1,234
1,243
1,324
.....
....
+4,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers?
A. 24,000
B. 26,664
C. 40,440
D. 60,000
E. 66,660
OA E
Source: Official Guide
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
The addition problem above shows four of the 24 different
This topic has expert replies
-
BTGmoderatorDC
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Last edited by BTGmoderatorDC on Tue Dec 31, 2019 3:58 am, edited 1 time in total.
This question can be solved quickly with approximation.BTGmoderatorDC wrote:1,234
1,243
1,324
.....
....
+4,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers?
A. 24,000
B. 26,664
C. 40,440
D. 60,000
E. 66,660
OA E
Source: Official Guide
There will be 3! (6) numbers starting with 1 , similarly 6 numbers starting with 2, 3 and 4 respectively.
Numbers starting with 1 are in 1000 e.g (1234, 1243 etc ) So sum will be >6000 (as there are 6 numbers starting with 1)
Similarly, Sum of numbers starting with 2 will be >12000, 3 will be 18000, 4 will be 24000
Sum of all these numbers will be > (6000+12000+18000+24000) = >60,000
Only option E has value >60,000.
Hence Answer is E
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Since we're adding 24 numbers, we know that:BTGmoderatorDC wrote:1,234
1,243
1,324
.....
....
+4,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers?
A. 24,000
B. 26,664
C. 40,440
D. 60,000
E. 66,660
OA E
Source: Official Guide
Six numbers will be in the form 1---
Six numbers will be in the form 2---
Six numbers will be in the form 3---
Six numbers will be in the form 4---
Let's first see what the sum is when we say all 24 numbers are 1000, 2000, 3000 or 4000
The sum = (6)(1000) + (6)(2000) + (6)(3000) + (6)(4000)
= 6(1000 + 2000 + 3000 + 4000)
= 6(10,000)
= 60,000
Since the 24 numbers are actually greater than 1000, 2000, etc, we know that the actual sum must be greater than 60,000
Answer: E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7244
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
BTGmoderatorDC wrote:1,234
1,243
1,324
.....
....
+4,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,3,4 exact;y once in each integer. What is the sum of these 24 integers?
A. 24,000
B. 26,664
C. 40,440
D. 60,000
E. 66,660
OA E
Source: Official Guide
Since there are 24 different integers, each of the digits (1, 2, 3 and 4) will appear in each of the place values (thousands, hundreds, tens and ones) exactly 6 times. Therefore, the sum of the 24 integers will be as follows:
6(1000 + 2000 + 3000 + 4000) + 6(100 + 200 + 300 + 400) + 6(10 + 20 + 30 + 40) + 6(1 + 2 + 3 + 4)
6(10,000) + 6(1,000) + 6(100) + 6(10)
60,000 + 6,000 + 600 + 60
66,660
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
