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# A company's director messaged an important notice on his phone to 'X'

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1412
Location: India
A company's director messaged an important notice on his phone to 'X'  [#permalink]

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19 Jul 2018, 10:39
00:00

Difficulty:

65% (hard)

Question Stats:

54% (02:17) correct 46% (02:17) wrong based on 37 sessions

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A company's director messaged an important notice on his phone to 'X' of his immediate reportees. Each of these X people further forwarded this message to X more people. Apart from this, this message was not sent or received by anyone else and no one received message more than once. What is the value of X?

(1) In total, the message was received by 30 people after it was sent by the director.

(2) The first 'X' people who were sent the message directly by the director, constitute 1/6 of the total number of people who received this message, after it was sent by the director.

(this question is inspired by the following OG question:
Math Expert
Joined: 02 Aug 2009
Posts: 7099
Re: A company's director messaged an important notice on his phone to 'X'  [#permalink]

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19 Jul 2018, 18:23
A company's director messaged an important notice on his phone to 'X' of his immediate reportees. Each of these X people further forwarded this message to X more people. Apart from this, this message was not sent or received by anyone else and no one received message more than once. What is the value of X?

so X people sent to x*x=x^2......total =X+x^2
So we require to know X

(1) In total, the message was received by 30 people after it was sent by the director.
So x(x+1)=30.....5*6=30
x=5
Sufficient

(2) The first 'X' people who were sent the message directly by the director, constitute 1/6 of the total number of people who received this message, after it was sent by the director.
Total =x(x+1)
So x=$$\frac{x(x+1)}{6}.......6x=x^2+X.......5x=x^2.....X=5$$
Sufficient

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: A company's director messaged an important notice on his phone to 'X' &nbs [#permalink] 19 Jul 2018, 18:23
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