ScottTargetTestPrep · Answer

Solution:

Since 24 is divisible by 3, 24^3 x 38^5 is divisible by 3 and thus has a remainder of 0 when divided by 3. Therefore, if the expression has any nonzero remainder when divided by 3, it has to come from 17^7. Notice that 17 has a remainder of 2 when divided by 3; thus, the remainder when 17^7 is divided by 3 is equal to the remainder when 2^7 is divided by 3. Since 2^7 = 128 and 128/3 = 42 R 2, the remainder is 2.

Answer: D

RahulKumarSinha · Answer

Hi, I have a doubt that, isn't the remainder -1 & 2 the same, in case of division by 3 ?

HarshavardhanR · Answer

When we are asked to find the remainder when a number is divided by another number, in reality, can this remainder be negative?

For instance, 23 when divided by 3 -> what still remains is what we call remainder. What remains is a 2. By definition, remainder can never be negative. It is "what still remains".

It is important to remember that negative remainder is only for making the calculations easy. It should never be the final answer. Think of negative remainder as a useful Work-In-Process (WIP) entity. It is never the final answer.

Hence, -1 should not be the final answer. It should be 2 only.

Hope this helps!
___
Harsha
Passionate about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com

BrushMyQuant · Answer

We need to find the remainder when  24^3*38^5 + 17^7  is divided by 3?

Remainder of  24^3*38^5 + 17^7  by 3 = Remainder of  24^3*38^5  by 3 + Remainder of  17^7  by 3
= 0 + Remainder of  17^7  by 3  
 
 We solve these problems by using Binomial Theorem, where we split the number into two parts, one part is a multiple of the divisor(3) and a big number, other part is a small number.

=>  17^{7}  =  (18-1)^{7}

Watch this video to  MASTER BINOMIAL Theorem

Now, if we use Binomial Theorem to expand this then all the terms except the last term will be a multiple of 3
=> All terms except the last term will give remainder of 0 when divided by 3
=> Problem is reduced to what is the remainder when the last term (i.e. 7C7 * 18^0 * (-1)^7) is divided by 3
=> Remainder of -1 is divided by 3 
 => Remainder of -1 + 3 = 2

So,  Answer will be D 
Hope it Helps!

Watch following video to MASTER Remainders by 2, 3, 5, 9, 10 and Binomial Theorem

https://www.youtube.com/watch?v=h1HTEhmUb1w

What is the remainder when 24^3*38^5 + 17^7 is divided by 3 ?

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What is the remainder when 24^3*38^5 + 17^7 is divided by 3 ?

Prep Toolkit

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