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# Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests!

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Knewton GMAT Representative
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Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 06:01
Hi all - great response on the last Knewton challenge! This time, we'll be choosing a winner at random. Your answers must be clear and well-developed in order to be included in the pool. The competition closes on Friday, so look out for a post announcing the winner. In the meantime, try your hand at this tricky data sufficiency problem:

If $$4^w = n$$, what is the units digit of n?

1. w is an even integer
2. w > 0

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Edit: by bb:
The winner will be determined based on a random drawing. The replies will be hidden until the winner is announced.
The winner will get access to the GMAT Club Tests for 1 year (\$250 value)

Last edited by bb on 23 Sep 2011, 12:04, edited 3 times in total.
Update
 Knewton GMAT Discount Codes Kaplan GMAT Prep Discount Codes Veritas Prep GMAT Discount Codes
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 06:23

Stmt 1:W is even so 4^2=16 unit digit is 6 but 4^-2=1/16=0.0625 so unit digit is 0

as -2 is also even number. so not sufficient.

Stmt 2:w>0.....4^1=4 unit digit 4 but 4^2=16 unit digit is 6 so not sufficient

Taking 1 & 2 together we get 4^2...4^4...4^6.....etc
In all cases unit digit is 6 .........hence 1&2 together are sufficient to answer.........

Hope I am correct.....
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 06:35
Statement 1)

4^2 = 16
4^4= 256
4^6= 64*64 = ____6

4^-2= .0625

4^-4= .004

Insuff.

Statement 2) 4^1=4 ; 4^2 = 16; 4^3=64; 4^4 =256

Infuff.

Using A and B together,
4^2 = 16
4^4= 256
4^6= 64*64 = ____6

Units digit is 6. Sufficient.
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 09:02
1
KUDOS
Here is my take on the Problem :

If 4^w = n, what is the units digit of n?

1. w is an even integer
2. w > 0

Before we get into the two statements, we need to understand what we have :

We know that Unit digit of 4^w will follow a pattern (for all w>0 )
And for W=0 it becomes 1 and for negative numbers we cannot predict anything.

When w>0 ; we have a pattern for unit's digits:
4^1 = 4
4^2 = 6
4^3 = 4
4^4 = 6
.
.........

a) If "w" is odd -> the unit digit is 4
b) if "w" is even -> The unit digit is 6.

Now lets jump into the statements given :

(1) W is a even integers We cannot be very sure because "w" can also be "0" or negative numbers.

INSUFFICIENT

(2) w>0
This alone again will not help us to determine anything about the unit's digit.

INSUFFICIENT

(1) + (2) Combining both the statements

We come to know "W" cannot be zero neither negative and "W" is even.

Hence, we can conclude the unit's digit for 4^w is 6.

Both the statements together is required to answer this question.Hence the Correct answer choice is C
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Thanks,
GC24

Please click Kudos ,if my post helped you

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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 09:04
Expert's post
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 09:19
Ans is D IMHO

Solution:
4^0= units place is 1
4^1= units place is 4
4^2= units place is 6
4^3=units place is 4
4^4=units place is 6 and so on.

We can observre a trend here.
Statement 1 : W is even means 0 or 2 or 4 e.t.c In this case units place can be either 1 or 6

St 2 : w > 0
So units place can be 4 or 6.

Both statement alone give us an answer.
Both combined also give us a single answer as 6.

Hence the above answer based on given options.

Posted from GMAT ToolKit
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Last edited by hoogly on 23 Sep 2011, 01:58, edited 2 times in total.
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 11:01
The answer is (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

1) w is an even integer. If we pick w to be negative then the units digit is 0 and if w is positive the answer is 6 so NOT sufficient
2) w > 0. If we pick w to be 1 we get unit as 4, w = 2 we get unit as 6. so it is NOT sufficient

If we combine them to have w is even and positive then the only possible answer is 6. so both options combined are SUFFICIENT. therefore the answer is The answer is (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 11:23

As per statement 1:
w is even number. So it can be 0, 2, 4,....
For all even number except 0, unit digit of n is 6.
For 0 unit digit for n is 1. so not sufficient.

As per statement 2:
w is any number greater than 0. so unit digit of n changes with different value of w.
for example:
when w is 1 then unit digit of n is 4,
when w is 2 then unit digit of n is 6,
when w is 3 then unit digit of n is 4,
so not sufficient.

When statement 1 and 2 are evaluated together then w can be 2,4,6,8.... For all these values of w, unit digit of n is 6.

Thus option C is correct.
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 11:50

statement one is sufficient as it says that w is an even integer ..So for example w is 2 then = 16 so the unit digit is 6

Next example w is 4 = 96 again unit digit is 6

even if you solve w to be 6 the unit digit will be 6 everytime...

statement 2 is not sufficient because if w>0 w can be 1 in that case unit digit is 4

w can be 2 = 16 unit digit will be 6...So not sufficient..

