unit digit

[daretodream]

What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

[ajith]

What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

The units digit of 6^15 is 6
Units digits of 7^4 is 1
Units digit of 9^3 is 9

Hence the unit's digit of 6^15 - 7^4 - 9^3 is 16-9-1 = 6

[harsh.champ]

What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

The units digit of 6^15 is 6
Units digits of 7^4 is 1
Units digit of 9^3 is 9

Hence the unit's digit of 6^15 - 7^4 - 9^3 is 16-9-1 = 6

Why are we taking 16 instead of 6??
Shouldn't the answer go like [spoiler]6-9-1= -4 which would be E.[/spoiler]

[shashank.ism]

What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

The units digit of 6^15 is 6
Units digits of 7^4 is 1
Units digit of 9^3 is 9

Hence the unit's digit of 6^15 - 7^4 - 9^3 is 16-9-1 = 6

Why are we taking 16 instead of 6??
Shouldn't the answer go like [spoiler]6-9-1= -4 which would be E.[/spoiler]

6^15 ----------- 6
7^4 --------1
9^3 --------- 9
now 6 -1 =5
so we have to calculate unit digit of xxxxxxxxxxxx5 -yyyyyyyy9 .... just try to substract u will do it by 15-9 only and it will give u value as 6 Ans C.

[thephoenix]

What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

The units digit of 6^15 is 6
Units digits of 7^4 is 1
Units digit of 9^3 is 9

Hence the unit's digit of 6^15 - 7^4 - 9^3 is 16-9-1 = 6

Why are we taking 16 instead of 6??
Shouldn't the answer go like [spoiler]6-9-1= -4 which would be E.[/spoiler]

the no. with 6^15 is bigger than rest two there when u will add the other two u get 0 as unit dig and when u sub 0 from 6 the unit dig of 6^15 u get 6 as the unit dig
so C

[harshavardhanc]

What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

The units digit of 6^15 is 6
Units digits of 7^4 is 1
Units digit of 9^3 is 9

Hence the unit's digit of 6^15 - 7^4 - 9^3 is 16-9-1 = 6

Why are we taking 16 instead of 6??
Shouldn't the answer go like [spoiler]6-9-1= -4 which would be E.[/spoiler]

you are very close.....!!! Actually, you are precisely thinking on the lines on Vedic Maths principles!! Bravo!!

observe that you have got -4 as your answer!! it is not same as 4. Since units digit cannot be a negative value, think by how much value is it less than the base of this subtraction (10) . it is 6 less than 10.

There you go !! you've got your answer.

I'm pasting a link below, which will tell you more about this Vedic subtraction technique. Please go through it whenever you get time :

https://www.scribd.com/doc/7150802/Vedic ... ubtraction

[abhi332]

What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

This can be easily solve but if the numbers are big, we can take a approach using the cyclicity of a number.
cyclicity of 6 is

6*6 = 36

36 * 6 --->6*6 = 36 ---> take unit digit of 36 i.e 6 and again multiply by 6

So we can see that 6 repeats itself in unit place in every multiplication

therefore cyclicity of 6 is 1, this means 6^n will always give 6 in unit digit

6^15 will have 6 in unit place

similary, cyclicity of 7 can be found as follows

7 * 7 = 49

49 * 7 --->9 *7 = 63

63 * 7 ----> 3*7 =21

21 * 7-----> 1* 7 = 7

7 * 7 this is repetition again
cyclicity of 7 is 4 (7,9,3,1)

7^4 unit digit can be found by dividing power by cyclicity = 4/ 4 will give remainder 0

0 wil point to 1 in (7,9,3,1) as 0 is above 1 . (7--->1, 9--->2, 3--->3, 1--->4,0)

therefore , unit digit is 1

9^3
cyclicity is 2 i.e (9,1)

if I divide 3/2 remainder is 1 which gives 9 as (9--->1, 1--->2,0)

6^15 - 7^4 - 9^3

Now we can have 6 - 1-9 = 6-10

as we are dealing with unit digit 10 will become 0 therefore

6 -10 ---> 6 - 0 = 6

[abhi332]

This was in my notes:

Numbers 2,3,7 and 8 have a cyclicity of 4

Numbers 0,1,5 and 6 have a cyclicity of 1 (ie) all the powers will have the same unit digit.Same holds for 0,1 and 6

If 4 is the number in the unit place of the base number then the unit digit will be "4" if the power is odd and it will be "6" if the power is even.
eg. 4^123 will have unit digit of 4 since 123 is odd.

for 9 the unit digit will be "9" for odd powers and "1" for even powers. eg 9^234 has unit digit as "1" since 234 is even.

