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

Redeem

x < y, z < y and x ≠ 0

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

x < y, z < y and x ≠ 0

by sanju09 » Tue Mar 09, 2010 2:10 am
How many three digit positive integers, with digits x, y and z in the hundred's, ten's and unit's place respectively, exist such that x < y, z < y and x ≠ 0?
(A) 240
(B) 245
(C) 285
(D) 320
(E) 720
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 |
User avatar
Master | Next Rank: 500 Posts
Posts: 102
Joined: Sat Feb 20, 2010 5:38 am
Location: IIM Ahmedabad
Thanked: 10 times

by firdaus117 » Tue Mar 09, 2010 5:05 am
It is evident that middle digit of the number is to be the largest of three digits in the number as per condition.
For y=1,no numbers possible as x is not equal to zero.
For y=2,x=1 and z=0,1 total numbers possible=1*2
For y=3,x=1,2 and z=0,1,2 total numbers possible=2*3
For y=4,x=1,2,3 and z=0,1,2,3 total numbers possible=3*4
-------------------------------------------------------------------------
---------------------------------------------------------------------------
For y=9,total numbers possible=8*9
Total numbers=1*2+2*3+3*4+.........+8*9=240 Option A
P.S.We can get the sum of above series by writing the general term as n(n+1)=n^2+n and using the formulas for sum of squares of natural numbers and sum of natural numbers.
Last edited by firdaus117 on Tue Mar 09, 2010 5:07 am, edited 1 time in total.
Top
User avatar
Legendary Member
Posts: 1275
Joined: Thu Sep 21, 2006 11:13 pm
Location: Arabian Sea
Thanked: 125 times
Followed by:2 members

by ajith » Tue Mar 09, 2010 5:06 am
sanju09 wrote:How many three digit positive integers, with digits x, y and z in the hundred's, ten's and unit's place respectively, exist such that x < y, z < y and x ≠ 0?
(A) 240
(B) 245
(C) 285
(D) 320
(E) 720
The middle digit y can take values from 2-9

when y is 9 x can take values from 1-8 and z can take values from 0-8
Total num = 8*9
when y is 8 x can take values from 1-7 and z can take values from 0-7
Total num = 7*8

....

[spoiler]Total num = 9*8+8*7+7*6+6*5+5*4+4*3+3*2+2*1 =240[/spoiler]
Always borrow money from a pessimist, he doesn't expect to be paid back.
Top
Post new topic Post Reply
• Page 1 of 1