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e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2722
Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 34% (02:17) correct 66% (02:14) wrong based on 47 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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Re: Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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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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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.

_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2722
Re: Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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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?
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GPA: 4
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Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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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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e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2722
Question of the Week - 38 (A and B are distinct single digit integers)  [#permalink]

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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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Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com Question of the Week - 38 (A and B are distinct single digit integers)   [#permalink] 06 Mar 2019, 01:42
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# Question of the Week - 38 (A and B are distinct single digit integers)

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