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# Question of the Week - 38 (A and B are distinct single digit integers)

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3239
Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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01 Mar 2019, 01:22
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Difficulty:

95% (hard)

Question Stats:

38% (02:25) correct 63% (02:14) wrong based on 56 sessions

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Question of the Week #38

A and B are distinct natural numbers. Is A + B odd?

Statement 1: Unit digit of A x B is 6.
Statement 2: $$A^3 + B^3$$ is divisible by 10.

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Joined: 31 Oct 2013
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Re: Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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01 Mar 2019, 02:22
EgmatQuantExpert wrote:
Question of the Week #38

A and B are distinct natural numbers. Is A + B odd?

Statement 1: Unit digit of A x B is 6.
Statement 2: $$A^3 + B^3$$ is divisible by 10.

Statement 1: A*B = x6......Unit digit is 6.

A = 23

B = 12

Unit digit is 23*12 =xx6

23 + 12 = 35=odd.

Again,

A=6
B=16

6*16 =x6

A + B = 6 + 16 = 22=even

NOT sufficient.

Statement 2:

A^3 + B^3 is divisible by 10.

It means unit digit of A^3 + B^3 is 0.

0 represent even integers.

A + B must be even.

statement 2 is sufficient.
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Re: Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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01 Mar 2019, 03:22
sum or subtraction of an even and odd integer will only result in odd integer....

now
#1
unit digit of a*b= 6
a =1, b=6 ; sum odd
a=6,b=6; sum even
in sufficient
#2[/b] $$A^3 + B^3$$ is divisible by 10
it means both a & b have unit digits as 0 ; i.e both are even integers
so sum of a+b ; will not be odd integer
IMO B sufficient

EgmatQuantExpert wrote:
Question of the Week #38

A and B are distinct natural numbers. Is A + B odd?

Statement 1: Unit digit of A x B is 6.
Statement 2: $$A^3 + B^3$$ is divisible by 10.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3239
Re: Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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01 Mar 2019, 04:17
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5931
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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01 Mar 2019, 04:25
EgmatQuantExpert wrote:
Archit3110 wrote:

$$A^3 + B^3$$ is divisible by 10
it means both a & b have unit digits as 0 ; i.e both are even integers

Hey Archit3110,

Considering the highlighted sentence above, can we say it is always true?

EgmatQuantExpert
well the highlighted part wont be true always ; given that A^3 + B^3 divisible by 10 ; so either of A or B can be 0 and other can be a factor of 10
but since its mentioned in the question that A & B are natural numbers , so either of them cannot be '0' in this case ,and a natural no ending with 0 would be an even integer only in this case..
had it been given in question that a & b are whole number then #2 would have been insufficient....
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Joined: 04 Jan 2015
Posts: 3239
Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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06 Mar 2019, 00:42
1

Solution

Given:

• A and B are distinct natural numbers.

To Find:

• Is A+B odd?

Approach and Working:

• A+B is odd when one out of A or B is even and another is odd as Even +Odd = Odd

So, we have to find whether the even-odd nature of A and B is different or not.

Analyse Statement 1: Unit digit of A x B is 6.

Unit digit of A x B can be 6 when units digit of (A, B) = (1, 6) or (2,3) or (4,4) or (2,8), or (4,9) or (7,8), or (6,6) etc.
However, in some cases the even-odd nature of (A, B) is different and in some cases the even-odd nature of (A, B) is same.

Hence, we cannot find the answer from statement 1.

Analyse Statement 2: $$A^3 + B^3$$ is divisible by 10.

For $$A^3 + B^3$$ to be divisible by 10, the units digit of $$A^3 + B^3$$ must be 0.

• The units digit of $$A^3 + B^3$$ can be 0 when units digit (A, B) is (1, 9), or (2, 8), or (3, 7), or (4, 6), or (5, 5), or (6, 4), or (7, 3), or (8, 2), or (9, 1), or (0,0).

In all the given cases, the nature of (A, B) is same.
Hence, $$A^3 + B^3$$ is always an even number.

Therefore, statement 2 alone is sufficient to find the answer.

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Question of the Week - 38 (A and B are distinct single digit integers)   [#permalink] 06 Mar 2019, 00:42
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