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01 Oct 2018, 04:47
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If x and y are positive integers and r is the remainder when \((7^{4x+3} + y)\) is divided by 10, what is the value of r ?
(1) x = 10
(2) y = 2
(1) x = 10
(2) y = 2
01 Oct 2018, 04:53
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Bunuel
If x and y are positive integers and r is the remainder when \((7^{4x+3} + y)\) is divided by 10, what is the value of r ?
(1) x = 10
(2) y = 2
(1) x = 10
(2) y = 2
Question: What is the remainder when \((7^{4x+3} + y)\) is divided by 10
CONCEPT: When a number is divided by 10 then the remainder will always be the unit digit of the number e.g. 37 divided by 10 leaves remainder 7 and 125 divided by 10 leaves remainder 5
i.e. we need to calculate the unit digit of \((7^{4x+3} + y)\)
but Unit digit of \((7^{4x+3})\) is always same as unit digit of \(7^3\) because cyclicity of unit digit of 7 is 4 i.e. Unit digit of powers of 7 repeat after every 4 powers
Hence we only need to know the Unit digit of y to answer the question
Statement 1: x = 10
NOT SUFFICIENT
Statement 2: y = 2
SUFFICIENT
Answer: Option B
auradediligodo
15 Oct 2019, 12:38
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Bunuel
If x and y are positive integers and r is the remainder when \((7^{4x+3} + y)\) is divided by 10, what is the value of r ?
(1) x = 10
(2) y = 2
(1) x = 10
(2) y = 2
Knowing the ciclicity of 7 the problem becomes a cakewalk.
considering consecutive powers of 7 the unit digits will be
9 (7*7)
3 (9*7)
1 (3*7)
7 (1*7)
every time the power of 7 is a multiple of 4 the unit digit will be 1.
The question stems states: 7^(4x+3)
Hence the unit digit of 7 will be always 3.
According to statement 1 we still miss y. Hence insufficient
Statement 2 gives us y and hence it is sufficient
Option B
