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

Question

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

M36-66

Archit3110 · Answer

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..

anshkool4u · Answer

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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Archit3110 · Answer

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."

ShankSouljaBoi · Answer

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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Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

anshkool4u · Answer

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.

exc4libur · Answer

(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

Answer (A)

Bunuel · Answer

Official Solution:

What is the value of a positive integer  x ? 
 
(1)  x  is three times the sum of its digits
 
First let's check how many digit number  x  can be.
 
Can  x  be a single-digit number? No. Only 0 satisfices  x=3x  but we are told that  x  is positive.
 
Can  x  be a three-digit number? No. The maximum sum of the digits of a three-digit number is  9+9+9=27  and thrice of that is not a three-digit number. The same for four or more digit numbers: thrice the sum of the digits will always be less than the number itself.
 
Can  x  be a two-digit number? Say  x=10a+b , then we'd have that  10a+b=3(a + b) :
 
 \frac{a}{b}=\frac{2}{7} . Since both  a  and  b  are positive digits (1, 2, 3, 4, 5, 6, 7, 8, 9), then  a=2  and  b=7 . So,  x=27 . Sufficient.
 
(2)  x  is a two-digit number. Clearly insufficient.

Answer: A

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

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