GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Sep 2019, 09:35

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A number is interesting if on adding the sum of the digits of the numb

Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Apr 2019
Posts: 214
A number is interesting if on adding the sum of the digits of the numb  [#permalink]

### Show Tags

19 Aug 2019, 10:08
1
00:00

Difficulty:

55% (hard)

Question Stats:

45% (03:02) correct 55% (02:09) wrong based on 22 sessions

### HideShow timer Statistics

A number is interesting if on adding the sum of the digits of the number and the product of the digits of the number, the result is equal to the number. What fraction of numbers between 10 and 100 (both 10 and 100 included) is interesting?

(A) 0.01

(B) 0.1

(C) 0.11

(D) 0.16

(E) 0.23
Director
Joined: 19 Oct 2018
Posts: 852
Location: India
Re: A number is interesting if on adding the sum of the digits of the numb  [#permalink]

### Show Tags

19 Aug 2019, 10:59
1
We can write any 2-digit number in the form of 10x+y, where x can take integral values from 1 to 9, and y can take integral values from 0 to 9.

10x+y= x+y+xy
10x=(y+1)x
y+1=10
y=9

Hence, any 2-digit number that has unit digit 9 can be written as the sum of product of its digits, and sum of its digits.
Total possible "interesting" numbers= 9 (19, 29, 39, 49, 59, 69, 79, 89, and 99)

Hovkial wrote:
A number is interesting if on adding the sum of the digits of the number and the product of the digits of the number, the result is equal to the number. What fraction of numbers between 10 and 100 (both 10 and 100 included) is interesting?

(A) 0.01

(B) 0.1

(C) 0.11

(D) 0.16

(E) 0.23
Intern
Joined: 09 Oct 2018
Posts: 7
Re: A number is interesting if on adding the sum of the digits of the numb  [#permalink]

### Show Tags

20 Aug 2019, 00:19
1. From 10 to 100 there are 91 numbers
2.
100 is not interesting, so we can set the interesting number ab
in order to be interesting:
ab=a*b+(a+b)
=> 10*a+b=a*(b+1)+b => b=9
so any number has the form a9 is interesting: 19, 29,...99
=> there are 9 numbers
So fraction is 9/91, nearly 0.1
Manager
Joined: 20 Jul 2012
Posts: 118
GMAT 1: 650 Q47 V33
Re: A number is interesting if on adding the sum of the digits of the numb  [#permalink]

### Show Tags

20 Aug 2019, 10:43
Hovkial wrote:
A number is interesting if on adding the sum of the digits of the number and the product of the digits of the number, the result is equal to the number. What fraction of numbers between 10 and 100 (both 10 and 100 included) is interesting?

(A) 0.01

(B) 0.1

(C) 0.11

(D) 0.16

(E) 0.23

Let ab be the number.

So a+b+a*b = 10a+b
=> 9a =a*b
=> a = 0 or b =9, a cannot be 0 as it will be single digit number then but we need numbers between 10 and 100
So, b = 9

The numbers can be 19, 29, 39, 49, 59, 69, 79, 89, 99. Total 9 numbers.
Total numbers between 10 and 100 = 100-10+1 = 91.

Fraction of numbers which are interesting = 9 / 91 ~ 0.1. So A.
Re: A number is interesting if on adding the sum of the digits of the numb   [#permalink] 20 Aug 2019, 10:43
Display posts from previous: Sort by