Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Didn't find a shorter way: 6^17= (6*6*6*6*6)^5*6=7286^3*6 We need only the tenth digit therefore- 86*86*86*6= 7396*86 96*86=...56--- 56*6= ...36 Correct answer is B - 6

Just like cyclicity of the last digit, we can observe the cyclicity of the last 2 digits in this case : (which is possible because there is no cyclicity in the unit's digit, it is always 6) 6^2 = 36 6^3 = 16 6^4 = 96 6^5 = 76 6^6 = 56 6^7 = 36 .. and then it repeats

So for 6^17, it will have the same tens digit as 6^12, 6^7, 6^2 ... or 3

So the logic here is simple. Consider the number 6^x, lets say that you know the tens digit of this number, can you find out the tens digit of 6^(x+1) ?

What we know is that the last digit of 6^x will always be 6 (which is easy enough to see). Now the fact of the matter is that the ten's digit of 6^(x+1) is only dependent on the tens digit of 6^x.

Because Ten's digit of 6^(x+1) = 6*(Ten's digit of 6^x) + 3 (carried over during the multiplication of the units digits 6 with the new 6).

Like 6^3 = 216 So 6^4, units digit is 6 and ten's digit is 6*1+3 = 9

Hence, as soon as the ten's digit of 6^x becomes the same as the ten's digit of 6^y, the pattern of tens digit will start to repeat itself

The pattern here is 3,1,9,7,5,3,1,9,7,5,3,1,9,7,5,3,1,9,7,5,3..... The cyclicity of the pattern is five, so every 5th element in this series will be the same hence 2nd,7th,12th,17th have to be the same
_________________

What is the tens digit of 6^17? (A) 1 (B) 3 (C) 5 (D) 7 (E) 9

There are several ways to deal with this problems some easier some harder, but almost all of them are based on the pattern recognition.

The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in pattern of 5: {3, 1, 9, 7, 5}: The tens digit of 6^2=36 is 3; The tens digit of 6^3=216 is 1; The tens digit of 6^4=...96 is 9 (how to calculate: multiply 16 by 6 to get ...96 as the last two digits); The tens digit of 6^5=...76 is 7 (how to calculate: multiply 96 by 6 to get ...76 as the last two digit); The tens digit of 6^6=...56 is 5 (how to calculate: multiply 76 by 6 to get ...56 as the last two digits); The tens digit of 6^7=...36 is 3 again (how to calculate: multiply 56 by 6 to get ...36 as the last two digits).

Hence, 6^2, 6^7, 6^12, 6^17, 6^22, ... will have the same tens digit of 3.

well, this question demands calculation to see a pattern of tens digits keep calculating till it's confirmed that u have hit a pattern. 6^1 = 6 6^2 = 36 6^3 = 216 now don't multiply 216 by 6, rather we are interested in only first two digits to know the outcome so 6^4 = 96 ( 16 x 6) 6^5 = 576 ( 96 x 6) 6^ 6 = 456 ( 76 x 6) 7^ 6 =336 ( 56 x 6) so now we have the pattern in tens digit i.e. 3 in (6^2), 1 in (6^3), 9 in (6^4), 7 in (6^5), 5 in (6^6), 3 in (6^7),

so the tens digit is 3 for the 2,7,12 and 17 times.. IMO B
_________________

Fire the final bullet only when you are constantly hitting the Bull's eye, till then KEEP PRACTICING.

A WAY TO INCREASE FROM QUANT 35-40 TO 47 : http://gmatclub.com/forum/a-way-to-increase-from-q35-40-to-q-138750.html

Q 47/48 To Q 50 + http://gmatclub.com/forum/the-final-climb-quest-for-q-50-from-q47-129441.html#p1064367

Three good RC strategies http://gmatclub.com/forum/three-different-strategies-for-attacking-rc-127287.html

Note that when you multiply, you don't have to finish it all the way, knowing the tens digit should suffice.... Also, using the table we have we can calculate \(6^{10}\) and \(6^{17}\). We work with what we already have above/

bunuel would you please post me a link on the topic of exponents and powers from gmat math book if it has been finished..i want to learn and master way u hav solved the problem

bunuel would you please post me a link on the topic of exponents and powers from gmat math book if it has been finished..i want to learn and master way u hav solved the problem

What is the tens digit of 6^17? (A) 1 (B) 3 (C) 5 (D) 7 (E) 9

There are several ways to deal with this problems some easier some harder, but almost all of them are based on the pattern recognition.

