The addition problem above shows four of the 24 different

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

The addition problem above shows four of the 24 different

by BTGmoderatorDC » Sun Dec 29, 2019 6:22 pm

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

Last edited by BTGmoderatorDC on Tue Dec 31, 2019 3:58 am, edited 1 time in total.

Quote

Source: Beat The GMAT — Problem Solving | Sun Dec 29, 2019 6:22 pm

SampathKp: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Nov 13, 2019 9:42 pm

by SampathKp » Sun Dec 29, 2019 7:16 pm

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

This question can be solved quickly with approximation.

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

Quote

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

by Brent@GMATPrepNow » Mon Dec 30, 2019 6:56 am

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 we're adding 24 numbers, we know that:
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

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jan 05, 2020 8:05 pm

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
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