BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

student came along and erased

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

student came along and erased

by sanju09 » Thu Jan 14, 2010 5:25 am
A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining number is 35 7/17 (read thirty five whole number seven upon seventeen). What was the number erased?
(A) 7
(B) 8
(C) 9
(D) 10
(E) None of these
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 189
Joined: Thu Apr 03, 2008 2:03 pm
Location: USA
Thanked: 21 times

by rohan_vus » Thu Jan 14, 2010 6:41 am
The avg with erased integer is 35 7/17..which means the number of remaining integers got be multiple of 17 ..as sum of integers is always an integer

Let consider orig no of integers be n..sum of consecutive integers = n*(n+1)/2 ---(1)
Sum of integers with erased integer = (n-1) *(35 + 7/17)-----(2)

Diff of (1) and (2) is the erased integer -
(1) should be greater than (2) and that can only happen if (n-1) is multiple of 17 and (n-1)/2 should be close to 35..--(3)

With this consideration , lets pick n-1 = 68 as its fairly close to our condition (3)

Sum of orig integers = 69*35
Sum with erased integers = 68*35 + 28
So erased integer is 69*35 - 68*35 - 28 ==> 35-28= 7...

A is the ans
Top
Senior | Next Rank: 100 Posts
Posts: 98
Joined: Mon Nov 23, 2009 2:30 pm
Thanked: 26 times
Followed by:1 members

by ace_gre » Thu Jan 14, 2010 1:14 pm
(1) should be greater than (2) and that can only happen if (n-1) is multiple of 17 and (n-1)/2 should be close to 35..--(3)
Hi Rohan, I am having difficulty in understanding the reasoning here. Can you help explain more on how you pick n-1=68??

Thanks!
Top
Post new topic Post Reply
• Page 1 of 1