If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002,

Expert replies

Previous Topic Next Topic

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

by BTGmoderatorDC » Sun Aug 12, 2018 2:46 pm

Timer

00:00

Answers

Stats

Difficulty—

If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 and x is 999, what is the value of x?

A. 999
B. 1001
C. 1003
D. 1004
E. 1005

OA D

Source: Manhattan GMAT

Like this post

Source: Beat The GMAT — Problem Solving | Sun Aug 12, 2018 2:46 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Aug 12, 2018 3:18 pm

BTGmoderatorDC wrote:If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 and x is 999, what is the value of x?

A. 999
B. 1001
C. 1003
D. 1004
E. 1005

Sum of the 10 terms = (quantity)(average) = 10*999 = 9990.
If we add the units digits of the nine given terms, we get:
3+4+6+7+8+1+1+2+4 = 36.
The sum of the nine given terms has a units digit of 6.
The sum of all ten terms has a units digit of 0.
Since (units digit of 6) + (units digit of 4) = (units digit of 0), x must have a units digit of 4.

The correct answer is D.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Mon Aug 13, 2018 11:02 am

BTGmoderatorDC wrote:If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 and x is 999, what is the value of x?

A. 999
B. 1001
C. 1003
D. 1004
E. 1005

OA D

Source: Manhattan GMAT

We can also treat this as a weighted average. Find how much each term differs from the average of 999:

993 --> -6
994 --> -5
996 --> -3
997 --> -2
998 --> -1
1001 --> +2
1001 --> +2
1002 --> +3
1004 --> +5

Quickly eliminate the ones that cancel each other out (-5 and +5, etc):
993 --> -6
994 --> -5
996 --> -3
997 --> -2
998 --> -1
1001 --> +2
1001 --> +2
1002 --> +3
1004 --> +5

We're left with -6, -1, and +2 --> a total of -5. If we want to balance at 999, we need to counterbalance the -5 with +5:
999 + 5 = 1004.

The answer is D.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

Like this post

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Sat Aug 18, 2018 6:38 pm

BTGmoderatorDC wrote:If the average of 993, 994, 996, 997, 998, 1001, 1001, 1002, 1004 and x is 999, what is the value of x?

A. 999
B. 1001
C. 1003
D. 1004
E. 1005

Since the numbers are "pretty" large and each is "pretty" close to the average, without using the conventional formula (i.e., average = sum/quantity), we can determine the value of x by using the difference between each known number and the average. If we subtract 999, the average, from each number, we have:

-6, -5, -3, -2, -1, 2, 2, 3, 5

We see that the sum of the differences is (-17) + 12 = -5. To counter the -5 (i.e., 5 less than the average), we need a value that is 5 more than the average. That is, we need x to be 999 + 5 = 1004 so that the average of all values (including x) will be 999.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 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