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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 12:09
Ans according to me is C

Soln: 4^w=n

Let us simplify this statement a bit-
plugging different values for w:

4^w=Units Digit(w is a positive integer)
4^1=4
4^2=6
4^3=4
4^4=6
4^5=4
4^6=6
Clearly, units digit is 4 if w is odd and units digit is 6 if w is even

Now consider
4^w=Units digit(w is a negative integer)
4^-1=0.25,units digit=0
4^-2=0.0625,units digit=0
4^-3=0.015625,units digit=0
Clearly here units digit is 0

Statement I= w is even integer:Insufficient since we dont know if w is positive or negative
Statement II=w>0:Insufficient since we don't know if w is odd or even

I+II=W is a positive ,even integer
Hence Units digit is 6
Therefore C
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  20 Sep 2011, 21:37

4^w=n..... if no other data is given, we can determine the fact that the units digit is 4 or 6 **. OR if w=0, n=1

A negative 'w' will give fractional values of n ; whose 'unit digit' doesnt make any sense. So w has to be greater than/equal to 0. Statement 2 clears the air by stating w>0. So w is not 0. Hence n not equal to 1. n can still end in 4 0r 6. So we strike out option B
whenever w is odd unit digit is 4...and whenever w is even unit digit is 6 At this point we can say that solution is 6 and strike out options A and D
We needed both satements to arrive at this answer, E can be striked out Hence C is correct.

**(4^1=4,4^2=16......whenever the digit 6 is multiplied by 4...the result will have a number ending in 4(4x6=24).....which in turn when multiplie by 4 again ends in 6(4x4=16)...and so on....)=>
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  21 Sep 2011, 04:05
4^w = n, what is the units digit of n?

Considering (i) When w is even integer, it can be ...,-4,-2,0,2,4,......
When w=0, 4^0 = 1, units digit is 1
When w=2, 4^2 = 16, units digit is 6
When w=-2, 4^-2 = 1/16=0.0625, units digit is 0.

We do not get a unique solution. Hence (i) is insufficient

Considering (ii) When w > 0, it can be 1,2,3,......
Also, we are not sure if it is an integer.
When w=1, 4^1 = 4, units digit is 4
When w=2, 4^2 = 16, units digit is 6
When w=3, 4^3 = 64, units digit is 4.

We do not get a unique solution. Hence (ii) is insufficient

Considering (i) and (ii), we get w > 0 and w is an even integer.
So, it can be 2,4,6,8,.....
When w=2, 4^2 = 16, units digit is 6
When w=4, 4^4 = 256, units digit is 6

And the units digit will always be 6, as we multiply all the results by 4^2= 16 and
any two numbers, whose units digit is 6, are multiplied will give a number with 6 as its unit digit.

We do get a unique solution. Hence answer is C.

---------------
ISH

Last edited by justharish on 22 Sep 2011, 07:27, edited 1 time in total.
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  21 Sep 2011, 04:19
A
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  21 Sep 2011, 04:56
If ,4^w=n what is the units digit of n?

- Rules, if w = 0 Units of N=1, if w<0 Units of n = 0, if w>0 and odd, N = 4 (4,64,1024...), if w>0 and even n = 6 (16,256...)

1. w is an even integer - Insufficient, Units of N = 0 or 6
2. w > 0 - Insufficient Units of N = 4 or 6

Both together, w is even integer, and w>0 n= 6

C - Both together
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  21 Sep 2011, 08:17

Option A says that w is an even integer. so w can be 0 also. If w is 0, the unit's digit will be 1. If w is a positive integer greater than 0, then unit's digit will be 6 and if w is a negative integer, then it will be a fraction. So option A alone is not sufficient.

Option B says that w>0, but doesn't specify whether it is an integer or not. So for different values of w, we will get different unit's digits.

Combining both A and B, w is an even integer greater than 0. so unit's place will always be 6.

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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  21 Sep 2011, 15:41
C.

1 - W is Even
If W = 2, units digit of N = 6 (for every even integer).
However, if W=(-2) the units digit of N will be "0"
therefore - not sufficient.

2 - w>0
Of course not sufficient, for example:
W=1/2 - N units digit will be 2
W=1 - Units digit is 4
NOT SUFFICIENT.

(1)+(2)

We know W is positive and even and integer.
so the last digit will always be 6.
For example W=2, N=16. W=4, N = 256
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  22 Sep 2011, 03:06
If 4^w=n , what is the units digit of n?

1. 4^2 = 16 4^4 = 256, 4^6 = 4096 => pattern - units digit is "6" - Sufficient
2. 4^1/2 = 2, 4^1 = 4, 4^2 = 16, 4^3 = 64 => different outcomes - Insufficient

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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  22 Sep 2011, 09:44
C
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  22 Sep 2011, 12:50
$$4^1=4$$
$$4^2=16$$
$$4^3=64$$
$$4^4=256$$

Conclusion 1 $$4^e$$=units digit of 6 where e is even
Conclusion 2 $$4^o=$$units digit of 4 where o is odd

1) is insufficient since n can have 2 values "6" or "0" because 0 is an even integer and $$4^0=1$$
2) is insufficient because "n" can have 2 values "6" or "4"

Together they are sufficient as it will result in only 1 value i.e. "6"
Ans= C
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Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink]  22 Sep 2011, 13:20
Before we even look at the statements, the sentence doesn't tell whether it is a positive exponent or if it is an integer, so we have to keep that in mind.
Now, seeing statement 1, tells us that it is an integer indeed, but we still know nothing about its sign. If w < 0 then the units digit is 0.
If w > 0 then the units digit is 6.
Hence NOT SUFFICIENT. We keep answers BCE.

Statement 2 tells us that w is greater than zero, but it fails to address whether it is an integer or not. Therefore NOT SUFFICIENT. We keep answers CE.

Using both statements together we know exactly what we need to know. The coefficient w is greater than zero AND is an integer. We could conclude that the units digit is 6 (we don't have to, though).

Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests!   [#permalink] 22 Sep 2011, 13:20

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# Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests!

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