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

It is currently 25 Feb 2020, 10:51

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

In a four-digit number, the sum of the digits in the units place and

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Joined: 25 Jan 2010
Posts: 99
Location: Calicut, India
In a four-digit number, the sum of the digits in the units place and  [#permalink]

Show Tags

New post 15 Jul 2011, 08:04
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

26% (03:36) correct 74% (02:52) wrong based on 30 sessions

HideShow timer Statistics

In a four-digit number, the sum of the digits in the units place and the tens place is equal to the sum of the digits in the hundreds and the thousands places. The sum of the digits in the tens and hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digits in the units place can be

A) 6
B) 7
C) 8
D) 5
E) 2
Intern
Intern
avatar
Joined: 18 Jul 2011
Posts: 35
Re: In a four-digit number, the sum of the digits in the units place and  [#permalink]

Show Tags

New post 22 Jul 2011, 08:15
2
1
cleetus wrote:
In a four-digit number, the sum of the digits in the units place and the tens place is equal to the sum of the digits in the hundreds and the thousands places. The sum of the digits in the tens and hundreds place is twice the sum of the other two digits. If the sum of the digits of the number is more than 20, then the digits in the units place can be
A) 6
B) 7
C) 8
D) 5
E) 2


Let's call the number ABCD.
We're given the following information:
(1) A + B = C + D
(2) B + C = 2(A + D) = 2A + 2D
(3) A + B + C + D > 20

This isn't much to go on, so we should try to derive some more information from what we're given. First, keep in mind that A, B, C, and D are digits - numbers between 0 and 9 inclusive, except for A which can not be 0. Based on equation (2) we can guess that A and D will be smaller than B and C. In fact, since B + C <= 18, we know that A + D <= 9. If A + D = 9, then B and C would both be 9 and in order to fulfill equation (1) A and D would have to be 9/2, but this isn't a digit... so we can do even better A + D < 9. Finally, if we know A and D we can find B and C by combining a different form of equation (1) and equation (2)
D - A = B - C
2A + 2D = B + C
This is a lot better than where we started.

Since this is a "can be" question, we should proceed by elimination. We'll start with the largest answer first as this puts more restrictions on A, and once we have A and D we can find B and C.

Suppose D = 8. Then A = 0 - NO
Suppose D = 7. Then A = 1 and B + C = 16 and B - C = 6. This implies B = 11. NO
Suppose D = 6.
And A = 1. So, B + C = 14 and B - C = 5. This implies B = 19/2. NO
And A = 2. So, B + C = 16 and B - C = 4. This implies B = 10. NO
Suppose D = 5.
And A = 1. So, B + C = 12 and B - C = 4. This implies B = 8 and ABCD = 1845, but 1 + 8 + 4 + 5 = 18 < 20. NO
And A = 2. So, B + C = 14 and B - C = 3. This implies B = 17/2. NO
And A = 3. So, B + C = 16 and B - C = 2. This implies B = 9 and ABCD = 3975, and 3 + 9 + 7 + 5 = 24 > 20. YES

BenchPrepGURU
GMAT Club Bot
Re: In a four-digit number, the sum of the digits in the units place and   [#permalink] 22 Jul 2011, 08:15
Display posts from previous: Sort by

In a four-digit number, the sum of the digits in the units place and

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





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