The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in pattern of 5: {3, 1, 9, 7, 5}: The tens digit of 6^2=36 is 3; The tens digit of 6^3=216 is 1; The tens digit of 6^4=...96 is 9 (how to calculate: multiply 16 by 6 to get ...96 as the last two digits); The tens digit of 6^5=...76 is 7 (how to calculate: multiply 96 by 6 to get ...76 as the last two digit); The tens digit of 6^6=...56 is 5 (how to calculate: multiply 76 by 6 to get ...56 as the last two digits); The tens digit of 6^7=...36 is 3 again (how to calculate: multiply 56 by 6 to get ...36 as the last two digits).

Hence, 6^2, 6^7, 6^12, 6^17, 6^22, ... will have the same tens digit of 3.

Answer: B.

i have noticed that every number has 6 as the unit digit..is it the same for other numbers that they repeat each of the unit's digit throughout when it is being raised to powers of consecutive integers

What is the tens digit of 6^17? (A) 1 (B) 3 (C) 5 (D) 7 (E) 9

There are several ways to deal with this problems some easier some harder, but almost all of them are based on the pattern recognition.

The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in pattern of 5: {3, 1, 9, 7, 5}: The tens digit of 6^2=36 is 3; The tens digit of 6^3=216 is 1; The tens digit of 6^4=...96 is 9 (how to calculate: multiply 16 by 6 to get ...96 as the last two digits); The tens digit of 6^5=...76 is 7 (how to calculate: multiply 96 by 6 to get ...76 as the last two digit); The tens digit of 6^6=...56 is 5 (how to calculate: multiply 76 by 6 to get ...56 as the last two digits); The tens digit of 6^7=...36 is 3 again (how to calculate: multiply 56 by 6 to get ...36 as the last two digits).

Hence, 6^2, 6^7, 6^12, 6^17, 6^22, ... will have the same tens digit of 3.

Answer: B.

i have noticed that every number has 6 as the unit digit..is it the same for other numbers that they repeat each of the unit's digit throughout when it is being raised to powers of consecutive integers

Posted from my mobile device

No. You could test that very easily yourself. Is the units digit of 2^2 equal 2? No, its 4.

• Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base. • Integers ending with 2, 3, 7 and 8 have a cyclicity of 4.

What is the tens digit of 6^17? (A) 1 (B) 3 (C) 5 (D) 7 (E) 9

There are several ways to deal with this problems some easier some harder, but almost all of them are based on the pattern recognition.

The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in pattern of 5: {3, 1, 9, 7, 5}: The tens digit of 6^2=36 is 3; The tens digit of 6^3=216 is 1; The tens digit of 6^4=...96 is 9 (how to calculate: multiply 16 by 6 to get ...96 as the last two digits); The tens digit of 6^5=...76 is 7 (how to calculate: multiply 96 by 6 to get ...76 as the last two digit); The tens digit of 6^6=...56 is 5 (how to calculate: multiply 76 by 6 to get ...56 as the last two digits); The tens digit of 6^7=...36 is 3 again (how to calculate: multiply 56 by 6 to get ...36 as the last two digits).

Hence, 6^2, 6^7, 6^12, 6^17, 6^22, ... will have the same tens digit of 3.

Answer: B.

.

Hi Bunuel,

Can we do this in following way

6^17 = (2*3)^17

(2^16*3^16) *2*3

now 2 repeats in pattern 2,4,8,6 and 3 repeats in pattern 3,9,7,1 so when we multiply 2^16*3^16 last digit is 6 now multiply 6 *6 so its 36 so tens digit is 3.

If Question like this appears in GMAT. and we are asked to find the last two digits this could be used

Rule Express Even numbers in the form ( 2^10) ^even which will have last two digits as 76 or ( 2^10) ^odd where last two digits is 24

For Odd numbers Express them 3^4k, 7 ^ 4k, 9 ^2k

Question was 6^17

So (2^ 17 ) ( 3^17)

= {(2^10)^1 * 2^7} { (3^4)^3 * 3^5}

So last two digits (2^10)^1= 24 So last two digits 2^7= 28

Last two digits of this number (3^4)^3 = (81)^3= last two digits are 41 (1 will be the last digit and second last digit will be 4 that i got by multiplying 8 *3 last two digits of this number 3^5 = 43

So (24 * 28) * (41* 43)

Don't do complete multiplication just do it till you get two digits

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...