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tricky
Source: Beat The GMAT — Problem Solving |
sorry brother, i just edited my post as 615 is actually 6^15 means 6 to the power 15...same follows for others..please check the edited post...now try the questionedge wrote:615 - 74 - 93 = 448, the units digit of which is 8...
Princeton Review CAT - 710(Q-51, V-37) --> silly mistakes screwed up my VERBAL
Units digit of 6^15 is 6
Units digit of 7^4 is 1
Units digit of 9^3 is 9
So, (6^15)-(7^4)-(9^3)=(...xxxx6)-(2401)-(729)=6
Hence, the units digit is C
Units digit of 7^4 is 1
Units digit of 9^3 is 9
So, (6^15)-(7^4)-(9^3)=(...xxxx6)-(2401)-(729)=6
Hence, the units digit is C
the upd (unit place digit) in 6 power 15 is 6 its really easy to know upds of any power by just knowing the recurring upd concept
as
6^1=6
6^2=36
6^3=216
so as and all
upd concept for 7 is
7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16807
7^6=117649
7^7=823543
7^8=5764801
if u observe opds here u can simply say 7,9,3,1 are coming
so for all natural numbers in the power of 7 divisible by 4 (4,8,12,16......) we get upd as 1
for numbers when divided by 4 gives reminder 1 ( 1,5,9,13........) we get upd as 7
for nums when div by 4 gives reminder 2 (2,6,10,14..........) we get upd as 9
for nums when divided by 4 gives reminder 3 (3,7,11,15.........) we get upd as 3
so in this case upd is 1
so like same in the case of 9^3 upd is 9
now come to prob by their upds
6-1-9=5-9=15-9=6
so the ans is 6[/b][/i]
as
6^1=6
6^2=36
6^3=216
so as and all
upd concept for 7 is
7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16807
7^6=117649
7^7=823543
7^8=5764801
if u observe opds here u can simply say 7,9,3,1 are coming
so for all natural numbers in the power of 7 divisible by 4 (4,8,12,16......) we get upd as 1
for numbers when divided by 4 gives reminder 1 ( 1,5,9,13........) we get upd as 7
for nums when div by 4 gives reminder 2 (2,6,10,14..........) we get upd as 9
for nums when divided by 4 gives reminder 3 (3,7,11,15.........) we get upd as 3
so in this case upd is 1
so like same in the case of 9^3 upd is 9
now come to prob by their upds
6-1-9=5-9=15-9=6
so the ans is 6[/b][/i]
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gmatboost
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To summarize:
0: 0, 0, 0, 0
1: 1, 1, 1, 1
2: 2, 4, 8, 6
3: 3, 9, 7, 1
4: 4, 6, 4, 6
5: 5, 5, 5, 5
6: 6, 6, 6, 6
7: 7, 9, 3, 1
8: 8, 4, 2, 6
9: 9, 1, 9, 1
You can practice recalling the patterns for each digit while on the train or doing something else. They all repeat after 1, 2, or 4. All you need to remember to go from one to the next is the previous one's digit. So, don't worry about
7^1= 7
7^2= 49
7^3= 7 * 9 = 63
7^4= 7 * 3 = 21
7, 9, 3, 1
0: 0, 0, 0, 0
1: 1, 1, 1, 1
2: 2, 4, 8, 6
3: 3, 9, 7, 1
4: 4, 6, 4, 6
5: 5, 5, 5, 5
6: 6, 6, 6, 6
7: 7, 9, 3, 1
8: 8, 4, 2, 6
9: 9, 1, 9, 1
You can practice recalling the patterns for each digit while on the train or doing something else. They all repeat after 1, 2, or 4. All you need to remember to go from one to the next is the previous one's digit. So, don't worry about
Just think7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16807
7^6=117649
7^7=823543
7^8=5764801
7^1= 7
7^2= 49
7^3= 7 * 9 = 63
7^4= 7 * 3 = 21
7, 9, 3, 1
Greg Michnikov, Founder of GMAT Boost
GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.
Also, check out the most useful GMAT Math blog on the internet here.
GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.
Also, check out the most useful GMAT Math blog on the internet here.
