GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 29 May 2020, 03:30

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

a, b, c, d and e are all non-zero distinct single digit integers. What

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Director
Director
User avatar
Joined: 24 Aug 2007
Posts: 598
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
a, b, c, d and e are all non-zero distinct single digit integers. What  [#permalink]

Show Tags

New post Updated on: 09 May 2010, 08:10
4
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (08:34) correct 0% (00:00) wrong based on 12 sessions

HideShow timer Statistics

a b c d e
x 4
-----------
e d c b a


a, b, c, d and e are all non-zero distinct single digit integers. What are the values of a, b, c, d and e?

Originally posted by ykaiim on 09 May 2010, 05:40.
Last edited by ykaiim on 09 May 2010, 08:10, edited 1 time in total.
Manager
Manager
avatar
Joined: 25 Jun 2009
Posts: 211
Re: a, b, c, d and e are all non-zero distinct single digit integers. What  [#permalink]

Show Tags

New post 09 May 2010, 08:01
1
2
ykaiim wrote:
a b c d e
x 4
-----------
e d c b a
-----------

What are the values of a, b, c, d and e?


Okay, let me give it a shot to this one...! I am assuming that a,b,c,d,e are distinct integers..!

First thing to note the 5 digit number is multiplied by 4 and gives a 5 digit number again .. that means abcde has to be equal or less than 24999 else the abcde when multiplied by 4 will become 6 digit number.

Given:
ABCDE
x 4
= EDCBA

The answer is:
21978
x 4
= 87912

But rather than just give you the answer, here's how I figured it out. First, it is obvious that A must be an even number, because we are multiplying by 4 (an even number). The last digit will therefore be even. It can't be 0, because that would make ABCDE a four-digit number. It can't be more than 2, because that would result in a six-digit answer. So A = 2.

2BCDE
x 4
= EDCB2

So what can E be? The choices are E = {3, 8} because 3 x 4 = 12 and 8 x 4 = 32. But a value of 3 doesn't work in the result (3????) because it is too small.

2BCD8
x 4
= 8DCB2

Since the final number is 8 and we have 2 x 4, that means there is no carry from the prior multiplication (4 x B + carry). So B can't be anything higher than 1, possibly 0.

Looking at the other side of the equation, we have 4D + 3 = (a number ending in 0 or 1). In other words, 4D must end in 7 or 8. Obviously only 8 works, because 4 is an even number. Working forward again, that means B = 1.

21CD8
x 4
= 8DC12

So what values of 4D result in a number ending 8? 4 x 2 = 8, 4 x 7 = 28. Now 2 is already taken and the problem said the digits were unique. So D = 7.

21C78
x 4
= 87C12

Finally, we have a carry of 3 (from 28 + 3 = 31). And when we calculate 4C + 3 it must also result in a carry of 3 and a last digit of C. In other words:
4C + 3 = 30 + C

This is easy to solve:
3C = 27
C = 9

Thus the final answer is:
21978
x 4
= 87912
Manager
Manager
avatar
Joined: 23 May 2010
Posts: 186
Re: a, b, c, d and e are all non-zero distinct single digit integers. What  [#permalink]

Show Tags

New post 27 Aug 2010, 05:43
1
I am sure it can be DS question if not the PS one !!1....tricky time consuming
is there any other way ...?
Director
Director
User avatar
Joined: 24 Aug 2007
Posts: 598
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Re: a, b, c, d and e are all non-zero distinct single digit integers. What  [#permalink]

Show Tags

New post 27 Aug 2010, 19:53
No, I think nitish explained well.
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10474
Location: Pune, India
Re: a, b, c, d and e are all non-zero distinct single digit integers. What  [#permalink]

Show Tags

New post 27 Jun 2016, 20:51
ykaiim wrote:
a b c d e
x 4
-----------
e d c b a
-----------
a, b, c, d and e are all non-zero distinct single digit intergers.

What are the values of a, b, c, d and e?


A 5 digit number multiplied by 4 gives another 5 digit number. So a will be either 1 or 2.
edbca has 4 as a factor so a will be 2.
4 times 2 b c d e will begin with 8 or 9 so e = 8 or 9. But 8 times 4 will give a units digit of 2. So e = 8.

2 b c d 8
........* 4
8 d c b 2

So now you have
b c d(+3)
....*4
d c b

4 times a three digit number gives another 3 digit number. So b must be 1.
So 4d + 3 =_ 1
4d = _ 8
d = 7

2 1 c 7 8
..........*4
8 7 c 1 2

4c + 3 = 3 c
c = 9

abcde = 21978
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15015
Re: a, b, c, d and e are all non-zero distinct single digit integers. What  [#permalink]

Show Tags

New post 15 May 2020, 07:01
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: a, b, c, d and e are all non-zero distinct single digit integers. What   [#permalink] 15 May 2020, 07:01

a, b, c, d and e are all non-zero distinct single digit integers. What

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne