Q. What is the units digit of a^36?
a) a^2 has 9 as the units digit
b) a^3 has 3 as the units digit
Unit Digit
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- sunnyjohn
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IMO : B
overall you should know that every number from 0-9, has recurring format of unit digit when multiplied by itself.
for eg:
3^1 = 3 <-- unit digit of mulplication
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = 3
similarly... 9 7 1 3 9 7 3 1...
so over all we are only interested to know the unit digit of 'a'. If we know that we can tell the unit digit of a^36.
Option A)
it give us two possible unit digit of a ==> 7 and 3 : INSUFFICIENT
Option B)
it give us only one option : 7 ==> Hence SUFFICIENT
so Answer should be B.
overall you should know that every number from 0-9, has recurring format of unit digit when multiplied by itself.
for eg:
3^1 = 3 <-- unit digit of mulplication
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = 3
similarly... 9 7 1 3 9 7 3 1...
so over all we are only interested to know the unit digit of 'a'. If we know that we can tell the unit digit of a^36.
Option A)
it give us two possible unit digit of a ==> 7 and 3 : INSUFFICIENT
Option B)
it give us only one option : 7 ==> Hence SUFFICIENT
so Answer should be B.
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heshamelaziry wrote:Q. What is the units digit of a^36?
a) a^2 has 9 as the units digit
b) a^3 has 3 as the units digit
Rephrase
What is a^36 (mod 10)
(a) a^2 (mod 10) = 9
(b) a^3 (mod 10) = 3
a. a^2 = 9 (mod 10); a^36 (mod 10) = 9^18 (mod 10) = (-1)^18 = 1 Sufficient
2. a^3 = 3 (mod 10); a^36 (mod 10) = 3^12 (mod 10) = 1 sufficient
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sunnyjohn wrote:IMO : B
overall you should know that every number from 0-9, has recurring format of unit digit when multiplied by itself.
for eg:
3^1 = 3 <-- unit digit of mulplication
3^2 = 9
3^3 = 7
3^4 = 1
3^5 = 3
similarly... 9 7 1 3 9 7 3 1...
so over all we are only interested to know the unit digit of 'a'. If we know that we can tell the unit digit of a^36.
Option A)
it give us two possible unit digit of a ==> 7 and 3 : INSUFFICIENT
Option B)
it give us only one option : 7 ==> Hence SUFFICIENT
so Answer should be B.
a^2 = 9 (mod 10)
a = 3 or -3 ( mod 10) = 3 or 7
Having 2 values for a (mod 10) doesn't entail that a^36 (mod 10) can have multiple values.
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We can also solve quickly through algebra and common sense.heshamelaziry wrote:Q. What is the units digit of a^36?
a) a^2 has 9 as the units digit
b) a^3 has 3 as the units digit
1) a^2 ends in 9
Well, a^36 = (a^2)^18
If we know that a^2 ends in 9, it's certainly possible to calculate the units digit of (...9)^18 - sufficient.
2) a^3 ends in 3
Well, a^36 = (a^3)^12
If we know that a^3 ends in 3, it's certainly possible to calculate the units digit of (...3)^12 - sufficient.
Each statement is sufficient alone: choose D.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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