mgmat 4b V.Good Qs

Expert replies

vkb16: Master | Next Rank: 500 Posts; Posts: 122; Joined: Mon Dec 15, 2008 12:03 am; Thanked: 2 times

by vkb16 » Thu Mar 12, 2009 4:51 am

If x is a positive integer, what is the units digit of x2?

(1) The units digit of x4 is 1.

(2) The units digit of x is 3.

OA is B, but I cannot understand the reason why?
I think its E

Like this post

Source: Beat The GMAT — Data Sufficiency | Thu Mar 12, 2009 4:51 am

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Thu Mar 12, 2009 5:01 am

Units digit cycle as follows for 3:

3 9 7 1 3 9 7 1

From smt II if u know the units digit of x is 3 then u know the units digit of x^2 will be 9.

Hence SUFF

Stmt I

The number could have units digit of 1 or 3 SO X^2 units digit could be 1 or 9

INSUFF

B

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Thu Mar 12, 2009 5:41 am

cramya wrote: Stmt I

The number could have units digit of 1 or 3 SO X^2 units digit could be 1 or 9

INSUFF

Great solution - just wanted to point out that there are other possibilities here: if the units digit of x^4 is 1, then the units digit of x could be 1, 3, 7 or 9.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

vkb16: Master | Next Rank: 500 Posts; Posts: 122; Joined: Mon Dec 15, 2008 12:03 am; Thanked: 2 times

by vkb16 » Sun Mar 15, 2009 9:29 pm

this might be a no-brainer one for u guys, but

(2) The units digit of x is 3.

are we assuming that x is a single unit number? or a double digit number?
I mean it just says the ''units'' digit is 3... it can mean the number is 3,13,23,43, etc??

Like this post

Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

by Morgoth » Sun Mar 15, 2009 10:10 pm

vkb16 wrote:this might be a no-brainer one for u guys, but

(2) The units digit of x is 3.

are we assuming that x is a single unit number? or a double digit number?
I mean it just says the ''units'' digit is 3... it can mean the number is 3,13,23,43, etc??

It doesnt matter weather you take single digit or double digit number, the units digit will always be same.

You can try for all those numbers, the resulting units digit will always be 1

3^4 = 81
13^4 = 28561
so on and so forth.

Hence for all the numbers ending in 3 the units digit will always be 1 if and only if that number is raised to the power of 4,

Similarly, if the number with units digit of 3 raised to the power of 2 the resulting number's units digit will always be 9.

hope this helps.

Like this post

vkb16: Master | Next Rank: 500 Posts; Posts: 122; Joined: Mon Dec 15, 2008 12:03 am; Thanked: 2 times

by vkb16 » Mon Mar 16, 2009 4:08 am

thanks a lot!

Like this post

lilu: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Dec 10, 2008 5:13 pm; Location: SF, CA; Thanked: 12 times

by lilu » Thu Mar 19, 2009 3:23 pm

I have another question:
Are there any other numbers 1-9 that besides 3 that have similar "special" properties? (I mean the way the units repeat when raising to powers in numbers that end with 3)

Thank you!
Liliya

Like this post

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Thu Mar 19, 2009 3:39 pm

lilu wrote:I have another question:
Are there any other numbers 1-9 that besides 3 that have similar "special" properties? (I mean the way the units repeat when raising to powers in numbers that end with 3)

Thank you!
Liliya

All of them!

Only focusing on the units digit:

1^n always ends in 1
2^n follows the pattern 2, 4, 8, 6, ...
3^n follows the pattern 3, 9, 7, 1, ...
4^n follows the patter 4, 6, ...
5^n always ends in 5
6^n always ends in 6
7^n follows the pattern 7, 9, 3, 1, ...
8^n follows the pattern 8, 4, 2, 6, ...
9^n follows the pattern 9, 1, ...
0^n always ends in 0

Last edited by Stuart@KaplanGMAT on Thu Mar 19, 2009 9:06 pm, edited 1 time in total.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

Like this post

lilu: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Dec 10, 2008 5:13 pm; Location: SF, CA; Thanked: 12 times

by lilu » Thu Mar 19, 2009 8:33 pm

Thank you so much, Stuart!
I'm making a flash card!

and what about 4?

Like this post

Jose Ferreira: GMAT Instructor; Posts: 99; Joined: Thu Mar 05, 2009 5:14 pmFollowed by: 9 members; Location: NYC; Thanked: 43 times; GMAT Score:800

by Jose Ferreira » Thu Mar 19, 2009 8:55 pm

Hi Liliya,

4 follows the pattern 4, 6, 4, 6

While memorizing these patterns could be helpful, it is more important to understand HOW we arrive at these patterns, so that you have the tools you need to answer the question even if you forget one of the patterns on test day.

The most important point is that when we multiply any two numbers together, all we need to know in order to find the ones digit of the product is the ones digit of each of the two numbers.

Let's take the example of 7.

7^1 = 7.
7^2 = 49, so the ones digit is 9.

To find the ones digit of 7^3, we do NOT need to multiply 7 * 49. Instead, we can ignore everything but the ones digit, and simply multiply 7 * 9 = 63. Thus, the ones digit of 7^3 is 3.

Similarly, to find the ones digit of 7^4, we do NOT need to multiply 7 * 7 * 7 * 7, or even to multiply 63 (the previous result) by 7. Instead, we can ignore everything but the ones digit, and simply multiply 7 * 3 = 21. Thus, the ones digit of 7^4 is 1.

We can continue like this.
7^5 has a ones digit of 7 * 1 = 7.
7^6 has a ones digit of 7 * 7 = 49, so 9.
7^7 has a ones digit of 7 * 9 = 63, so 3.
7^8 has a ones digit of 7 * 3 = 21, so 1.

This gives us the pattern 7, 9, 3, 1, 7, 9, 3, 1.

Jose Ferreira
Founder and CEO, Knewton, Inc.
https://www.knewton.com/gmat

Like this post

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Thu Mar 19, 2009 9:06 pm

lilu wrote:Thank you so much, Stuart!
I'm making a flash card!

and what about 4?

Sorry, I was traumatized by 4 as a child!

Modified my post, no clue why I left 4 out

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review