Ultimate Quant Marathon Blog For IIM CAT

For All Your Quant Queries

Problem Of The Week 26

with 3 comments


A three digit number is such that the sum of the digit in the hundred’s place and the ten’s place is 1 more than the digit in the unit’s place. It is also given that the digit in the ten’s place exceeds the square of the digit in the hundred’s place by 1, and that the square of the digit in the units place diminished by 7 is the same as the sum of the squares of the other two digits. What is the number?

(1) 346                 (2) 256                 (3) 458                 (4) 526       (5) None of These.

Written by Implex

September 24, 2008 at 6:47 pm

3 Responses

Subscribe to comments with RSS.

  1. option 2 256
    Worked through the options😛
    Sorry:)

    milind

    September 25, 2008 at 5:03 pm

  2. the problem is pretty easy let the number be xyz, x can’t be zero

    x+y=z+1
    y=x^2+1
    z^2-7=x^2+y^2
    subtract first two
    we get z=x(x+1) as x and z are digits, and x not 0
    then obviously z=2,6 as these two are the only solutions possible
    but with z=2 z^2-7 is negative , hence rejected

    so x=2 z=6 and y=5
    our number is 256

    outtimed

    September 25, 2008 at 10:20 pm

  3. the problem is pretty easy let the number be xyz, x can’t be zero

    x+y=z+1
    y=x^2+1
    z^2-7=x^2+y^2
    subtract first two
    we get z=x(x+1) as x and z are digits, and x not 0
    then obviously z=2,6 as these two are the only solutions possible
    but with z=2 z^2-7 is negative , hence rejected

    so x=2 z=6 and y=5
    our number is 256

    outtimed

    September 25, 2008 at 10:21 pm


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: