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# If a and b are two integers such that a is even, b is odd an

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If a and b are two integers such that a is even, b is odd an  [#permalink]

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Updated on: 26 Jan 2014, 12:22
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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.

Originally posted by guerrero25 on 26 Jan 2014, 01:22.
Last edited by guerrero25 on 26 Jan 2014, 12:22, edited 1 time in total.
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Re: If a and b are two integers such that a is even, b is odd an  [#permalink]

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26 Jan 2014, 09:25
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From statement 2) we conclude that the unit's digit of b is 5. The question itself says that a is even. Any even number multiplied by another number whose unit's digit is 5 should give us a number with zero as the unit digit. So B) should be sufficient. Why is C) the answer then?
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Re: If a and b are two integers such that a is even, b is odd an  [#permalink]

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27 Jan 2014, 00:14
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2
a is even --> a has the following unit integers: 0, 2, 4, 6, 8
b is odd --> b has the following unit integers: 1, 3, 5, 7, 9
Since neither b nor a has a remainder of 1 when divided by 10, b only have unit integers of 3, 5, 7, 9.

Statement 1: The units digit of a^3 is the same as the units digit of a --> a can be integer ending with 0 or 4 or 6 ==> Insufficient.
Statement 2: The units digit of b^4 is the same as the units digit of b --> only b ending with 5 satisfies the statement ==> Sufficient

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If a and b are two integers such that a is even  [#permalink]

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21 Jul 2016, 10:14
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 the product ab?

A The units digit of a^3 is the same as the units digit of a
.
B The units digit of b^4 is the same as the units digit of b
.
I am not convinced by the OA , using A i can say a might be 0/4/6 hence its not sufficient

using B i can say b might be 1/5/9 , since b cannot be 1 it leaves me with 5/9 using this information i cannot predict the units digit of ab so how can the answer be C and not E

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If a and b are two integers such that a is even, b is odd an  [#permalink]

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Updated on: 21 Jul 2016, 10:31
ashwini86 wrote:
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 the product ab?

A The units digit of a^3 is the same as the units digit of a
.
B The units digit of b^4 is the same as the units digit of b
.
I am not convinced by the OA , using A i can say a might be 0/4/6 hence its not sufficient

using B i can say b might be 1/5/9 , since b cannot be 1 it leaves me with 5/9 using this information i cannot predict the units digit of ab so how can the answer be C and not E

Hi! There,

In statement B we can not consider 9 as 9^4 will give 1 as the units digit. So the only contender is 5.

And as 'a' is even, which when multiplied by 5, will only give 0 as the units digit. Hence, B is the answer
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Originally posted by Divyadisha on 21 Jul 2016, 10:27.
Last edited by Vyshak on 21 Jul 2016, 10:31, edited 1 time in total.
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If a and b are two integers such that a is even, b is odd an  [#permalink]

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21 Jul 2016, 10:27
ashwini86 wrote:
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 the product ab?

A The units digit of a^3 is the same as the units digit of a
.
B The units digit of b^4 is the same as the units digit of b
.
I am not convinced by the OA , using A i can say a might be 0/4/6 hence its not sufficient

using B i can say b might be 1/5/9 , since b cannot be 1 it leaves me with 5/9 using this information i cannot predict the units digit of ab so how can the answer be C and not E

Topic Merged. Please search for the topic before posting.

Using B, you can infer that unit's digit of b is 5. 9 cannot be the units digit as 9^4 will result in 1.

Once you know that unit's digit of b is 5 and a is even, product ab will definitely have unit's digit as 0.

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Re: If a and b are two integers such that a is even, b is odd an  [#permalink]

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21 Jul 2016, 10:46
ashwini86 wrote:
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 the product ab?

A The units digit of a^3 is the same as the units digit of a
.
B The units digit of b^4 is the same as the units digit of b
.
I am not convinced by the OA , using A i can say a might be 0/4/6 hence its not sufficient

using B i can say b might be 1/5/9 , since b cannot be 1 it leaves me with 5/9 using this information i cannot predict the units digit of ab so how can the answer be C and not E

Hi! There,

In statement B we can not consider 9 as 9^4 will give 1 as the units digit. So the only contender is 5.

And as 'a' is even, which when multiplied by 5, will only give 0 as the units digit. Hence, B is the answer

Hi Divya,

the question says remainder when b is divided by 10 is not 1 , why are we assuming remainder of b^4 by 10 too thus eliminating 9
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Re: If a and b are two integers such that a is even, b is odd an  [#permalink]

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21 Jul 2016, 10:52
ashwini86 wrote:
ashwini86 wrote:
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 the product ab?

A The units digit of a^3 is the same as the units digit of a
.
B The units digit of b^4 is the same as the units digit of b
.
I am not convinced by the OA , using A i can say a might be 0/4/6 hence its not sufficient

using B i can say b might be 1/5/9 , since b cannot be 1 it leaves me with 5/9 using this information i cannot predict the units digit of ab so how can the answer be C and not E

Hi! There,

In statement B we can not consider 9 as 9^4 will give 1 as the units digit. So the only contender is 5.

And as 'a' is even, which when multiplied by 5, will only give 0 as the units digit. Hence, B is the answer

Hi Divya,

the question says remainder when b is divided by 10 is not 1 , why are we assuming remainder of b^4 by 10 too thus eliminating 9

We are not assuming remainder of b^4/10 to be 1. The statement says b^4 should result in the same units digit as the units digit of b. Only 5 satisfies the given statement.
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If a and b are two integers such that a is even, b is odd an  [#permalink]

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21 Jul 2016, 14:30
Aloha Everyone
here is my solution =>
Here we need to get the UD of both A and B
the unit digit of A can be 0,2,4,6,8 and for B can be 3,5,7,9 (here one is excluded as remainder with 10 with be one which isnt allowed as per question stem)
Now as per statement 1 => the unit digit of A can be 6 or 4 and we dont know the Unit digit of B
SO its insufficient
Now as per statement 2 the UD of B has to be 5.
But A is even => thus zero must be the UD of A*B .
Thus sufficient
Go smash that B

Peace out
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Re: If a and b are two integers such that a is even, b is odd an  [#permalink]

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21 Jul 2016, 15:33
1
ashwini86 wrote:
ashwini86 wrote:
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 the product ab?

A The units digit of a^3 is the same as the units digit of a
.
B The units digit of b^4 is the same as the units digit of b
.
I am not convinced by the OA , using A i can say a might be 0/4/6 hence its not sufficient

using B i can say b might be 1/5/9 , since b cannot be 1 it leaves me with 5/9 using this information i cannot predict the units digit of ab so how can the answer be C and not E

Hi! There,

In statement B we can not consider 9 as 9^4 will give 1 as the units digit. So the only contender is 5.

And as 'a' is even, which when multiplied by 5, will only give 0 as the units digit. Hence, B is the answer

Hi Divya,

the question says remainder when b is divided by 10 is not 1 , why are we assuming remainder of b^4 by 10 too thus eliminating 9

Let's take a look at the option that will result in same units digit.

1^ anything will give 1 as the units digit. But since the question says remainder when b is divided by 10 is not 1, we have to drop this out.
5^anything will give 5 as the units digit.
6^anything will give 6 as the units digit. But b is odd and hence we have to knock this off.

We are left with only 5 in this case.

Hope it is clear now
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If a and b are two integers such that a is even, b is odd an  [#permalink]

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17 Oct 2016, 21:28
(B)
If a is even, its units digit will be 0/2/4/6/8. If b is odd and does not leave a remainder of 1 when divided by 10, its units digit will be 3/5/7/9.

Statement (1). If the units digit of a3 is the same as the unit’s digit of a, the units digit must be 0/4/6. Different values, when multiplied by b, will give different units digits and so statement (1) is not sufficient.

Statement (2). If units digit of b4 is the same as the units digit of b, the unit’s digit must be 1 or 5. But, b, on being divided by 10, should not leave a remainder of 1, hence unit’s digit of 1 is not possible. This implies that unit’s digit of b is 5. Then a × b will definitely have a units digit of 0 since a is even. Statement (2) is sufficient.
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Re: If a and b are two integers such that a is even, b is odd an  [#permalink]

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18 Oct 2016, 09:59
gaurav_raos wrote:
(B)
If a is even, its units digit will be 0/2/4/6/8. If b is odd and does not leave a remainder of 1 when divided by 10, its units digit will be 3/5/7/9.

Statement (1). If the units digit of a3 is the same as the unit’s digit of a, the units digit must be 0/4/6. Different values, when multiplied by b, will give different units digits and so statement (1) is not sufficient.

Statement (2). If units digit of b4 is the same as the units digit of b, the unit’s digit must be 1 or 5. But, b, on being divided by 10, should not leave a remainder of 1, hence unit’s digit of 1 is not possible. This implies that unit’s digit of b is 5. Then a × b will definitely have a units digit of 0 since a is even. Statement (2) is sufficient.

Thanks for the correct explanation. Helped me to understand. Kudos.
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Re: If a and b are two integers such that a is even, b is odd an  [#permalink]

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18 Oct 2016, 10:50
guerrero25 wrote:
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.

FROM STATEMENT - I ( INSUFFICIENT )

$$a$$ = Even and units digit of $$a^3$$ is same as $$a$$

So, a can take the following values -

a = { 4 , 6 }

FROM STATEMENT - I ( SUFFICIENT )

$$b$$ = Odd and units digit of $$b^4$$ is same as $$b$$ and b is not 1

So, b can take the following values -

b = { 5 }

Hence Statement 2 is sufficient for solving the question...

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If a and b are two integers such that a is even, b is odd an  [#permalink]

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09 Mar 2017, 19:04
guerrero25 wrote:
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.

Solution: Remember, if a is even, its units digit will be 0/2/4/6/8. If b is odd and does not leave a remainder of 1 when divided by 10, its units digit will be 3/5/7/9.

First, let’s examine Statement (1). If the units digit of $$a^3$$ is the same as the unit’s digit of a, the units digit must be 0/4/6. Different values, when multiplied by b, will give different units digits and so statement (1) is not sufficient.

Now, let’s examine Statement (2). If units digit of $$b^4$$ is the same as the units digit of b, the unit’s digit must be 1 or 5. But, b, on being divided by 10, should not leave a remainder of 1, hence unit’s digit of 1 is not possible. This implies that unit’s digit of b is 5. Then a × b will definitely have a units digit of 0 since a is even. Statement (2) is sufficient.
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Re: If a and b are two integers such that a is even, b is odd an  [#permalink]

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24 May 2017, 23:54
yup, the correct answer is b, I almost forgot that a is an even number
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Re: If a and b are two integers such that a is even, b is odd an  [#permalink]

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Re: If a and b are two integers such that a is even, b is odd an   [#permalink] 13 Apr 2019, 07:35
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