If a and b are two integers such that a is even, b is odd and neither

Question

If a and b are two integers such that a is even, b is odd and neither of them leaves a remainder of 1 when divided by 10, what is the units digit of a × b?

(1) The units digit of a^3 is the same as the units digit of a.

(2) The units digit of b^4 is the same as the units digit of b.

sanjitscorps18 · Answer

If a and b are two integers such that a is even, b is odd and neither of them leaves a remainder of 1 when divided by 10, what is the units digit of a × b

possible last digits of a = 0, 2, 4, 6, 8
possible last digits of b = 1, 3, 5, 7, 9

However since the number does not leave a remainder of 1 when divided by 10 it cannot have 1 in the end. Hence possible last digits of b = 3, 5, 7, 9

(1) The units digit of a^3 is the same as the units digit of a. --> this mean a can have units digit as only 6, 0
No information about b hence insufficient

(2) The units digit of b^4 is the same as the units digit of b. --> this means b can have units digit as only 5
No information about a hence insufficient

Combining we get a x b would always have units digit as 0. Hence its sufficient.

Option C

100mitra · Answer

Correct Option B
Statement 2 is sufficient

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PyjamaScientist · Answer

Statement 2 is enough.

Because the only possible value of units place of b will be 5. And since we know that a is an even number, hence the product of 5 and a will leave 0 in the Unit's place.

PyjamaScientist · Answer

In your analysis, Why did you not consider 0 as the possible Units Digit of "a"?

100mitra · Answer

Hello Friend, a * b = Now with a we have 3 match {0, 4, 6} & b only {5} a = 0, b = 5 (0*5 = 0, 0÷10 makes no sense) a = 4, b = 5 (4*5 = 20, 20÷10, reminder 2, not 1) a = 6, b = 5 (6*5 = 30, 30÷10, reminder 3, not 1) Hence, I didn't took that possible situation to consider "zero"

PyjamaScientist · Answer

Question says, neither of (a) and (b) leaves a remainder 1 when divided by 10. Why are you trying to find the remainder of a*b when divided by 10?

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

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If a and b are two integers such that a is even, b is odd and neither

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If a and b are two integers such that a is even, b is odd and neither

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