[shashank.ism]

What is the units digit of 6^15 - 7^4 - 9^3?
A:8
B:7
C:6
D:5
E:4

The units digit of 6^15 is 6
Units digits of 7^4 is 1
Units digit of 9^3 is 9

Hence the unit's digit of 6^15 - 7^4 - 9^3 is 16-9-1 = 6

Why are we taking 16 instead of 6??
Shouldn't the answer go like [spoiler]6-9-1= -4 which would be E.[/spoiler]

you are very close.....!!! Actually, you are precisely thinking on the lines on Vedic Maths principles!! Bravo!!

observe that you have got -4 as your answer!! it is not same as 4. Since units digit cannot be a negative value, think by how much value is it less than the base of this subtraction (10) . it is 6 less than 10.

There you go !! you've got your answer.

I'm pasting a link below, which will tell you more about this Vedic subtraction technique. Please go through it whenever you get time :

https://www.scribd.com/doc/7150802/Vedic ... ubtraction

Harshavardhanc you have given a very good link ..I got many other methods in vedic mathematics to solve other problems too..
Vedic mathematics is really cool...If I expertise it .I would really be able to solve faster...thanks

[abhi332]

I don't believe in applying vedic maths as there are lots of variations in vedic maths.

In exam time there will be lots of stress in solving problem applying particular rules of vedic math might be time consuming.

Better Learn multiplication from 1 to 30

square of a number from 1 to 30

cube of a number from 1 to 20

fraction from 1/2 to 1/19 in terms of percentage. example 1/2 if 50 %

also use rule divide by 2 and multiply 2 by rule

some tricks just as back-solving or divisibility in ans choice or unit digits (bit of trick to eliminate the ans)

IMO, nothing else is require to make life more simpler instead of complicating it

[shashank.ism]

I don't believe in applying vedic maths as there are lots of variations in vedic maths.

In exam time there will be lots of stress in solving problem applying particular rules of vedic math might be time consuming.

Better Learn multiplication from 1 to 30

square of a number from 1 to 30

cube of a number from 1 to 20

fraction from 1/2 to 1/19 in terms of percentage. example 1/2 if 50 %

also use rule divide by 2 and multiply 2 by rule

some tricks just as back-solving or divisibility in ans choice or unit digits (bit of trick to eliminate the ans)

IMO, nothing else is require to make life more simpler instead of complicating it

Abhi you have summed a few of things which are actually required for every GMAT taker...its always necessary as these things come handy during solving problem..
But as I have gone through the link i found some of vedic mathematic calculation are much easier. So I would say don't go for all . just master the things which would really come handy ...If its seems to be clumsy leave it..
I mean there could be an option that could be considered....
isn't it??

[abhi332]

I actually mean that someone should not be to much dependable on vedic maths.

of-course if you feel comfortable in something you should definitely follow it.

Vedic maths is all about shortcuts, and there are thousands of rules and variation for all the shortcuts.

from my experience depending too much vedic match may not be good. but, yes we can take some tricks which we can find easy to use during exam time.

[shashank.ism]

I actually mean that someone should not be to much dependable on vedic maths.

of-course if you feel comfortable in something you should definitely follow it.

Vedic maths is all about shortcuts, and there are thousands of rules and variation for all the shortcuts.

from my experience depending too much vedic match may not be good. but, yes we can take some tricks which we can find easy to use during exam time.

yeah abhi you are very correct ...I meant the same...no issues..
I just wanted to stress on importance of vedic mathematics. I noted down few good formulae today..its really working for me..