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Tough & unclear unit digit------Experts needed

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by Mo2men » Thu Nov 24, 2016 3:41 am
The units digit of N^p and N^q are 6 and 4 respectively. What is the greatest value of the two-digit number N, which satisfies the above condition?

(1) p is a positive even integer
(2) q is a positive odd integer

source: e-gmat

I do not understand how OA: B???
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Source: — Data Sufficiency |
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by melguy » Thu Nov 24, 2016 9:02 am
Statement 1

Firstly notice that we can end up with N^p as 6 in two different ways
1) 6x6 (regardless of how many times) will give unit digit as 6. So this number can be 96.
2) (4x4)x(4x4) sets of blue and red regardless of how many times you multiply will always give unit digit as 6. So lets pick this number as 94.

When multiplying we are only concerned with unit digits so the result will be the same for 4 or 94 and 6 or 96.

Let's try values

96� is greater than 94�
96² is smaller than 94�

Insufficient

Statement 2

92³ = Unit digit will be 8
94³ = Unit Digit will be 4
98³ = Unit Digit will be 2

Notice that the only number that should satisfy the condition when the number ends is 4 as 4^an odd number = 4. You can try with 8 or 2 but this condition won't suffice. So the largest number will be 94.

Sufficient

Answer is B
Last edited by melguy on Fri Nov 25, 2016 3:26 am, edited 2 times in total.
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by crackverbal » Thu Nov 24, 2016 10:59 pm
Hi Mo2men,

This is really a tricky question.

This is how I went about it.

Since the question asks about greatest two digit integer value of "N" and the units of N is 6 and 4 when raised to p and q.

The only possibilities for units digit has to be 2,4 and 8.

Since it is greatest 2 digit number, it could be either 92 or 98 or 94.

But the real problem is we don't the know value of p and q.

94^100 > 98 ^ 6

So lets look at the statements.

Statement I is insufficient: p is a even.

Still all there could be a possibility that is it could be

(92)^4=> The units digit is 6 and (92)^6 => The units digit is 4

OR

(98)^4=> The units digit is 6 and (98)^2 => The units digit is 4.

So not sufficient.

Statement II is sufficient: q is odd.

So now only possibility has to be 94.

Because odd powers of 2 and 8 won't end in 4 and 6.

So N has to be 94.

So sufficient.

Answer is B.

Hope its clear.
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