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What is the value of a positive integer x? (1) x is three times the

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What is the value of a positive integer x? (1) x is three times the  [#permalink]

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New post 10 Dec 2018, 02:32
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

29% (02:34) correct 71% (01:56) wrong based on 163 sessions

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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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New post 11 Dec 2018, 02:29
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

IMO E should be answer..
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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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New post 11 Dec 2018, 03:06
1
Answer is A.
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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Re: What is the value of a positive integer x? (1) x is three times the  [#permalink]

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New post 11 Dec 2018, 03:19
anshkool4u wrote:
Answer is A.
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

quoting your line :
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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New post 24 Dec 2018, 00:42
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

Answer A

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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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New post 24 Dec 2018, 01:17
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What is the value of a positive integer x? (1) x is three times the  [#permalink]

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New post 07 Jan 2019, 10:13
Archit3110 wrote:
anshkool4u wrote:
Answer is A.
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

quoting your line :
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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What is the value of a positive integer x? (1) x is three times the   [#permalink] 07 Jan 2019, 10:13
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