Find the unit's digit in the product 2467^153*341^72

Question

Competition Mode Question

What is the unit's digit in the product  2467^{153} * 341^{72} ?

(A) 0
(B) 1
(C) 2
(D) 7
(E) 9

Find the unit's digit in the product (2467)^153 * (341)^72

(A) 0
(B) 1
(C) 2
(D) 7
(E) 9

CareerGeek · Accepted Answer

Unit digit of  2467^{153}∗341^{72}  is same as unit digit of  7^{153}∗1^{72} 
=  7^{153} 
=  7^{4*38 + 1}  (Since cyclicity of 7 is 4)
=  7^1 
=  7

IMO Option D

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eakabuah · Answer

2467^153 x 341^72
Taking each of the terms separately and computing the unit digits correspondingly, we get
341^72
but the unit digit of 341 is 1. all powers of 1 will result in 1, hence the unit digit of 341^72=1
2467^153
the unit digit of 2467 = 7. The unit digits of the powers of 7 are as follows:
7^1=7
7^2=9
7^3=3
7^4=1
7^5=7
7^6=9
so we can see that the cyclicity of the powers of 7 is 4
hence 153/4 =38*4 + 1
Therefore the unit digit lies at the 5th position or 5th power of 7
i.e. unit digit of 7^153 = unit digit of 7^5 = 7

hence unit digit of 2467^153 x 341^72 = 7x1 = 7.

The answer is therefore D.

Kanika3agg · Answer

Ans D - 7

2467^153∗341^72

Units digit of the product is dependent on the units digits of 2467^153 and 341^72. The units digits of 1^72 would be 1 because 1's cyclicity is 1.
Units digit of 2467^153 is 7. The cyclicity of 7 is 4. 
7^0 =1
7^1 =1
7^2 = 9
7^3 = 3
7^4 = 1
7^5 = 7

So, the multiplication of these two numbers would be 7*1 = 7

madgmat2019 · Answer

153=4K+1

7^4k+1 = last digit is 7
341^72 = last digit is 1
so 7*1 =7

OA:D

unraveled · Answer

Since unit digit of 341 is 1 which would always result in unit digit of 1, on multiplying with  2467^{153}  it would be equal to unit digit of  7^{153} .
 2467^{153} * 341^{72} = 2467^{153} * 1^{72}  
  = 7^{153}  
  = 7^{38*4 + 1}  
  = 7^{38*4} * 7^1 
 = 1 * 7
 = 7

Answer (D).

Archit3110 · Answer

cyclicity of 7 ; 7,9,3,1
unit digit of 
 2467^153 = 7
and 341^72 = 1
so answer IMO D ; 7

What is the unit's digit in the product 2467^153∗341^72?

(A) 0
(B) 1
(C) 2
(D) 7
(E) 9

exc4libur · Answer

units:2467^{153}∗341^{72}=7^{153}*1^{72}=7^{153}

cycles :(7,9,3,1)=4

7^{153}…\frac{153}{4}=remainder =1st.of=(7,9,3,1)=7

Answer (D)

Raxit85 · Answer

7^153* 1^72;
153/4 = 1 remainder (and 0 remainder for 72/4)
7 ^1 * 1 ^4 = 7 * 1 = 7. 
Ans. D

QuantMadeEasy · Answer

Cyclicity of 7 is 4 and that of 1 is 1

Hence, unit digit of 7^153 is 7 and 1^72 is 1

Unit digit of the expression is 7

D is correct

Mohammadmo · Answer

A number with 7 in unit's digit to the powers has the cycle of numbers 7,9,3,1 respectively.
So, the sycle is 4.
153÷4=38+1.
So, 2467^153 has 7 in its unit's digit.
7×1=7
Option D

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Enrique92 · Answer

Units first number 7 >>> Therefore we need to know the cicle of 7 >>> (7,4,1,7,4,1) >>> The cicle repeats each three numbers.

153/3= 51 >> remainder = 0 therefore the units digit of the first number is 1 since the last number of the cicle is 1 (No remainder so last number of the cicle)

Units digit second number is 1, therefore the units digit of this number to any power will be 1.

1*1=1

lacktutor · Answer

What is the unit's digit in the product  2467^{153}∗341^{72} ??

...7^{153}

...7^{1}=...7 
 ...7^{2}=...9 
 ...7^{3}=...3 
 ...7^{4}=...1 
..................
 ...7^{5}=...7 
 ...7^{6}=...9 
 ...7^{7}=...3 
 ...7^{8}=...1 
It is repeated in every four terms. So, 
 ...7^{149}=...7 
 ...7^{150}=...9 
 ...7^{151}=...3 
 ...7^{152} =...1
 ... 7^{153} =...7

341^{72}=...1^{72} =...1
Units digit of this number always ends with 1.

Units digit is 7*1=7
 
 The answer is D.

.................

EgmatQuantExpert · Answer

Solution

Given  
• We are given an expression: 2467^153∗341^72

To find  
• The units digit of 2467^153∗341^72

Approach and Working out  
• The units digit of 2467^153∗341^72 is same as the units digit of 7^153∗1^72
Units digits of 7^153∗1^72 = Units digits of 7^153∗ Units digits of 1^72
• = Units digits of 7^153 * 1
Units digits of 7^153 = Units digits of 7^(4*38 +1) = Units digits of 7^1 = 7

Hence, Units digits of 7^153∗1^72 = 7 * 1 = 7

Thus, option D is the correct answer.

Correct Answer: Option D

CrackverbalGMAT · Answer

Solution:

The unit digit of the product depends on the unit digit of 7^153 and 1^72

Cyclicity of 7 is 4

=>153/4 leaves a remainder of 1

=> Unit digit is 7^153 = 7

Unit digit of 341^72 would be1

=> Unit digit of the product = 7*1
 = 7  (option d) 
  Devmitra Sen (GMAT, SME)

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Find the unit's digit in the product 2467^153*341^72

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Find the unit's digit in the product 2467^153*341^72

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