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Math Expert V
Joined: 02 Sep 2009
Posts: 59720
What is the value of a positive integer x? (1) x is three times the  [#permalink]

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10 00:00

Difficulty:   95% (hard)

Question Stats: 31% (02:34) correct 69% (02:01) wrong based on 177 sessions

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What is the value of a positive integer x?

(1) x is three times the sum of its digits
(2) x is a two-digit number

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GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5479
Location: India
Concentration: Sustainability, Marketing
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Re: What is the value of a positive integer x? (1) x is three times the  [#permalink]

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Bunuel wrote:
What is the value of a positive integer x?

(1) x is three times the sum of its digits
(2) x is a two-digit number

GMATinsight :

Sir could you please review my solution and check where am I going wrong, correct answer given is A .. I am not sure why so..

we need to find the value of +ve integer X

stmnt 1: X = 3* ( sum of its digits)

its not clear how many digit number it is , if its 1 digit no then X= 3 .A if its a 2 digit no then X= 3*(10A+B) .. so on so value of X would vary as we are not sure of the value of 2 digits it can be (11,12 .. so on ) so x can be X= 3(2); 6 or 3(3); 9 or else it can be a 3 digit no as well eg 111 ; 3* (3); 9 100 : 3(1); 3
in sufficient

Stmnt 2:
X is a two digit no..
again value of 2 digit not clear so X cannot be determined , in sufficient

From 1 & 2:
x is a 2 digit no and it is 3 times the sum of the digits ;
this would be again in sufficient as we would get many values of X as 2 digit no can be many

Manager  S
Joined: 18 Oct 2018
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GMAT 1: 710 Q50 V36 GPA: 4
Re: What is the value of a positive integer x? (1) x is three times the  [#permalink]

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2
1
From stmnt 1,we know X=3*( sum of digits of X)
Now,supposing X is A3 digit no.,999,sum of digits =27,and 3 times 27= 81,a 2 digit no.which is contradictory in itself.
Considering X=100,sum of digits=1,hence 3 times 1=1,a one digit no.
This means X should be a 2 digit no.
Let X=10a+b
Then 10a+b= 3*(a+b)
Or 7a=2b,or a=3.5b.
Now,for the 2 digit no.X,a and b should both be integers,and should be 0<a,b<=9.
Only digits satisfying this are 2 and 7.
So,X=27= 3*(2+7)
Sufficient.

Stmnt 2 is insufficient

So,A

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GMAT Club Legend  V
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Re: What is the value of a positive integer x? (1) x is three times the  [#permalink]

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anshkool4u wrote:
From stmnt 1,we know X=3*( sum of digits of X)
Now,supposing X is A3 digit no.,999,sum of digits =27,and 3 times 27= 81,a 2 digit no.which is contradictory in itself.
Considering X=100,sum of digits=1,hence 3 times 1=1,a one digit no.
This means X should be a 2 digit no.
Let X=10a+b
Then 10a+b= 3*(a+b)
Or 7a=2b,or a=3.5b.
Now,for the 2 digit no.X,a and b should both be integers,and should be 0<a,b<=9.
Only digits satisfying this are 2 and 7.
So,X=27= 3*(2+7)
Sufficient.

Stmnt 2 is insufficient

So,A

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anshkool4u

Let X=10a+b
Then 10a+b= 3*(a+b)
Or 7a=2b,or a=3.5b.

this would be 3.5a=b

Now,for the 2 digit no.X,a and b should both be integers,and should be 0<a,b<=9. " how did you come up to this range"? agree that a and b have to be between 0-9 but why specifically you have mentioned that "be 0<a,b<=9."
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Re: What is the value of a positive integer x? (1) x is three times the  [#permalink]

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Let X be of form pq . So basically X =10P + Q

A---> 3x = P + Q
---> 2Q = 7P
For this to hold P should be 2 and Q should be 7
27 is the unique no.
Sufficient

B---> No unique value. Insufficient

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Math Expert V
Joined: 02 Sep 2009
Posts: 59720
Re: What is the value of a positive integer x? (1) x is three times the  [#permalink]

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Bunuel wrote:
What is the value of a positive integer x?

(1) x is three times the sum of its digits
(2) x is a two-digit number

_________________
Manager  S
Joined: 18 Oct 2018
Posts: 90
Location: India
GMAT 1: 710 Q50 V36 GPA: 4
What is the value of a positive integer x? (1) x is three times the  [#permalink]

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Archit3110 wrote:
anshkool4u wrote:
From stmnt 1,we know X=3*( sum of digits of X)
Now,supposing X is A3 digit no.,999,sum of digits =27,and 3 times 27= 81,a 2 digit no.which is contradictory in itself.
Considering X=100,sum of digits=1,hence 3 times 1=1,a one digit no.
This means X should be a 2 digit no.
Let X=10a+b
Then 10a+b= 3*(a+b)
Or 7a=2b,or a=3.5b.
Now,for the 2 digit no.X,a and b should both be integers,and should be 0<a,b<=9.
Only digits satisfying this are 2 and 7.
So,X=27= 3*(2+7)
Sufficient.

Stmnt 2 is insufficient

So,A

Posted from my mobile device

anshkool4u

Let X=10a+b
Then 10a+b= 3*(a+b)
Or 7a=2b,or a=3.5b.

this would be 3.5a=b

Now,for the 2 digit no.X,a and b should both be integers,and should be 0<a,b<=9. " how did you come up to this range"? agree that a and b have to be between 0-9 but why specifically you have mentioned that "be 0<a,b<=9."

Hi Archit,
the range quoted is because if a=0, then the no. ab would just become a single digit no.
and since 3.5a=b, value of b cannot be 0 because a cannot be 0.

I hope that makes it clear.
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Re: What is the value of a positive integer x? (1) x is three times the  [#permalink]

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2
Bunuel wrote:
What is the value of a positive integer x?

(1) x is three times the sum of its digits
(2) x is a two-digit number

(2) x is a two-digit number insufic.

(1) x is three times the sum of its digits sufic.

digits: {0,1,2,3,4,5,6,7,9}

if x = one-digit number: A, then A=3A is only possible if A=0, but x≥1; out.
if x = three-digit number: then 100 ≤ x ≤ 999, but the max possible sum of digits = {9,9,9} = 27; out.
if x = two-digit number: 10A+B, then 10A+B=3(A+B)… 7A=2B…A=2B/7=integer;
since 1≤A≤9, 0≤B≤9 and A=2B/7=integer… B has multiple of 7: B=(0,7);
B=0; A=2B/7…A=0…but A≥1; out;
B=7; A=2B/7…A=2…so, x=27 Re: What is the value of a positive integer x? (1) x is three times the   [#permalink] 25 Oct 2019, 07:22
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