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# Jamboree and GMAT Club Contest: If N = ( 1436)^A*(1054)^B. Where A and

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Re: Jamboree and GMAT Club Contest: If N = ( 1436)^A*(1054)^B. Where A and [#permalink]

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20 Nov 2015, 11:52
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B because the first term - the units digit is 6 and any power will result as 6 as units digit.
Second term is important as because 4 to the power even term gives 6 as units digit and for odd its 4.
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Re: Jamboree and GMAT Club Contest: If N = ( 1436)^A*(1054)^B. Where A and [#permalink]

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20 Nov 2015, 21:41
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If N = ( 1436)^A*(1054)^B. Where A and B are positive integers. What is the units digit of N?

(1) A + B = 6
(2) B = 2

This seems easy.

For units digit, U need to know about the units place digit of the numbers multiplied.

From given equation 1436^6- Units digit will always be 6.
6^1=6 odd power
6^2=36 even power
6^3=216 odd power
6^4=1296 even power....... continues

For 1054^B- we need to know the units place only so main focus will be on that only.
4^1=4 odd power
4^2=16 even power
4^3=64 odd power
4^4=256 even power.......continues

Statement-1 A+B=6. It could be 5+1 or 2+4 so 6*4 or 6*6 units place values are different, we are getting 2 values, so statement is not sufficient.

Statement-2 B=2 For A units digit value is fixed but in this case, B's units digit value is fixed too (which was required). Hence we get answer as 6*6= 6 as units digit-
Hence Sufficient

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Re: Jamboree and GMAT Club Contest: If N = ( 1436)^A*(1054)^B. Where A and [#permalink]

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21 Nov 2015, 09:53
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Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If N = ( 1436)^A*(1054)^B. Where A and B are positive integers. What is the units digit of N?

(1) A + B = 6
(2) B = 2

If we modify the original condition, n=( 1436)^A*(1054)^B=(...6)(1054)^B. (Numbers with the units digit of 6 results in the units digit of 6 no matter what we multiply). We only need to know B so the answer becomes (B).

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Re: Jamboree and GMAT Club Contest: If N = ( 1436)^A*(1054)^B. Where A and [#permalink]

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28 Nov 2015, 08:49
Bunuel wrote:

Jamboree and GMAT Club Contest Starts

QUESTION #14:

If N = ( 1436)^A*(1054)^B. Where A and B are positive integers. What is the units digit of N?

(1) A + B = 6
(2) B = 2

Check conditions below:

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JAMBOBREE OFFICIAL SOLUTION:

The unit’s digit of N can be calculated by multiplying the unit’s place of (1436)^A with the unit’s digit of (1054)^B.

Units digit of (1436)^A will be 6 as we know that 6 raised to any positive integer will always result in an integer whose units digit is 6

To calculate the units digit of (1054)^B can be calculated by using the cyclicity concept. Now according to cyclicity concept 4 raised to any positive odd integer will always result in an integer with unit’s digit as 4 and 4 raised to any positive even integer will always result in an integer with unit’s digit as 6.

Statement 1

In the equation A + B = 6 if we take different values of A we will have different values of B. so B can be odd or even.
Hence If B is even then the unit’s digit of (1436)^A*(1054)^B will be 6
And If B is odd then the units digit of (1436)^A*(1054)^B will be 4

Hence as we do not have a definite answer for the questions asked so the statement is insufficient

Statement 2
As B= 2 so the units digit of (1436)^A^(1054)^B will be 6. We have a definite answer for the question asked. So this statement is sufficient to answer.

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Re: Jamboree and GMAT Club Contest: If N = ( 1436)^A*(1054)^B. Where A and [#permalink]

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19 Apr 2016, 14:56
for A positive unit's digit of 6^A will be 6 irrespective of value of A
as for B is positive, unit's digit of 4^B will be 4 or 6 depending on value of B
statement 1 gives no information on value of B insufficient
statement 2 gives clearly the value of B sufficient

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Re: Jamboree and GMAT Club Contest: If N = ( 1436)^A*(1054)^B. Where A and [#permalink]

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13 Sep 2017, 19:35
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Re: Jamboree and GMAT Club Contest: If N = ( 1436)^A*(1054)^B. Where A and   [#permalink] 13 Sep 2017, 19:35

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