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

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Knewton GMAT Representative
Joined: 17 Aug 2011
Posts: 26

Kudos [?]: 20 [0], given: 0

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

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20 Sep 2011, 07:01
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, 13:04, edited 3 times in total. Update Kudos [?]: 20 [0], given: 0 Intern Joined: 11 Nov 2009 Posts: 27 Kudos [?]: 15 [0], given: 1 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 07:23 My Answer is C......both are necessary to answer the question....... 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..... Kudos [?]: 15 [0], given: 1 Manager Joined: 26 May 2011 Posts: 155 Kudos [?]: 28 [0], given: 10 Concentration: Entrepreneurship, Finance GPA: 3.22 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 07:35 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. Kudos [?]: 28 [0], given: 10 Manager Status: :) Joined: 29 Jun 2010 Posts: 120 Kudos [?]: 50 [1], given: 54 WE: Information Technology (Consulting) Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 10:02 1 This post received 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 _________________ Thanks, GC24 Please click Kudos ,if my post helped you Kudos [?]: 50 [1], given: 54 Founder Joined: 04 Dec 2002 Posts: 15880 Kudos [?]: 29108 [0], given: 5270 Location: United States (WA) GMAT 1: 750 Q49 V42 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 10:04 Moderator level members and higher will be able to see all replies _________________ Founder of GMAT Club Just starting out with GMAT? Start here... or use our Daily Study Plan Co-author of the GMAT Club tests Kudos [?]: 29108 [0], given: 5270 Manager Status: Head Turner ! am I ? Affiliations: RHCE , CCNA, MCSE and Now GMAT ;) Joined: 29 Jul 2011 Posts: 138 Kudos [?]: 205 [0], given: 28 Location: India WE: Operations (Computer Hardware) Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 10:19 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 _________________ _______________________________________________ Am i worth a Kudo ? Life's around GMAT for the Moment Last edited by hoogly on 23 Sep 2011, 02:58, edited 2 times in total. Kudos [?]: 205 [0], given: 28 Joined: 31 Dec 1969 Kudos [?]: [0], given: Location: Russian Federation Concentration: Entrepreneurship, International Business GMAT 3: 740 Q40 V50 GMAT 4: 700 Q48 V38 GMAT 5: 710 Q45 V41 GMAT 6: 680 Q47 V36 GMAT 9: 740 Q49 V42 GMAT 11: 500 Q47 V33 GMAT 14: 760 Q49 V44 WE: Supply Chain Management (Energy and Utilities) Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 12:01 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. Kudos [?]: [0], given: Intern Status: Application submitted Joined: 12 Jun 2010 Posts: 38 Kudos [?]: 15 [0], given: 1 Location: NYC Schools: Stern Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 12:23 My answer would be C. 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. Kudos [?]: 15 [0], given: 1 Director Status: My Thread Master Bschool Threads-->Krannert(Purdue),WP Carey(Arizona),Foster(Uwashngton) Joined: 28 Jun 2011 Posts: 879 Kudos [?]: 245 [0], given: 57 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 12:50 The answer is A.... 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.. Hence answer is A _________________ Kudos [?]: 245 [0], given: 57 Intern Joined: 26 May 2011 Posts: 13 Kudos [?]: 3 [0], given: 0 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 13:09 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 Kudos [?]: 3 [0], given: 0 Manager Joined: 17 Sep 2011 Posts: 180 Kudos [?]: 79 [0], given: 34 Concentration: Strategy, Operations Schools: ISB '15 GMAT 1: 720 Q48 V40 GPA: 3.18 WE: Supply Chain Management (Manufacturing) Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 20 Sep 2011, 22:37 ANSWER: C 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....)=> Kudos [?]: 79 [0], given: 34 Intern Joined: 28 Jul 2011 Posts: 2 Kudos [?]: [0], given: 0 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 21 Sep 2011, 05:05 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, 08:27, edited 1 time in total. Kudos [?]: [0], given: 0 Intern Joined: 04 May 2011 Posts: 12 Kudos [?]: 11 [0], given: 0 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 21 Sep 2011, 05:19 A Kudos [?]: 11 [0], given: 0 Director Status: Can't wait for August! Joined: 13 Sep 2011 Posts: 988 Kudos [?]: 352 [0], given: 109 Location: United States (MA) Concentration: Marketing, Strategy GMAT 1: 660 Q44 V37 GMAT 2: 680 Q45 V38 GMAT 3: 710 Q45 V42 GPA: 3.32 WE: Information Technology (Retail) Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 21 Sep 2011, 05:56 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 Kudos [?]: 352 [0], given: 109 Intern Joined: 04 Aug 2010 Posts: 39 Kudos [?]: 6 [0], given: 2 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 21 Sep 2011, 09:17 Correct Answer is Option C. 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. So C is the answer. Kudos [?]: 6 [0], given: 2 Senior Manager Joined: 08 Nov 2010 Posts: 392 Kudos [?]: 129 [0], given: 161 WE 1: Business Development Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 21 Sep 2011, 16:41 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 _________________ Kudos [?]: 129 [0], given: 161 Manager Joined: 27 Jul 2010 Posts: 86 Kudos [?]: 22 [0], given: 6 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 22 Sep 2011, 04:06 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 A is the answer. Kudos [?]: 22 [0], given: 6 Retired Moderator Joined: 10 May 2010 Posts: 823 Kudos [?]: 437 [0], given: 192 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 22 Sep 2011, 10:44 C _________________ The question is not can you rise up to iconic! The real question is will you ? Kudos [?]: 437 [0], given: 192 Intern Status: Target 660 -> 720(Q49,V41) retaking in Feb 2012 Joined: 22 Aug 2011 Posts: 6 Kudos [?]: 5 [0], given: 6 Location: United States GMAT 1: 660 Q47 V34 WE: Information Technology (Computer Software) Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 22 Sep 2011, 13:50 $$4^1=4$$ $$4^2=16$$ $$4^3=64$$ $$4^4=256$$ 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 Kudos [?]: 5 [0], given: 6 Intern Joined: 20 Sep 2011 Posts: 1 Kudos [?]: [0], given: 7 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] ### Show Tags 22 Sep 2011, 14:20 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). The answer is C. Kudos [?]: [0], given: 7 Re: Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests! [#permalink] 22 Sep 2011, 14:20 Go to page 1 2 3 Next [ 55 posts ] Display posts from previous: Sort by # Knewton Challenge: Win a Knerd Shirt and GMAT Club Tests!  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Moderator: HKD1710  HOT DEALS FOR NOVEMBER Economist GMAT - Free Free 1-week trial + Free Test Kaplan Courses - Save$475 $225 Discount +$250 Bonus Target Test Prep - $800$50 Discount + $750 Bonus [GMAT ClubTests and Premium MBA Bundle] EMPOWERgmat -$99/mo GMAT Club tests included 2nd month GMAT Club Tests - Free Included with every course purchaseof \$149 or more - Full List is here

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